1,1,216,0,3.160104," ","integrate(cos(d*x+c)**5*(a+a*cos(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{8 a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{4 a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{11 a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right) \cos^{5}{\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) + 8*a*sin(c + d*x)**5/(15*d) + 5*a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 4*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 11*a*sin(c + d*x)*cos(c + d*x)**5/(16*d) + a*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a*cos(c) + a)*cos(c)**5, True))","A",0
2,1,168,0,1.855414," ","integrate(cos(d*x+c)**4*(a+a*cos(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{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{3 a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\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 + 8*a*sin(c + d*x)**5/(15*d) + 4*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + a*sin(c + d*x)*cos(c + d*x)**4/d + 5*a*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + a)*cos(c)**4, True))","A",0
3,1,144,0,0.911678," ","integrate(cos(d*x+c)**3*(a+a*cos(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{2 a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right) \cos^{3}{\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) + 2*a*sin(c + d*x)**3/(3*d) + 5*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + a*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a*cos(c) + a)*cos(c)**3, True))","A",0
4,1,92,0,0.450642," ","integrate(cos(d*x+c)**2*(a+a*cos(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{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 \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\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 + 2*a*sin(c + d*x)**3/(3*d) + a*sin(c + d*x)*cos(c + d*x)**2/d + a*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)*cos(c)**2, True))","A",0
5,1,66,0,0.200233," ","integrate(cos(d*x+c)*(a+a*cos(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 \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right) \cos{\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*sin(c + d*x)/d, Ne(d, 0)), (x*(a*cos(c) + a)*cos(c), True))","A",0
6,1,17,0,0.114931," ","integrate(a+a*cos(d*x+c),x)","a x + a \left(\begin{cases} \frac{\sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \cos{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + a*Piecewise((sin(c + d*x)/d, Ne(d, 0)), (x*cos(c), True))","A",0
7,1,49,0,4.921880," ","integrate((a+a*cos(d*x+c))*sec(d*x+c),x)","a x + a \left(\begin{cases} \frac{x \tan{\left(c \right)} \sec{\left(c \right)}}{\tan{\left(c \right)} + \sec{\left(c \right)}} + \frac{x \sec^{2}{\left(c \right)}}{\tan{\left(c \right)} + \sec{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\log{\left(\tan{\left(c + d x \right)} + \sec{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + a*Piecewise((x*tan(c)*sec(c)/(tan(c) + sec(c)) + x*sec(c)**2/(tan(c) + sec(c)), Eq(d, 0)), (log(tan(c + d*x) + sec(c + d*x))/d, True))","A",0
8,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**2,x)","a \left(\int \cos{\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(cos(c + d*x)*sec(c + d*x)**2, x) + Integral(sec(c + d*x)**2, x))","F",0
9,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**3,x)","a \left(\int \cos{\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(cos(c + d*x)*sec(c + d*x)**3, x) + Integral(sec(c + d*x)**3, x))","F",0
10,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**4,x)","a \left(\int \cos{\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(cos(c + d*x)*sec(c + d*x)**4, x) + Integral(sec(c + d*x)**4, x))","F",0
11,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**5,x)","a \left(\int \cos{\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(cos(c + d*x)*sec(c + d*x)**5, x) + Integral(sec(c + d*x)**5, x))","F",0
12,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**6,x)","a \left(\int \cos{\left(c + d x \right)} \sec^{6}{\left(c + d x \right)}\, dx + \int \sec^{6}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)*sec(c + d*x)**6, x) + Integral(sec(c + d*x)**6, x))","F",0
13,1,343,0,3.529921," ","integrate(cos(d*x+c)**4*(a+a*cos(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{3 a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 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{5 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{5 a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{16 a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{8 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{11 a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{2 a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} \cos^{4}{\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 + 3*a**2*x*sin(c + d*x)**4/8 + 15*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 + 5*a**2*x*cos(c + d*x)**6/16 + 3*a**2*x*cos(c + d*x)**4/8 + 5*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 16*a**2*sin(c + d*x)**5/(15*d) + 5*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 8*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 11*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 2*a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + a)**2*cos(c)**4, True))","A",0
14,1,221,0,1.981227," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \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{3 a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{2 a^{2} \sin^{3}{\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{5 a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**4/4 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*a**2*x*cos(c + d*x)**4/4 + 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) + 3*a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 2*a**2*sin(c + d*x)**3/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + a**2*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a*cos(c) + a)**2*cos(c)**3, True))","A",0
15,1,211,0,1.021892," ","integrate(cos(d*x+c)**2*(a+a*cos(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{a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{4 a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{2 a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} \cos^{2}{\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 + a**2*x*sin(c + d*x)**2/2 + 3*a**2*x*cos(c + d*x)**4/8 + a**2*x*cos(c + d*x)**2/2 + 3*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 4*a**2*sin(c + d*x)**3/(3*d) + 5*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 2*a**2*sin(c + d*x)*cos(c + d*x)**2/d + a**2*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)**2*cos(c)**2, True))","A",0
16,1,107,0,0.475972," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**2,x)","\begin{cases} a^{2} x \sin^{2}{\left(c + d x \right)} + a^{2} x \cos^{2}{\left(c + d x \right)} + \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} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{a^{2} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**2 + a**2*x*cos(c + d*x)**2 + 2*a**2*sin(c + d*x)**3/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**2/d + a**2*sin(c + d*x)*cos(c + d*x)/d + a**2*sin(c + d*x)/d, Ne(d, 0)), (x*(a*cos(c) + a)**2*cos(c), True))","A",0
17,1,78,0,0.248651," ","integrate((a+a*cos(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} + a^{2} x + \frac{a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 a^{2} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{2} & \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*x + a**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*a**2*sin(c + d*x)/d, Ne(d, 0)), (x*(a*cos(c) + a)**2, True))","A",0
18,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c),x)","a^{2} \left(\int 2 \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \cos^{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*cos(c + d*x)*sec(c + d*x), x) + Integral(cos(c + d*x)**2*sec(c + d*x), x) + Integral(sec(c + d*x), x))","F",0
19,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**2,x)","a^{2} \left(\int 2 \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \cos^{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*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(sec(c + d*x)**2, x))","F",0
20,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**3,x)","a^{2} \left(\int 2 \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int \cos^{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*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(sec(c + d*x)**3, x))","F",0
21,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**4,x)","a^{2} \left(\int 2 \cos{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int \cos^{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*cos(c + d*x)*sec(c + d*x)**4, x) + Integral(cos(c + d*x)**2*sec(c + d*x)**4, x) + Integral(sec(c + d*x)**4, x))","F",0
22,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,1,379,0,3.652501," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{5 a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{5 a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{8 a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{5 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{4 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 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^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{3} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**3*x*sin(c + d*x)**6/16 + 15*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*a**3*x*sin(c + d*x)**4/8 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 5*a**3*x*cos(c + d*x)**6/16 + 9*a**3*x*cos(c + d*x)**4/8 + 5*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 8*a**3*sin(c + d*x)**5/(5*d) + 5*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 4*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 9*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*a**3*sin(c + d*x)**3/(3*d) + 11*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 3*a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*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, Ne(d, 0)), (x*(a*cos(c) + a)**3*cos(c)**3, True))","A",0
24,1,272,0,2.076636," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{9 a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 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{9 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \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{9 a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{2 a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{3} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**3*x*sin(c + d*x)**4/8 + 9*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**3*x*sin(c + d*x)**2/2 + 9*a**3*x*cos(c + d*x)**4/8 + a**3*x*cos(c + d*x)**2/2 + 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) + 9*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*a**3*sin(c + d*x)**3/d + a**3*sin(c + d*x)*cos(c + d*x)**4/d + 15*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*a**3*sin(c + d*x)*cos(c + d*x)**2/d + a**3*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)**3*cos(c)**2, True))","A",0
25,1,224,0,1.028382," ","integrate(cos(d*x+c)*(a+a*cos(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 \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 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{2 a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{5 a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 a^{3} \sin{\left(c + d x \right)} \cos{\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 \cos{\left(c \right)} + a\right)^{3} \cos{\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*sin(c + d*x)**2/2 + 3*a**3*x*cos(c + d*x)**4/8 + 3*a**3*x*cos(c + d*x)**2/2 + 3*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 2*a**3*sin(c + d*x)**3/d + 5*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 3*a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + a**3*sin(c + d*x)/d, Ne(d, 0)), (x*(a*cos(c) + a)**3*cos(c), True))","A",0
26,1,121,0,0.502115," ","integrate((a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + a^{3} x + \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^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 a^{3} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**2/2 + 3*a**3*x*cos(c + d*x)**2/2 + a**3*x + 2*a**3*sin(c + d*x)**3/(3*d) + a**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*a**3*sin(c + d*x)/d, Ne(d, 0)), (x*(a*cos(c) + a)**3, True))","A",0
27,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c),x)","a^{3} \left(\int 3 \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \cos^{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*cos(c + d*x)*sec(c + d*x), x) + Integral(3*cos(c + d*x)**2*sec(c + d*x), x) + Integral(cos(c + d*x)**3*sec(c + d*x), x) + Integral(sec(c + d*x), x))","F",0
28,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**2,x)","a^{3} \left(\int 3 \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \cos^{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*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(3*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(sec(c + d*x)**2, x))","F",0
29,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**3,x)","a^{3} \left(\int 3 \cos{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int 3 \cos^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int \cos^{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*cos(c + d*x)*sec(c + d*x)**3, x) + Integral(3*cos(c + d*x)**2*sec(c + d*x)**3, x) + Integral(cos(c + d*x)**3*sec(c + d*x)**3, x) + Integral(sec(c + d*x)**3, x))","F",0
30,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,1,434,0,3.866523," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{5 a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a^{4} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{15 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{5 a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{4} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{5 a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{32 a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{5 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{16 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{9 a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{8 a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{11 a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{4 a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{15 a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{4 a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{4} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**4*x*sin(c + d*x)**6/16 + 15*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*a**4*x*sin(c + d*x)**4/4 + 15*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + a**4*x*sin(c + d*x)**2/2 + 5*a**4*x*cos(c + d*x)**6/16 + 9*a**4*x*cos(c + d*x)**4/4 + a**4*x*cos(c + d*x)**2/2 + 5*a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 32*a**4*sin(c + d*x)**5/(15*d) + 5*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 16*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 9*a**4*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 8*a**4*sin(c + d*x)**3/(3*d) + 11*a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 4*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 15*a**4*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 4*a**4*sin(c + d*x)*cos(c + d*x)**2/d + a**4*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + a)**4*cos(c)**2, True))","A",0
34,1,280,0,2.167138," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{3 a^{4} x \sin^{4}{\left(c + d x \right)}}{2} + 3 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + 2 a^{4} x \sin^{2}{\left(c + d x \right)} + \frac{3 a^{4} x \cos^{4}{\left(c + d x \right)}}{2} + 2 a^{4} x \cos^{2}{\left(c + d x \right)} + \frac{8 a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{3 a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{4 a^{4} \sin^{3}{\left(c + d x \right)}}{d} + \frac{a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{6 a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{a^{4} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{4} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*x*sin(c + d*x)**4/2 + 3*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2 + 2*a**4*x*sin(c + d*x)**2 + 3*a**4*x*cos(c + d*x)**4/2 + 2*a**4*x*cos(c + d*x)**2 + 8*a**4*sin(c + d*x)**5/(15*d) + 4*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 3*a**4*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 4*a**4*sin(c + d*x)**3/d + a**4*sin(c + d*x)*cos(c + d*x)**4/d + 5*a**4*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 6*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 2*a**4*sin(c + d*x)*cos(c + d*x)/d + a**4*sin(c + d*x)/d, Ne(d, 0)), (x*(a*cos(c) + a)**4*cos(c), True))","A",0
35,1,224,0,1.075119," ","integrate((a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{3 a^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + 3 a^{4} x \sin^{2}{\left(c + d x \right)} + \frac{3 a^{4} x \cos^{4}{\left(c + d x \right)}}{8} + 3 a^{4} x \cos^{2}{\left(c + d x \right)} + a^{4} x + \frac{3 a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{8 a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{5 a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{4 a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 a^{4} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*x*sin(c + d*x)**4/8 + 3*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**4*x*sin(c + d*x)**2 + 3*a**4*x*cos(c + d*x)**4/8 + 3*a**4*x*cos(c + d*x)**2 + a**4*x + 3*a**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 8*a**4*sin(c + d*x)**3/(3*d) + 5*a**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 4*a**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*a**4*sin(c + d*x)*cos(c + d*x)/d + 4*a**4*sin(c + d*x)/d, Ne(d, 0)), (x*(a*cos(c) + a)**4, True))","A",0
36,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c),x)","a^{4} \left(\int 4 \cos{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 6 \cos^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 4 \cos^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \cos^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**4*(Integral(4*cos(c + d*x)*sec(c + d*x), x) + Integral(6*cos(c + d*x)**2*sec(c + d*x), x) + Integral(4*cos(c + d*x)**3*sec(c + d*x), x) + Integral(cos(c + d*x)**4*sec(c + d*x), x) + Integral(sec(c + d*x), x))","F",0
37,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**2,x)","a^{4} \left(\int 4 \cos{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 6 \cos^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 4 \cos^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \cos^{4}{\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**4*(Integral(4*cos(c + d*x)*sec(c + d*x)**2, x) + Integral(6*cos(c + d*x)**2*sec(c + d*x)**2, x) + Integral(4*cos(c + d*x)**3*sec(c + d*x)**2, x) + Integral(cos(c + d*x)**4*sec(c + d*x)**2, x) + Integral(sec(c + d*x)**2, x))","F",0
38,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,1,882,0,6.505962," ","integrate(cos(d*x+c)**5/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{45 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{180 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{270 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{180 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{45 d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{24 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{246 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{374 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{314 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{66 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((45*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 180*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 270*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 180*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 45*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 24*tan(c/2 + d*x/2)**9/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 246*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 374*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 314*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 66*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d), Ne(d, 0)), (x*cos(c)**5/(a*cos(c) + a), True))","A",0
44,1,570,0,3.898345," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c)),x)","\begin{cases} - \frac{9 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{27 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{27 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{9 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^{7}{\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{48 \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{50 \tan^{3}{\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{24 \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} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*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) - 27*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) - 27*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) - 9*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)**7/(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) + 48*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) + 50*tan(c/2 + d*x/2)**3/(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) + 24*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), Ne(d, 0)), (x*cos(c)**4/(a*cos(c) + a), True))","A",0
45,1,325,0,2.320115," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{3 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{6 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{3 d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{10 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 6*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 3*d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 10*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d), Ne(d, 0)), (x*cos(c)**3/(a*cos(c) + a), True))","A",0
46,1,129,0,1.405053," ","integrate(cos(d*x+c)**2/(a+a*cos(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{\tan^{3}{\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{3 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{a \cos{\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) + tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**2 + a*d) + 3*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*cos(c)**2/(a*cos(c) + a), True))","A",0
47,1,27,0,0.751253," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{x}{a} - \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a - tan(c/2 + d*x/2)/(a*d), Ne(d, 0)), (x*cos(c)/(a*cos(c) + a), True))","A",0
48,1,20,0,0.507946," ","integrate(1/(a+a*cos(d*x+c)),x)","\begin{cases} \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x}{a \cos{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)/(a*d), Ne(d, 0)), (x/(a*cos(c) + a), True))","A",0
49,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)/(cos(c + d*x) + 1), x)/a","F",0
50,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**2/(cos(c + d*x) + 1), x)/a","F",0
51,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**3/(cos(c + d*x) + 1), x)/a","F",0
52,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**4/(cos(c + d*x) + 1), x)/a","F",0
53,1,700,0,9.743785," ","integrate(cos(d*x+c)**5/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{30 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{90 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{30 d x}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{24 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{138 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{160 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{63 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 90*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 30*d*x/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 24*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 138*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 160*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 63*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 18*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*cos(c)**5/(a*cos(c) + a)**2, True))","A",0
54,1,413,0,6.124350," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{21 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{42 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{21 d x}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{19 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{71 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{39 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((21*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 42*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 21*d*x/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 19*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 71*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 39*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*cos(c)**4/(a*cos(c) + a)**2, True))","A",0
55,1,201,0,3.637743," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{12 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{12 d x}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{14 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} + \frac{27 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - 12*d*x/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) - tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 14*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d) + 27*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**2 + 6*a**2*d), Ne(d, 0)), (x*cos(c)**3/(a*cos(c) + a)**2, True))","A",0
56,1,56,0,2.019392," ","integrate(cos(d*x+c)**2/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{a^{2}} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} - \frac{3 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a**2 + tan(c/2 + d*x/2)**3/(6*a**2*d) - 3*tan(c/2 + d*x/2)/(2*a**2*d), Ne(d, 0)), (x*cos(c)**2/(a*cos(c) + a)**2, True))","A",0
57,1,48,0,1.291185," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))**2,x)","\begin{cases} - \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2 + d*x/2)**3/(6*a**2*d) + tan(c/2 + d*x/2)/(2*a**2*d), Ne(d, 0)), (x*cos(c)/(a*cos(c) + a)**2, True))","A",0
58,1,44,0,0.895271," ","integrate(1/(a+a*cos(d*x+c))**2,x)","\begin{cases} \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x}{\left(a \cos{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**3/(6*a**2*d) + tan(c/2 + d*x/2)/(2*a**2*d), Ne(d, 0)), (x/(a*cos(c) + a)**2, True))","A",0
59,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
60,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**2/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
61,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**3/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
62,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**4/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
63,1,473,0,13.646727," ","integrate(cos(d*x+c)**5/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{390 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{780 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{390 d x}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{3 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} + \frac{34 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{388 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{1310 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} - \frac{765 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((390*d*x*tan(c/2 + d*x/2)**4/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 780*d*x*tan(c/2 + d*x/2)**2/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 390*d*x/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 3*tan(c/2 + d*x/2)**9/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) + 34*tan(c/2 + d*x/2)**7/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 388*tan(c/2 + d*x/2)**5/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 1310*tan(c/2 + d*x/2)**3/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d) - 765*tan(c/2 + d*x/2)/(60*a**3*d*tan(c/2 + d*x/2)**4 + 120*a**3*d*tan(c/2 + d*x/2)**2 + 60*a**3*d), Ne(d, 0)), (x*cos(c)**5/(a*cos(c) + a)**3, True))","A",0
64,1,240,0,8.555445," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{60 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{3} d} - \frac{60 d x}{20 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{3} d} + \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{3} d} - \frac{9 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{3} d} + \frac{75 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{3} d} + \frac{125 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-60*d*x*tan(c/2 + d*x/2)**2/(20*a**3*d*tan(c/2 + d*x/2)**2 + 20*a**3*d) - 60*d*x/(20*a**3*d*tan(c/2 + d*x/2)**2 + 20*a**3*d) + tan(c/2 + d*x/2)**7/(20*a**3*d*tan(c/2 + d*x/2)**2 + 20*a**3*d) - 9*tan(c/2 + d*x/2)**5/(20*a**3*d*tan(c/2 + d*x/2)**2 + 20*a**3*d) + 75*tan(c/2 + d*x/2)**3/(20*a**3*d*tan(c/2 + d*x/2)**2 + 20*a**3*d) + 125*tan(c/2 + d*x/2)/(20*a**3*d*tan(c/2 + d*x/2)**2 + 20*a**3*d), Ne(d, 0)), (x*cos(c)**4/(a*cos(c) + a)**3, True))","A",0
65,1,75,0,5.153525," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{a^{3}} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d} - \frac{7 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a**3 - tan(c/2 + d*x/2)**5/(20*a**3*d) + tan(c/2 + d*x/2)**3/(3*a**3*d) - 7*tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*cos(c)**3/(a*cos(c) + a)**3, True))","A",0
66,1,68,0,3.362752," ","integrate(cos(d*x+c)**2/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} - \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**5/(20*a**3*d) - tan(c/2 + d*x/2)**3/(6*a**3*d) + tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*cos(c)**2/(a*cos(c) + a)**3, True))","A",0
67,1,48,0,2.279457," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2 + d*x/2)**5/(20*a**3*d) + tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x*cos(c)/(a*cos(c) + a)**3, True))","A",0
68,1,63,0,1.633732," ","integrate(1/(a+a*cos(d*x+c))**3,x)","\begin{cases} \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{3} d} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**5/(20*a**3*d) + tan(c/2 + d*x/2)**3/(6*a**3*d) + tan(c/2 + d*x/2)/(4*a**3*d), Ne(d, 0)), (x/(a*cos(c) + a)**3, True))","A",0
69,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x)/a**3","F",0
70,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**2/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x)/a**3","F",0
71,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**3/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x)/a**3","F",0
72,1,530,0,29.670347," ","integrate(cos(d*x+c)**6/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{2940 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} + \frac{5880 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} + \frac{2940 d x}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} + \frac{5 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} - \frac{53 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} + \frac{334 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} - \frac{3038 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} - \frac{9835 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} - \frac{5845 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{280 a^{4} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 560 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 280 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{6}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2940*d*x*tan(c/2 + d*x/2)**4/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) + 5880*d*x*tan(c/2 + d*x/2)**2/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) + 2940*d*x/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) + 5*tan(c/2 + d*x/2)**11/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) - 53*tan(c/2 + d*x/2)**9/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) + 334*tan(c/2 + d*x/2)**7/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) - 3038*tan(c/2 + d*x/2)**5/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) - 9835*tan(c/2 + d*x/2)**3/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d) - 5845*tan(c/2 + d*x/2)/(280*a**4*d*tan(c/2 + d*x/2)**4 + 560*a**4*d*tan(c/2 + d*x/2)**2 + 280*a**4*d), Ne(d, 0)), (x*cos(c)**6/(a*cos(c) + a)**4, True))","A",0
73,1,280,0,19.066936," ","integrate(cos(d*x+c)**5/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{3360 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{3360 d x}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{15 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{132 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} - \frac{658 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{4340 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} + \frac{6825 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{4} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3360*d*x*tan(c/2 + d*x/2)**2/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 3360*d*x/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 15*tan(c/2 + d*x/2)**9/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 132*tan(c/2 + d*x/2)**7/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) - 658*tan(c/2 + d*x/2)**5/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 4340*tan(c/2 + d*x/2)**3/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d) + 6825*tan(c/2 + d*x/2)/(840*a**4*d*tan(c/2 + d*x/2)**2 + 840*a**4*d), Ne(d, 0)), (x*cos(c)**5/(a*cos(c) + a)**4, True))","A",0
74,1,95,0,12.004196," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{a^{4}} + \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{11 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} - \frac{15 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a**4 + tan(c/2 + d*x/2)**7/(56*a**4*d) - tan(c/2 + d*x/2)**5/(8*a**4*d) + 11*tan(c/2 + d*x/2)**3/(24*a**4*d) - 15*tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*cos(c)**4/(a*cos(c) + a)**4, True))","A",0
75,1,88,0,8.348783," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} + \frac{3 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2 + d*x/2)**7/(56*a**4*d) + 3*tan(c/2 + d*x/2)**5/(40*a**4*d) - tan(c/2 + d*x/2)**3/(8*a**4*d) + tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*cos(c)**3/(a*cos(c) + a)**4, True))","A",0
76,1,87,0,6.051125," ","integrate(cos(d*x+c)**2/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} - \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**7/(56*a**4*d) - tan(c/2 + d*x/2)**5/(40*a**4*d) - tan(c/2 + d*x/2)**3/(24*a**4*d) + tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*cos(c)**2/(a*cos(c) + a)**4, True))","A",0
77,1,85,0,4.464247," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))**4,x)","\begin{cases} - \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{4} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2 + d*x/2)**7/(56*a**4*d) - tan(c/2 + d*x/2)**5/(40*a**4*d) + tan(c/2 + d*x/2)**3/(24*a**4*d) + tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x*cos(c)/(a*cos(c) + a)**4, True))","A",0
78,1,83,0,3.423211," ","integrate(1/(a+a*cos(d*x+c))**4,x)","\begin{cases} \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{4} d} + \frac{3 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{4} d} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x}{\left(a \cos{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**7/(56*a**4*d) + 3*tan(c/2 + d*x/2)**5/(40*a**4*d) + tan(c/2 + d*x/2)**3/(8*a**4*d) + tan(c/2 + d*x/2)/(8*a**4*d), Ne(d, 0)), (x/(a*cos(c) + a)**4, True))","A",0
79,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))**4,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\cos^{4}{\left(c + d x \right)} + 4 \cos^{3}{\left(c + d x \right)} + 6 \cos^{2}{\left(c + d x \right)} + 4 \cos{\left(c + d x \right)} + 1}\, dx}{a^{4}}"," ",0,"Integral(sec(c + d*x)/(cos(c + d*x)**4 + 4*cos(c + d*x)**3 + 6*cos(c + d*x)**2 + 4*cos(c + d*x) + 1), x)/a**4","F",0
80,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c))**4,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\cos^{4}{\left(c + d x \right)} + 4 \cos^{3}{\left(c + d x \right)} + 6 \cos^{2}{\left(c + d x \right)} + 4 \cos{\left(c + d x \right)} + 1}\, dx}{a^{4}}"," ",0,"Integral(sec(c + d*x)**2/(cos(c + d*x)**4 + 4*cos(c + d*x)**3 + 6*cos(c + d*x)**2 + 4*cos(c + d*x) + 1), x)/a**4","F",0
81,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*cos(d*x+c))**4,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\cos^{4}{\left(c + d x \right)} + 4 \cos^{3}{\left(c + d x \right)} + 6 \cos^{2}{\left(c + d x \right)} + 4 \cos{\left(c + d x \right)} + 1}\, dx}{a^{4}}"," ",0,"Integral(sec(c + d*x)**3/(cos(c + d*x)**4 + 4*cos(c + d*x)**3 + 6*cos(c + d*x)**2 + 4*cos(c + d*x) + 1), x)/a**4","F",0
82,1,588,0,64.314738," ","integrate(cos(d*x+c)**7/(a+a*cos(d*x+c))**5,x)","\begin{cases} \frac{78120 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} + \frac{156240 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} + \frac{78120 d x}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} - \frac{35 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} + \frac{380 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} - \frac{2159 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} + \frac{10152 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} - \frac{82089 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} - \frac{260820 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} - \frac{155925 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5040 a^{5} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 10080 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5040 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{7}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((78120*d*x*tan(c/2 + d*x/2)**4/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) + 156240*d*x*tan(c/2 + d*x/2)**2/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) + 78120*d*x/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) - 35*tan(c/2 + d*x/2)**13/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) + 380*tan(c/2 + d*x/2)**11/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) - 2159*tan(c/2 + d*x/2)**9/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) + 10152*tan(c/2 + d*x/2)**7/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) - 82089*tan(c/2 + d*x/2)**5/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) - 260820*tan(c/2 + d*x/2)**3/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d) - 155925*tan(c/2 + d*x/2)/(5040*a**5*d*tan(c/2 + d*x/2)**4 + 10080*a**5*d*tan(c/2 + d*x/2)**2 + 5040*a**5*d), Ne(d, 0)), (x*cos(c)**7/(a*cos(c) + a)**5, True))","A",0
83,1,320,0,42.517013," ","integrate(cos(d*x+c)**6/(a+a*cos(d*x+c))**5,x)","\begin{cases} - \frac{5040 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} - \frac{5040 d x}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} + \frac{7 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} - \frac{65 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} + \frac{306 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} - \frac{1134 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} + \frac{6615 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} + \frac{10143 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1008 a^{5} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1008 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{6}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5040*d*x*tan(c/2 + d*x/2)**2/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d) - 5040*d*x/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d) + 7*tan(c/2 + d*x/2)**11/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d) - 65*tan(c/2 + d*x/2)**9/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d) + 306*tan(c/2 + d*x/2)**7/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d) - 1134*tan(c/2 + d*x/2)**5/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d) + 6615*tan(c/2 + d*x/2)**3/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d) + 10143*tan(c/2 + d*x/2)/(1008*a**5*d*tan(c/2 + d*x/2)**2 + 1008*a**5*d), Ne(d, 0)), (x*cos(c)**6/(a*cos(c) + a)**5, True))","A",0
84,1,116,0,28.097314," ","integrate(cos(d*x+c)**5/(a+a*cos(d*x+c))**5,x)","\begin{cases} \frac{x}{a^{5}} - \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{144 a^{5} d} + \frac{3 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{5} d} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{5} d} + \frac{13 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{5} d} - \frac{31 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/a**5 - tan(c/2 + d*x/2)**9/(144*a**5*d) + 3*tan(c/2 + d*x/2)**7/(56*a**5*d) - tan(c/2 + d*x/2)**5/(5*a**5*d) + 13*tan(c/2 + d*x/2)**3/(24*a**5*d) - 31*tan(c/2 + d*x/2)/(16*a**5*d), Ne(d, 0)), (x*cos(c)**5/(a*cos(c) + a)**5, True))","A",0
85,1,107,0,19.962576," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**5,x)","\begin{cases} \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{144 a^{5} d} - \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{28 a^{5} d} + \frac{3 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{5} d} - \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{12 a^{5} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**9/(144*a**5*d) - tan(c/2 + d*x/2)**7/(28*a**5*d) + 3*tan(c/2 + d*x/2)**5/(40*a**5*d) - tan(c/2 + d*x/2)**3/(12*a**5*d) + tan(c/2 + d*x/2)/(16*a**5*d), Ne(d, 0)), (x*cos(c)**4/(a*cos(c) + a)**5, True))","A",0
86,1,87,0,15.350549," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c))**5,x)","\begin{cases} - \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{144 a^{5} d} + \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{5} d} - \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{5} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2 + d*x/2)**9/(144*a**5*d) + tan(c/2 + d*x/2)**7/(56*a**5*d) - tan(c/2 + d*x/2)**3/(24*a**5*d) + tan(c/2 + d*x/2)/(16*a**5*d), Ne(d, 0)), (x*cos(c)**3/(a*cos(c) + a)**5, True))","A",0
87,1,68,0,11.578897," ","integrate(cos(d*x+c)**2/(a+a*cos(d*x+c))**5,x)","\begin{cases} \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{144 a^{5} d} - \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{5} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**9/(144*a**5*d) - tan(c/2 + d*x/2)**5/(40*a**5*d) + tan(c/2 + d*x/2)/(16*a**5*d), Ne(d, 0)), (x*cos(c)**2/(a*cos(c) + a)**5, True))","A",0
88,1,85,0,9.184229," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))**5,x)","\begin{cases} - \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{144 a^{5} d} - \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{56 a^{5} d} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{5} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2 + d*x/2)**9/(144*a**5*d) - tan(c/2 + d*x/2)**7/(56*a**5*d) + tan(c/2 + d*x/2)**3/(24*a**5*d) + tan(c/2 + d*x/2)/(16*a**5*d), Ne(d, 0)), (x*cos(c)/(a*cos(c) + a)**5, True))","A",0
89,1,102,0,7.602749," ","integrate(1/(a+a*cos(d*x+c))**5,x)","\begin{cases} \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{144 a^{5} d} + \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{28 a^{5} d} + \frac{3 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a^{5} d} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{12 a^{5} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16 a^{5} d} & \text{for}\: d \neq 0 \\\frac{x}{\left(a \cos{\left(c \right)} + a\right)^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**9/(144*a**5*d) + tan(c/2 + d*x/2)**7/(28*a**5*d) + 3*tan(c/2 + d*x/2)**5/(40*a**5*d) + tan(c/2 + d*x/2)**3/(12*a**5*d) + tan(c/2 + d*x/2)/(16*a**5*d), Ne(d, 0)), (x/(a*cos(c) + a)**5, True))","A",0
90,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))**5,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\cos^{5}{\left(c + d x \right)} + 5 \cos^{4}{\left(c + d x \right)} + 10 \cos^{3}{\left(c + d x \right)} + 10 \cos^{2}{\left(c + d x \right)} + 5 \cos{\left(c + d x \right)} + 1}\, dx}{a^{5}}"," ",0,"Integral(sec(c + d*x)/(cos(c + d*x)**5 + 5*cos(c + d*x)**4 + 10*cos(c + d*x)**3 + 10*cos(c + d*x)**2 + 5*cos(c + d*x) + 1), x)/a**5","F",0
91,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c))**5,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\cos^{5}{\left(c + d x \right)} + 5 \cos^{4}{\left(c + d x \right)} + 10 \cos^{3}{\left(c + d x \right)} + 10 \cos^{2}{\left(c + d x \right)} + 5 \cos{\left(c + d x \right)} + 1}\, dx}{a^{5}}"," ",0,"Integral(sec(c + d*x)**2/(cos(c + d*x)**5 + 5*cos(c + d*x)**4 + 10*cos(c + d*x)**3 + 10*cos(c + d*x)**2 + 5*cos(c + d*x) + 1), x)/a**5","F",0
92,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*cos(d*x+c))**5,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\cos^{5}{\left(c + d x \right)} + 5 \cos^{4}{\left(c + d x \right)} + 10 \cos^{3}{\left(c + d x \right)} + 10 \cos^{2}{\left(c + d x \right)} + 5 \cos{\left(c + d x \right)} + 1}\, dx}{a^{5}}"," ",0,"Integral(sec(c + d*x)**3/(cos(c + d*x)**5 + 5*cos(c + d*x)**4 + 10*cos(c + d*x)**3 + 10*cos(c + d*x)**2 + 5*cos(c + d*x) + 1), x)/a**5","F",0
93,1,129,0,39.013419," ","integrate(cos(d*x+c)**5/(a+a*cos(d*x+c))**6,x)","\begin{cases} - \frac{\tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{352 a^{6} d} + \frac{5 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{288 a^{6} d} - \frac{5 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{112 a^{6} d} + \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16 a^{6} d} - \frac{5 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{96 a^{6} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32 a^{6} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2 + d*x/2)**11/(352*a**6*d) + 5*tan(c/2 + d*x/2)**9/(288*a**6*d) - 5*tan(c/2 + d*x/2)**7/(112*a**6*d) + tan(c/2 + d*x/2)**5/(16*a**6*d) - 5*tan(c/2 + d*x/2)**3/(96*a**6*d) + tan(c/2 + d*x/2)/(32*a**6*d), Ne(d, 0)), (x*cos(c)**5/(a*cos(c) + a)**6, True))","A",0
94,1,124,0,30.356492," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**6,x)","\begin{cases} \frac{\tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{352 a^{6} d} - \frac{\tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{96 a^{6} d} + \frac{\tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{112 a^{6} d} + \frac{\tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{80 a^{6} d} - \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32 a^{6} d} + \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32 a^{6} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{\left(a \cos{\left(c \right)} + a\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(c/2 + d*x/2)**11/(352*a**6*d) - tan(c/2 + d*x/2)**9/(96*a**6*d) + tan(c/2 + d*x/2)**7/(112*a**6*d) + tan(c/2 + d*x/2)**5/(80*a**6*d) - tan(c/2 + d*x/2)**3/(32*a**6*d) + tan(c/2 + d*x/2)/(32*a**6*d), Ne(d, 0)), (x*cos(c)**4/(a*cos(c) + a)**6, True))","A",0
95,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**2, x)","F",0
98,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x), x)","F",0
99,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \cos{\left(c + d x \right)} + a}\, dx"," ",0,"Integral(sqrt(a*cos(c + d*x) + a), x)","F",0
100,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*sec(d*x+c),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*sec(c + d*x), x)","F",0
101,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*sec(d*x+c)**2,x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*sec(c + d*x)**2, x)","F",0
102,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*sec(d*x+c)**3,x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*sec(c + d*x)**3, x)","F",0
103,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)*sec(d*x+c)**4,x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*sec(c + d*x)**4, x)","F",0
104,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(3/2),x)","\int \left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)*cos(c + d*x), x)","F",0
107,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2),x)","\int \left(a \cos{\left(c + d x \right)} + a\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(3/2), x)","F",0
108,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c),x)","\int \left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)*sec(c + d*x), x)","F",0
109,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
125,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \cos{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(a*cos(c + d*x) + a), x)","F",0
127,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
128,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
129,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
130,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**4/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
131,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
134,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
135,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{1}{\left(a \cos{\left(c + d x \right)} + a\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(-3/2), x)","F",0
136,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
137,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
138,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
139,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
143,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{1}{\left(a \cos{\left(c + d x \right)} + a\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(-5/2), x)","F",0
144,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
145,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
146,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c)),x)","a \left(\int \sqrt{\cos{\left(c + d x \right)}}\, dx + \int \cos^{\frac{3}{2}}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sqrt(cos(c + d*x)), x) + Integral(cos(c + d*x)**(3/2), x))","F",0
149,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)**(1/2),x)","a \left(\int \frac{1}{\sqrt{\cos{\left(c + d x \right)}}}\, dx + \int \sqrt{\cos{\left(c + d x \right)}}\, dx\right)"," ",0,"a*(Integral(1/sqrt(cos(c + d*x)), x) + Integral(sqrt(cos(c + d*x)), x))","F",0
150,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)**(3/2),x)","a \left(\int \frac{1}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{1}{\sqrt{\cos{\left(c + d x \right)}}}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**(-3/2), x) + Integral(1/sqrt(cos(c + d*x)), x))","F",0
151,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sqrt(cos(c + d*x))/(cos(c + d*x) + 1), x)/a","F",0
178,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{1}{\cos^{\frac{3}{2}}{\left(c + d x \right)} + \sqrt{\cos{\left(c + d x \right)}}}\, dx}{a}"," ",0,"Integral(1/(cos(c + d*x)**(3/2) + sqrt(cos(c + d*x))), x)/a","F",0
179,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{1}{\cos^{\frac{5}{2}}{\left(c + d x \right)} + \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(1/(cos(c + d*x)**(5/2) + cos(c + d*x)**(3/2)), x)/a","F",0
180,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{1}{\cos^{\frac{7}{2}}{\left(c + d x \right)} + \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(1/(cos(c + d*x)**(7/2) + cos(c + d*x)**(5/2)), x)/a","F",0
181,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(9/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sqrt(cos(c + d*x))/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
186,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{1}{\cos^{\frac{5}{2}}{\left(c + d x \right)} + 2 \cos^{\frac{3}{2}}{\left(c + d x \right)} + \sqrt{\cos{\left(c + d x \right)}}}\, dx}{a^{2}}"," ",0,"Integral(1/(cos(c + d*x)**(5/2) + 2*cos(c + d*x)**(3/2) + sqrt(cos(c + d*x))), x)/a**2","F",0
187,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{1}{\cos^{\frac{7}{2}}{\left(c + d x \right)} + 2 \cos^{\frac{5}{2}}{\left(c + d x \right)} + \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(1/(cos(c + d*x)**(7/2) + 2*cos(c + d*x)**(5/2) + cos(c + d*x)**(3/2)), x)/a**2","F",0
188,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{1}{\cos^{\frac{9}{2}}{\left(c + d x \right)} + 2 \cos^{\frac{7}{2}}{\left(c + d x \right)} + \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(1/(cos(c + d*x)**(9/2) + 2*cos(c + d*x)**(7/2) + cos(c + d*x)**(5/2)), x)/a**2","F",0
189,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(11/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(9/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{1}{\cos^{\frac{7}{2}}{\left(c + d x \right)} + 3 \cos^{\frac{5}{2}}{\left(c + d x \right)} + 3 \cos^{\frac{3}{2}}{\left(c + d x \right)} + \sqrt{\cos{\left(c + d x \right)}}}\, dx}{a^{3}}"," ",0,"Integral(1/(cos(c + d*x)**(7/2) + 3*cos(c + d*x)**(5/2) + 3*cos(c + d*x)**(3/2) + sqrt(cos(c + d*x))), x)/a**3","F",0
196,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{1}{\cos^{\frac{9}{2}}{\left(c + d x \right)} + 3 \cos^{\frac{7}{2}}{\left(c + d x \right)} + 3 \cos^{\frac{5}{2}}{\left(c + d x \right)} + \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a^{3}}"," ",0,"Integral(1/(cos(c + d*x)**(9/2) + 3*cos(c + d*x)**(7/2) + 3*cos(c + d*x)**(5/2) + cos(c + d*x)**(3/2)), x)/a**3","F",0
197,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{1}{\cos^{\frac{11}{2}}{\left(c + d x \right)} + 3 \cos^{\frac{9}{2}}{\left(c + d x \right)} + 3 \cos^{\frac{7}{2}}{\left(c + d x \right)} + \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx}{a^{3}}"," ",0,"Integral(1/(cos(c + d*x)**(11/2) + 3*cos(c + d*x)**(9/2) + 3*cos(c + d*x)**(7/2) + cos(c + d*x)**(5/2)), x)/a**3","F",0
198,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**(3/2), x)","F",0
200,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*sqrt(cos(c + d*x)), x)","F",0
201,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/sqrt(cos(c + d*x)), x)","F",0
202,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/cos(c + d*x)**(3/2), x)","F",0
203,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/cos(c + d*x)**(5/2), x)","F",0
204,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(3/2),x)","\int \left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)*sqrt(cos(c + d*x)), x)","F",0
208,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)/cos(d*x+c)**(1/2),x)","\int \frac{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)/sqrt(cos(c + d*x)), x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)/cos(d*x+c)**(3/2),x)","\int \frac{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)/cos(c + d*x)**(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)/cos(d*x+c)**(5/2),x)","\int \frac{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)/cos(c + d*x)**(5/2), x)","F",0
211,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)/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*cos(d*x+c))**(3/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)/cos(d*x+c)**(5/4),x)","\int \frac{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}{\cos^{\frac{5}{4}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(3/2)/cos(c + d*x)**(5/4), x)","F",0
222,0,0,0,0.000000," ","integrate((a+a*cos(f*x+e))**(1/2)/cos(f*x+e)**(1/2),x)","\int \frac{\sqrt{a \left(\cos{\left(e + f x \right)} + 1\right)}}{\sqrt{\cos{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(e + f*x) + 1))/sqrt(cos(e + f*x)), x)","F",0
223,0,0,0,0.000000," ","integrate((a-a*cos(f*x+e))**(1/2)/(-cos(f*x+e))**(1/2),x)","\int \frac{\sqrt{- a \left(\cos{\left(e + f x \right)} - 1\right)}}{\sqrt{- \cos{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(-a*(cos(e + f*x) - 1))/sqrt(-cos(e + f*x)), x)","F",0
224,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
226,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
227,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a*(cos(c + d*x) + 1))*sqrt(cos(c + d*x))), x)","F",0
228,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**(3/2)), x)","F",0
229,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a*(cos(c + d*x) + 1))*cos(c + d*x)**(5/2)), x)","F",0
230,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(1+cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{\cos{\left(c + d x \right)} + 1}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/sqrt(cos(c + d*x) + 1), x)","F",0
233,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{\cos{\left(c + d x \right)} + 1}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(cos(c + d*x) + 1), x)","F",0
234,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(c + d x \right)} + 1} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(cos(c + d*x) + 1)*sqrt(cos(c + d*x))), x)","F",0
235,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(c + d x \right)} + 1} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(cos(c + d*x) + 1)*cos(c + d*x)**(3/2)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(c + d x \right)} + 1} \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(cos(c + d*x) + 1)*cos(c + d*x)**(5/2)), x)","F",0
237,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(7/2)/(1+cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
240,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
241,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{1}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
242,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{1}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a*(cos(c + d*x) + 1))**(3/2)*cos(c + d*x)**(3/2)), x)","F",0
243,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
247,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/(a*(cos(c + d*x) + 1))**(5/2), x)","F",0
248,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\int \frac{1}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a*(cos(c + d*x) + 1))**(5/2)*sqrt(cos(c + d*x))), x)","F",0
249,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(9/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,0,0,0,0.000000," ","integrate(1/cos(x)**(1/2)/(1+cos(x))**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(x \right)} + 1} \sqrt{\cos{\left(x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(cos(x) + 1)*sqrt(cos(x))), x)","F",0
262,0,0,0,0.000000," ","integrate(1/cos(x)**(1/2)/(a+a*cos(x))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\cos{\left(x \right)} + 1\right)} \sqrt{\cos{\left(x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a*(cos(x) + 1))*sqrt(cos(x))), x)","F",0
263,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a-a*cos(d*x+c))**(1/2),x)","\int \sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)} \cos^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(-a*(cos(c + d*x) - 1))*cos(c + d*x)**(3/2), x)","F",0
264,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a-a*cos(d*x+c))**(1/2),x)","\int \sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)} \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(-a*(cos(c + d*x) - 1))*sqrt(cos(c + d*x)), x)","F",0
265,0,0,0,0.000000," ","integrate((a-a*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(-a*(cos(c + d*x) - 1))/sqrt(cos(c + d*x)), x)","F",0
266,0,0,0,0.000000," ","integrate((a-a*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(-a*(cos(c + d*x) - 1))/cos(c + d*x)**(3/2), x)","F",0
267,0,0,0,0.000000," ","integrate((a-a*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(-a*(cos(c + d*x) - 1))/cos(c + d*x)**(5/2), x)","F",0
268,-1,0,0,0.000000," ","integrate((a-a*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,0,0,0,0.000000," ","integrate((1-cos(d*x+c))**(1/2)*cos(d*x+c)**(3/2),x)","\int \sqrt{1 - \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(1 - cos(c + d*x))*cos(c + d*x)**(3/2), x)","F",0
270,0,0,0,0.000000," ","integrate((1-cos(d*x+c))**(1/2)*cos(d*x+c)**(1/2),x)","\int \sqrt{1 - \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(1 - cos(c + d*x))*sqrt(cos(c + d*x)), x)","F",0
271,0,0,0,0.000000," ","integrate((1-cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\sqrt{1 - \cos{\left(c + d x \right)}}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(1 - cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
272,0,0,0,0.000000," ","integrate((1-cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{1 - \cos{\left(c + d x \right)}}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(1 - cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
273,0,0,0,0.000000," ","integrate((1-cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\sqrt{1 - \cos{\left(c + d x \right)}}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(1 - cos(c + d*x))/cos(c + d*x)**(5/2), x)","F",0
274,-1,0,0,0.000000," ","integrate((1-cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a-a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a-a*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/sqrt(-a*(cos(c + d*x) - 1)), x)","F",0
277,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a-a*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(-a*(cos(c + d*x) - 1)), x)","F",0
278,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a-a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-a*(cos(c + d*x) - 1))*sqrt(cos(c + d*x))), x)","F",0
279,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a-a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(-a*(cos(c + d*x) - 1))*cos(c + d*x)**(3/2)), x)","F",0
280,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a-a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- a \left(\cos{\left(c + d x \right)} - 1\right)} \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(-a*(cos(c + d*x) - 1))*cos(c + d*x)**(5/2)), x)","F",0
281,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(7/2)/(a-a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(1-cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(1-cos(d*x+c))**(1/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{1 - \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/sqrt(1 - cos(c + d*x)), x)","F",0
284,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(1-cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{1 - \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(1 - cos(c + d*x)), x)","F",0
285,0,0,0,0.000000," ","integrate(1/(1-cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{1 - \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(1 - cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
286,0,0,0,0.000000," ","integrate(1/(1-cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{1}{\sqrt{1 - \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(1 - cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
287,0,0,0,0.000000," ","integrate(1/(1-cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{1}{\sqrt{1 - \cos{\left(c + d x \right)}} \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(1 - cos(c + d*x))*cos(c + d*x)**(5/2)), x)","F",0
288,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(4/3)*(a+a*cos(d*x+c))**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(4/3)*(a+a*cos(d*x+c))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/3)*(a+a*cos(d*x+c))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)**(1/2),x)","a \left(\int \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(sqrt(sec(c + d*x)), x))","F",0
295,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)**(1/2),x)","a \left(\int \frac{\cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{1}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(1/sqrt(sec(c + d*x)), x))","F",0
296,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)**(3/2),x)","a \left(\int \frac{\cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{1}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(sec(c + d*x)**(-3/2), x))","F",0
297,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2*sec(d*x+c)**(1/2),x)","a^{2} \left(\int 2 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a**2*(Integral(2*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(sqrt(sec(c + d*x)), x))","F",0
302,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","a^{2} \left(\int \frac{2 \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{\cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{1}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**2*(Integral(2*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(1/sqrt(sec(c + d*x)), x))","F",0
303,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","a^{2} \left(\int \frac{2 \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{\cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{1}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a**2*(Integral(2*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(sec(c + d*x)**(-3/2), x))","F",0
304,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3*sec(d*x+c)**(1/2),x)","a^{3} \left(\int 3 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 3 \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a**3*(Integral(3*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(3*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(cos(c + d*x)**3*sqrt(sec(c + d*x)), x) + Integral(sqrt(sec(c + d*x)), x))","F",0
309,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","a^{3} \left(\int \frac{3 \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{3 \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{\cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{1}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**3*(Integral(3*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(3*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(1/sqrt(sec(c + d*x)), x))","F",0
310,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","a^{3} \left(\int \frac{3 \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 \cos^{2}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{\cos^{3}{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{1}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"a**3*(Integral(3*cos(c + d*x)/sec(c + d*x)**(3/2), x) + Integral(3*cos(c + d*x)**2/sec(c + d*x)**(3/2), x) + Integral(cos(c + d*x)**3/sec(c + d*x)**(3/2), x) + Integral(sec(c + d*x)**(-3/2), x))","F",0
311,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4*sec(d*x+c)**(1/2),x)","a^{4} \left(\int 4 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 6 \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int 4 \cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int \cos^{4}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}}\, dx + \int \sqrt{\sec{\left(c + d x \right)}}\, dx\right)"," ",0,"a**4*(Integral(4*cos(c + d*x)*sqrt(sec(c + d*x)), x) + Integral(6*cos(c + d*x)**2*sqrt(sec(c + d*x)), x) + Integral(4*cos(c + d*x)**3*sqrt(sec(c + d*x)), x) + Integral(cos(c + d*x)**4*sqrt(sec(c + d*x)), x) + Integral(sqrt(sec(c + d*x)), x))","F",0
316,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**4/sec(d*x+c)**(1/2),x)","a^{4} \left(\int \frac{4 \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{6 \cos^{2}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{4 \cos^{3}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{\cos^{4}{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx + \int \frac{1}{\sqrt{\sec{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**4*(Integral(4*cos(c + d*x)/sqrt(sec(c + d*x)), x) + Integral(6*cos(c + d*x)**2/sqrt(sec(c + d*x)), x) + Integral(4*cos(c + d*x)**3/sqrt(sec(c + d*x)), x) + Integral(cos(c + d*x)**4/sqrt(sec(c + d*x)), x) + Integral(1/sqrt(sec(c + d*x)), x))","F",0
317,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+a*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**(3/2)/(cos(c + d*x) + 1), x)/a","F",0
319,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sqrt(sec(c + d*x))/(cos(c + d*x) + 1), x)/a","F",0
320,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\frac{\int \frac{1}{\cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx}{a}"," ",0,"Integral(1/(cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x)/a","F",0
321,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\frac{\int \frac{1}{\cos{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(1/(cos(c + d*x)*sec(c + d*x)**(3/2) + sec(c + d*x)**(3/2)), x)/a","F",0
322,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**(3/2)/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
326,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sqrt(sec(c + d*x))/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
327,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\frac{\int \frac{1}{\cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 2 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx}{a^{2}}"," ",0,"Integral(1/(cos(c + d*x)**2*sqrt(sec(c + d*x)) + 2*cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x)/a**2","F",0
328,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\frac{\int \frac{1}{\cos^{2}{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} \sec^{\frac{3}{2}}{\left(c + d x \right)} + \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(1/(cos(c + d*x)**2*sec(c + d*x)**(3/2) + 2*cos(c + d*x)*sec(c + d*x)**(3/2) + sec(c + d*x)**(3/2)), x)/a**2","F",0
329,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**2/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**2/sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**3,x)","\frac{\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\cos^{3}{\left(c + d x \right)} + 3 \cos^{2}{\left(c + d x \right)} + 3 \cos{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sqrt(sec(c + d*x))/(cos(c + d*x)**3 + 3*cos(c + d*x)**2 + 3*cos(c + d*x) + 1), x)/a**3","F",0
334,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\frac{\int \frac{1}{\cos^{3}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 3 \cos^{2}{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + 3 \cos{\left(c + d x \right)} \sqrt{\sec{\left(c + d x \right)}} + \sqrt{\sec{\left(c + d x \right)}}}\, dx}{a^{3}}"," ",0,"Integral(1/(cos(c + d*x)**3*sqrt(sec(c + d*x)) + 3*cos(c + d*x)**2*sqrt(sec(c + d*x)) + 3*cos(c + d*x)*sqrt(sec(c + d*x)) + sqrt(sec(c + d*x))), x)/a**3","F",0
335,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**3/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**3/sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(9/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(7/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)*(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)*(a+a*cos(d*x+c))**(1/2),x)","\int \sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))*sqrt(sec(c + d*x)), x)","F",0
344,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/sqrt(sec(c + d*x)), x)","F",0
345,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/2)/sec(d*x+c)**(3/2),x)","\int \frac{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(cos(c + d*x) + 1))/sec(c + d*x)**(3/2), x)","F",0
346,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(7/2)/(1+cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(1+cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{\cos{\left(c + d x \right)} + 1}}\, dx"," ",0,"Integral(sec(c + d*x)**(3/2)/sqrt(cos(c + d*x) + 1), x)","F",0
364,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\sqrt{\cos{\left(c + d x \right)} + 1}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/sqrt(cos(c + d*x) + 1), x)","F",0
365,0,0,0,0.000000," ","integrate(1/sec(d*x+c)**(1/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(c + d x \right)} + 1} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(cos(c + d*x) + 1)*sqrt(sec(c + d*x))), x)","F",0
366,0,0,0,0.000000," ","integrate(1/sec(d*x+c)**(3/2)/(1+cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{\cos{\left(c + d x \right)} + 1} \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(cos(c + d*x) + 1)*sec(c + d*x)**(3/2)), x)","F",0
367,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(7/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**(3/2)/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
370,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/sqrt(a*(cos(c + d*x) + 1)), x)","F",0
371,0,0,0,0.000000," ","integrate(1/sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a*(cos(c + d*x) + 1))*sqrt(sec(c + d*x))), x)","F",0
372,0,0,0,0.000000," ","integrate(1/sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\cos{\left(c + d x \right)} + 1\right)} \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a*(cos(c + d*x) + 1))*sec(c + d*x)**(3/2)), x)","F",0
373,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**(3/2)/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
375,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(3/2),x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/(a*(cos(c + d*x) + 1))**(3/2), x)","F",0
376,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\int \frac{1}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a*(cos(c + d*x) + 1))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
377,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(3/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(5/2)/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(7/2)/sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(9/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(9/2)/sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*sec(d*x+c)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+a*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+a*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+a*cos(d*x+c))**2,x)","a^{2} \left(\int 2 \cos{\left(c + d x \right)} \cos^{m}{\left(c + d x \right)}\, dx + \int \cos^{2}{\left(c + d x \right)} \cos^{m}{\left(c + d x \right)}\, dx + \int \cos^{m}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(2*cos(c + d*x)*cos(c + d*x)**m, x) + Integral(cos(c + d*x)**2*cos(c + d*x)**m, x) + Integral(cos(c + d*x)**m, x))","F",0
400,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+a*cos(d*x+c)),x)","a \left(\int \cos{\left(c + d x \right)} \cos^{m}{\left(c + d x \right)}\, dx + \int \cos^{m}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)*cos(c + d*x)**m, x) + Integral(cos(c + d*x)**m, x))","F",0
401,0,0,0,0.000000," ","integrate(cos(d*x+c)**m/(a+a*cos(d*x+c)),x)","\frac{\int \frac{\cos^{m}{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**m/(cos(c + d*x) + 1), x)/a","F",0
402,0,0,0,0.000000," ","integrate(cos(d*x+c)**m/(a+a*cos(d*x+c))**2,x)","\frac{\int \frac{\cos^{m}{\left(c + d x \right)}}{\cos^{2}{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)**m/(cos(c + d*x)**2 + 2*cos(c + d*x) + 1), x)/a**2","F",0
403,1,286,0,8.964851," ","integrate(cos(d*x+c)**7*(a+b*cos(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{35 b x \sin^{8}{\left(c + d x \right)}}{128} + \frac{35 b x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{105 b x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{35 b x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{35 b x \cos^{8}{\left(c + d x \right)}}{128} + \frac{35 b \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{385 b \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{511 b \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{93 b \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\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 + 35*b*x*sin(c + d*x)**8/128 + 35*b*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 105*b*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 35*b*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 35*b*x*cos(c + d*x)**8/128 + 35*b*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 385*b*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 511*b*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 93*b*sin(c + d*x)*cos(c + d*x)**7/(128*d), Ne(d, 0)), (x*(a + b*cos(c))*cos(c)**7, True))","A",0
404,1,238,0,5.395508," ","integrate(cos(d*x+c)**6*(a+b*cos(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{16 b \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 b \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 b \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{b \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\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) + 16*b*sin(c + d*x)**7/(35*d) + 8*b*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*b*sin(c + d*x)**3*cos(c + d*x)**4/d + b*sin(c + d*x)*cos(c + d*x)**6/d, Ne(d, 0)), (x*(a + b*cos(c))*cos(c)**6, True))","A",0
405,1,216,0,3.267350," ","integrate(cos(d*x+c)**5*(a+b*cos(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{5 b x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 b x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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 + 5*b*x*sin(c + d*x)**6/16 + 15*b*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*b*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*b*x*cos(c + d*x)**6/16 + 5*b*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*b*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*b*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*cos(c))*cos(c)**5, True))","A",0
406,1,168,0,1.862879," ","integrate(cos(d*x+c)**4*(a+b*cos(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{8 b \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 b \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{b \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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) + 8*b*sin(c + d*x)**5/(15*d) + 4*b*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + b*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))*cos(c)**4, True))","A",0
407,1,144,0,0.919480," ","integrate(cos(d*x+c)**3*(a+b*cos(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{3 b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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 + 3*b*x*sin(c + d*x)**4/8 + 3*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b*x*cos(c + d*x)**4/8 + 3*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*b*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))*cos(c)**3, True))","A",0
408,1,92,0,0.461516," ","integrate(cos(d*x+c)**2*(a+b*cos(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{2 b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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) + 2*b*sin(c + d*x)**3/(3*d) + b*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a + b*cos(c))*cos(c)**2, True))","A",0
409,1,66,0,0.197837," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c)),x)","\begin{cases} \frac{a \sin{\left(c + d x \right)}}{d} + \frac{b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sin(c + d*x)/d + b*x*sin(c + d*x)**2/2 + b*x*cos(c + d*x)**2/2 + b*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a + b*cos(c))*cos(c), True))","A",0
410,1,17,0,0.117934," ","integrate(a+b*cos(d*x+c),x)","a x + b \left(\begin{cases} \frac{\sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \cos{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((sin(c + d*x)/d, Ne(d, 0)), (x*cos(c), True))","A",0
411,1,49,0,4.980917," ","integrate((a+b*cos(d*x+c))*sec(d*x+c),x)","a \left(\begin{cases} \frac{x \tan{\left(c \right)} \sec{\left(c \right)}}{\tan{\left(c \right)} + \sec{\left(c \right)}} + \frac{x \sec^{2}{\left(c \right)}}{\tan{\left(c \right)} + \sec{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\log{\left(\tan{\left(c + d x \right)} + \sec{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right) + b x"," ",0,"a*Piecewise((x*tan(c)*sec(c)/(tan(c) + sec(c)) + x*sec(c)**2/(tan(c) + sec(c)), Eq(d, 0)), (log(tan(c + d*x) + sec(c + d*x))/d, True)) + b*x","B",0
412,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)**2,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
413,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)**3,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*sec(c + d*x)**3, x)","F",0
414,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)**4,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*sec(c + d*x)**4, x)","F",0
415,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)**5,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \sec^{5}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*sec(c + d*x)**5, x)","F",0
416,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)**6,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \sec^{6}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*sec(c + d*x)**6, x)","F",0
417,1,343,0,4.020624," ","integrate(cos(d*x+c)**4*(a+b*cos(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{16 a b \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{8 a b \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{2 a b \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 b^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 b^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 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 \cos{\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) + 16*a*b*sin(c + d*x)**5/(15*d) + 8*a*b*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 2*a*b*sin(c + d*x)*cos(c + d*x)**4/d + 5*b**2*x*sin(c + d*x)**6/16 + 15*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*b**2*x*cos(c + d*x)**6/16 + 5*b**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*b**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*b**2*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*cos(c))**2*cos(c)**4, True))","A",0
418,1,221,0,2.021194," ","integrate(cos(d*x+c)**3*(a+b*cos(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{3 a b x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 a b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a b x \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 a b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{5 a b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{8 b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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 + 3*a*b*x*sin(c + d*x)**4/4 + 3*a*b*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*a*b*x*cos(c + d*x)**4/4 + 3*a*b*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 5*a*b*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 8*b**2*sin(c + d*x)**5/(15*d) + 4*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + b**2*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**2*cos(c)**3, True))","A",0
419,1,211,0,1.060469," ","integrate(cos(d*x+c)**2*(a+b*cos(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{4 a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 a b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 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 \cos{\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) + 4*a*b*sin(c + d*x)**3/(3*d) + 2*a*b*sin(c + d*x)*cos(c + d*x)**2/d + 3*b**2*x*sin(c + d*x)**4/8 + 3*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b**2*x*cos(c + d*x)**4/8 + 3*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))**2*cos(c)**2, True))","A",0
420,1,107,0,0.483436," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**2,x)","\begin{cases} \frac{a^{2} \sin{\left(c + d x \right)}}{d} + a b x \sin^{2}{\left(c + d x \right)} + a b x \cos^{2}{\left(c + d x \right)} + \frac{a b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{2 b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sin(c + d*x)/d + a*b*x*sin(c + d*x)**2 + a*b*x*cos(c + d*x)**2 + a*b*sin(c + d*x)*cos(c + d*x)/d + 2*b**2*sin(c + d*x)**3/(3*d) + b**2*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a + b*cos(c))**2*cos(c), True))","A",0
421,1,78,0,0.253937," ","integrate((a+b*cos(d*x+c))**2,x)","\begin{cases} a^{2} x + \frac{2 a b \sin{\left(c + d x \right)}}{d} + \frac{b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{b^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*sin(c + d*x)/d + b**2*x*sin(c + d*x)**2/2 + b**2*x*cos(c + d*x)**2/2 + b**2*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a + b*cos(c))**2, True))","A",0
422,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*sec(c + d*x), x)","F",0
423,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**2,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*sec(c + d*x)**2, x)","F",0
424,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**3,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*sec(c + d*x)**3, x)","F",0
425,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**4,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*sec(c + d*x)**4, x)","F",0
426,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,1,393,0,3.931615," ","integrate(cos(d*x+c)**3*(a+b*cos(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{9 a^{2} b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 a^{2} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 a^{2} b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 a^{2} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 a^{2} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 a b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{4 a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 b^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 b^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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 + 9*a**2*b*x*sin(c + d*x)**4/8 + 9*a**2*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*a**2*b*x*cos(c + d*x)**4/8 + 9*a**2*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*a**2*b*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*a*b**2*sin(c + d*x)**5/(5*d) + 4*a*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 3*a*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*b**3*x*sin(c + d*x)**6/16 + 15*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*b**3*x*cos(c + d*x)**6/16 + 5*b**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*b**3*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*cos(c))**3*cos(c)**3, True))","A",0
429,1,284,0,2.175087," ","integrate(cos(d*x+c)**2*(a+b*cos(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{2 a^{2} b \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 a^{2} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{9 a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{9 a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{15 a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{8 b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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) + 2*a**2*b*sin(c + d*x)**3/d + 3*a**2*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*a*b**2*x*sin(c + d*x)**4/8 + 9*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 9*a*b**2*x*cos(c + d*x)**4/8 + 9*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 15*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 8*b**3*sin(c + d*x)**5/(15*d) + 4*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + b**3*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**3*cos(c)**2, True))","A",0
430,1,233,0,1.078172," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**3,x)","\begin{cases} \frac{a^{3} \sin{\left(c + d x \right)}}{d} + \frac{3 a^{2} b x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} b x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 a b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 b^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\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*x*sin(c + d*x)**2/2 + 3*a**2*b*x*cos(c + d*x)**2/2 + 3*a**2*b*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*a*b**2*sin(c + d*x)**3/d + 3*a*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*b**3*x*sin(c + d*x)**4/8 + 3*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b**3*x*cos(c + d*x)**4/8 + 3*b**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*b**3*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))**3*cos(c), True))","A",0
431,1,128,0,0.522449," ","integrate((a+b*cos(d*x+c))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b \sin{\left(c + d x \right)}}{d} + \frac{3 a b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 a b^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{2 b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*sin(c + d*x)/d + 3*a*b**2*x*sin(c + d*x)**2/2 + 3*a*b**2*x*cos(c + d*x)**2/2 + 3*a*b**2*sin(c + d*x)*cos(c + d*x)/(2*d) + 2*b**3*sin(c + d*x)**3/(3*d) + b**3*sin(c + d*x)*cos(c + d*x)**2/d, Ne(d, 0)), (x*(a + b*cos(c))**3, True))","A",0
432,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{3} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3*sec(c + d*x), x)","F",0
433,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**2,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{3} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3*sec(c + d*x)**2, x)","F",0
434,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**3,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{3} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3*sec(c + d*x)**3, x)","F",0
435,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,1,495,0,6.451078," ","integrate(cos(d*x+c)**3*(a+b*cos(d*x+c))**4,x)","\begin{cases} \frac{2 a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 a^{3} b x \sin^{4}{\left(c + d x \right)}}{2} + 3 a^{3} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 a^{3} b x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 a^{3} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 a^{3} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{16 a^{2} b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{8 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{6 a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 a b^{3} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{15 a b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{15 a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + \frac{5 a b^{3} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{5 a b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{10 a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{11 a b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{16 b^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 b^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{b^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{4} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**4*sin(c + d*x)**3/(3*d) + a**4*sin(c + d*x)*cos(c + d*x)**2/d + 3*a**3*b*x*sin(c + d*x)**4/2 + 3*a**3*b*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*a**3*b*x*cos(c + d*x)**4/2 + 3*a**3*b*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*a**3*b*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 16*a**2*b**2*sin(c + d*x)**5/(5*d) + 8*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d + 6*a**2*b**2*sin(c + d*x)*cos(c + d*x)**4/d + 5*a*b**3*x*sin(c + d*x)**6/4 + 15*a*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 15*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 5*a*b**3*x*cos(c + d*x)**6/4 + 5*a*b**3*sin(c + d*x)**5*cos(c + d*x)/(4*d) + 10*a*b**3*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 11*a*b**3*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 16*b**4*sin(c + d*x)**7/(35*d) + 8*b**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*b**4*sin(c + d*x)**3*cos(c + d*x)**4/d + b**4*sin(c + d*x)*cos(c + d*x)**6/d, Ne(d, 0)), (x*(a + b*cos(c))**4*cos(c)**3, True))","A",0
439,1,459,0,4.021455," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**4,x)","\begin{cases} \frac{a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{8 a^{3} b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 a^{3} b \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{9 a^{2} b^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{9 a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{9 a^{2} b^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{9 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{15 a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{32 a b^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{16 a b^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{5 b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{4} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x*sin(c + d*x)**2/2 + a**4*x*cos(c + d*x)**2/2 + a**4*sin(c + d*x)*cos(c + d*x)/(2*d) + 8*a**3*b*sin(c + d*x)**3/(3*d) + 4*a**3*b*sin(c + d*x)*cos(c + d*x)**2/d + 9*a**2*b**2*x*sin(c + d*x)**4/4 + 9*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 9*a**2*b**2*x*cos(c + d*x)**4/4 + 9*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) + 15*a**2*b**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + 32*a*b**3*sin(c + d*x)**5/(15*d) + 16*a*b**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 4*a*b**3*sin(c + d*x)*cos(c + d*x)**4/d + 5*b**4*x*sin(c + d*x)**6/16 + 15*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*b**4*x*cos(c + d*x)**6/16 + 5*b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*cos(c))**4*cos(c)**2, True))","A",0
440,1,301,0,2.249744," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**4,x)","\begin{cases} \frac{a^{4} \sin{\left(c + d x \right)}}{d} + 2 a^{3} b x \sin^{2}{\left(c + d x \right)} + 2 a^{3} b x \cos^{2}{\left(c + d x \right)} + \frac{2 a^{3} b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{4 a^{2} b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{6 a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 a b^{3} x \sin^{4}{\left(c + d x \right)}}{2} + 3 a b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{3 a b^{3} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{3 a b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{5 a b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{8 b^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 b^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{b^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{4} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*sin(c + d*x)/d + 2*a**3*b*x*sin(c + d*x)**2 + 2*a**3*b*x*cos(c + d*x)**2 + 2*a**3*b*sin(c + d*x)*cos(c + d*x)/d + 4*a**2*b**2*sin(c + d*x)**3/d + 6*a**2*b**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*a*b**3*x*sin(c + d*x)**4/2 + 3*a*b**3*x*sin(c + d*x)**2*cos(c + d*x)**2 + 3*a*b**3*x*cos(c + d*x)**4/2 + 3*a*b**3*sin(c + d*x)**3*cos(c + d*x)/(2*d) + 5*a*b**3*sin(c + d*x)*cos(c + d*x)**3/(2*d) + 8*b**4*sin(c + d*x)**5/(15*d) + 4*b**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + b**4*sin(c + d*x)*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a + b*cos(c))**4*cos(c), True))","A",0
441,1,240,0,1.109294," ","integrate((a+b*cos(d*x+c))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b \sin{\left(c + d x \right)}}{d} + 3 a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} + 3 a^{2} b^{2} x \cos^{2}{\left(c + d x \right)} + \frac{3 a^{2} b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} + \frac{8 a b^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 b^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \cos{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*sin(c + d*x)/d + 3*a**2*b**2*x*sin(c + d*x)**2 + 3*a**2*b**2*x*cos(c + d*x)**2 + 3*a**2*b**2*sin(c + d*x)*cos(c + d*x)/d + 8*a*b**3*sin(c + d*x)**3/(3*d) + 4*a*b**3*sin(c + d*x)*cos(c + d*x)**2/d + 3*b**4*x*sin(c + d*x)**4/8 + 3*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b**4*x*cos(c + d*x)**4/8 + 3*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*cos(c))**4, True))","A",0
442,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*sec(d*x+c),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{4} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**4*sec(c + d*x), x)","F",0
443,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*sec(d*x+c)**2,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{4} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**4*sec(c + d*x)**2, x)","F",0
444,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**4*sec(d*x+c)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,1,1744,0,122.503519," ","integrate(cos(d*x+c)**2/(a+b*cos(d*x+c)),x)","\begin{cases} \tilde{\infty} x \cos{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{3 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{1}{b d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: a = - b \\\frac{\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{x \cos^{2}{\left(c \right)}}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} - \frac{d x}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} + \frac{\tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} + \frac{3 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + b d} & \text{for}\: a = b \\- \frac{a^{2} d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a^{2} d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a^{2} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a^{2} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a^{2} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a^{2} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a b d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a b d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{2 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{2 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - b^{3} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*cos(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (d*x*tan(c/2 + d*x/2)**3/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + d*x*tan(c/2 + d*x/2)/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + 3*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)) + 1/(b*d*tan(c/2 + d*x/2)**3 + b*d*tan(c/2 + d*x/2)), Eq(a, -b)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d))/a, Eq(b, 0)), (x*cos(c)**2/(a + b*cos(c)), Eq(d, 0)), (-d*x*tan(c/2 + d*x/2)**2/(b*d*tan(c/2 + d*x/2)**2 + b*d) - d*x/(b*d*tan(c/2 + d*x/2)**2 + b*d) + tan(c/2 + d*x/2)**3/(b*d*tan(c/2 + d*x/2)**2 + b*d) + 3*tan(c/2 + d*x/2)/(b*d*tan(c/2 + d*x/2)**2 + b*d), Eq(a, b)), (-a**2*d*x*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - a**2*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + a**2*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + a**2*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - a**2*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - a**2*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + a*b*d*x*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + a*b*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) + 2*a*b*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))) - 2*b**2*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)/(a*b**2*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 + a*b**2*d*sqrt(-a/(a - b) - b/(a - b)) - b**3*d*sqrt(-a/(a - b) - b/(a - b))*tan(c/2 + d*x/2)**2 - b**3*d*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
453,1,320,0,24.696627," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{x}{b} - \frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d} & \text{for}\: a = b \\\frac{x}{b} + \frac{1}{b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: a = - b \\\frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\\frac{a d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b d x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{a b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (x/b - tan(c/2 + d*x/2)/(b*d), Eq(a, b)), (x/b + 1/(b*d*tan(c/2 + d*x/2)), Eq(a, -b)), (sin(c + d*x)/(a*d), Eq(b, 0)), (x*cos(c)/(a + b*cos(c)), Eq(d, 0)), (a*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) - a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) + a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))) - b*d*x*sqrt(-a/(a - b) - b/(a - b))/(a*b*d*sqrt(-a/(a - b) - b/(a - b)) - b**2*d*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
454,1,172,0,4.024068," ","integrate(1/(a+b*cos(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x}{\cos{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{1}{b d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: a = - b \\\frac{x}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{b d} & \text{for}\: a = b \\\frac{\log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{\log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/cos(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (1/(b*d*tan(c/2 + d*x/2)), Eq(a, -b)), (x/(a + b*cos(c)), Eq(d, 0)), (tan(c/2 + d*x/2)/(b*d), Eq(a, b)), (log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*d*sqrt(-a/(a - b) - b/(a - b)) - b*d*sqrt(-a/(a - b) - b/(a - b))) - log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*d*sqrt(-a/(a - b) - b/(a - b)) - b*d*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
455,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c)),x)","\int \frac{\sec{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*cos(c + d*x)), x)","F",0
456,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*cos(d*x+c)),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*cos(c + d*x)), x)","F",0
457,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*cos(d*x+c)),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*cos(c + d*x)), x)","F",0
458,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*cos(d*x+c)),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*cos(c + d*x)), x)","F",0
459,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2,x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(-2), x)","F",0
465,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))**2,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*cos(c + d*x))**2, x)","F",0
466,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*cos(d*x+c))**2,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*cos(c + d*x))**2, x)","F",0
467,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*cos(d*x+c))**2,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*cos(c + d*x))**2, x)","F",0
468,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*cos(d*x+c))**2,x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*cos(c + d*x))**2, x)","F",0
469,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))**3,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*cos(c + d*x))**3, x)","F",0
476,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*cos(d*x+c))**3,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*cos(c + d*x))**3, x)","F",0
477,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*cos(d*x+c))**3,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*cos(c + d*x))**3, x)","F",0
478,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))**4,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*cos(c + d*x))**4, x)","F",0
485,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*cos(d*x+c))**4,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*cos(c + d*x))**4, x)","F",0
486,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**2, x)","F",0
488,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*cos(c + d*x), x)","F",0
489,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x)), x)","F",0
490,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*sec(c + d*x), x)","F",0
491,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
492,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*sec(c + d*x)**3, x)","F",0
493,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*cos(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)**2*(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(3/2),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2)*cos(c + d*x), x)","F",0
496,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2), x)","F",0
497,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2)*sec(c + d*x), x)","F",0
498,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*cos(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*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(3+4*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(3+4*cos(d*x+c))**(1/2),x)","\int \sqrt{4 \cos{\left(c + d x \right)} + 3} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(4*cos(c + d*x) + 3)*cos(c + d*x)**2, x)","F",0
511,0,0,0,0.000000," ","integrate(cos(d*x+c)*(3+4*cos(d*x+c))**(1/2),x)","\int \sqrt{4 \cos{\left(c + d x \right)} + 3} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(4*cos(c + d*x) + 3)*cos(c + d*x), x)","F",0
512,0,0,0,0.000000," ","integrate((3+4*cos(d*x+c))**(1/2),x)","\int \sqrt{4 \cos{\left(c + d x \right)} + 3}\, dx"," ",0,"Integral(sqrt(4*cos(c + d*x) + 3), x)","F",0
513,0,0,0,0.000000," ","integrate(sec(d*x+c)*(3+4*cos(d*x+c))**(1/2),x)","\int \sqrt{4 \cos{\left(c + d x \right)} + 3} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(4*cos(c + d*x) + 3)*sec(c + d*x), x)","F",0
514,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(3+4*cos(d*x+c))**(1/2),x)","\int \sqrt{4 \cos{\left(c + d x \right)} + 3} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(4*cos(c + d*x) + 3)*sec(c + d*x)**2, x)","F",0
515,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(3+4*cos(d*x+c))**(1/2),x)","\int \sqrt{4 \cos{\left(c + d x \right)} + 3} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(4*cos(c + d*x) + 3)*sec(c + d*x)**3, x)","F",0
516,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(3-4*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(3-4*cos(d*x+c))**(1/2),x)","\int \sqrt{3 - 4 \cos{\left(c + d x \right)}} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(3 - 4*cos(c + d*x))*cos(c + d*x)**2, x)","F",0
518,0,0,0,0.000000," ","integrate(cos(d*x+c)*(3-4*cos(d*x+c))**(1/2),x)","\int \sqrt{3 - 4 \cos{\left(c + d x \right)}} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(3 - 4*cos(c + d*x))*cos(c + d*x), x)","F",0
519,0,0,0,0.000000," ","integrate((3-4*cos(d*x+c))**(1/2),x)","\int \sqrt{3 - 4 \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(3 - 4*cos(c + d*x)), x)","F",0
520,0,0,0,0.000000," ","integrate(sec(d*x+c)*(3-4*cos(d*x+c))**(1/2),x)","\int \sqrt{3 - 4 \cos{\left(c + d x \right)}} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(3 - 4*cos(c + d*x))*sec(c + d*x), x)","F",0
521,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(3-4*cos(d*x+c))**(1/2),x)","\int \sqrt{3 - 4 \cos{\left(c + d x \right)}} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(3 - 4*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
522,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(3-4*cos(d*x+c))**(1/2),x)","\int \sqrt{3 - 4 \cos{\left(c + d x \right)}} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(3 - 4*cos(c + d*x))*sec(c + d*x)**3, x)","F",0
523,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/sqrt(a + b*cos(c + d*x)), x)","F",0
525,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
526,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*cos(c + d*x)), x)","F",0
527,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)/sqrt(a + b*cos(c + d*x)), x)","F",0
528,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/sqrt(a + b*cos(c + d*x)), x)","F",0
529,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/sqrt(a + b*cos(c + d*x)), x)","F",0
530,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a + b*cos(c + d*x))**(3/2), x)","F",0
533,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)/(a + b*cos(c + d*x))**(3/2), x)","F",0
534,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(-3/2), x)","F",0
535,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*cos(c + d*x))**(3/2), x)","F",0
536,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*cos(c + d*x))**(3/2), x)","F",0
537,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*cos(c + d*x))**(3/2), x)","F",0
538,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)/(a + b*cos(c + d*x))**(5/2), x)","F",0
543,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(-5/2), x)","F",0
544,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*cos(c + d*x))**(5/2), x)","F",0
545,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*cos(c + d*x))**(5/2), x)","F",0
546,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(3+4*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(3+4*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\sqrt{4 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(cos(c + d*x)**2/sqrt(4*cos(c + d*x) + 3), x)","F",0
549,0,0,0,0.000000," ","integrate(cos(d*x+c)/(3+4*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\sqrt{4 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(cos(c + d*x)/sqrt(4*cos(c + d*x) + 3), x)","F",0
550,0,0,0,0.000000," ","integrate(1/(3+4*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{4 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(1/sqrt(4*cos(c + d*x) + 3), x)","F",0
551,0,0,0,0.000000," ","integrate(sec(d*x+c)/(3+4*cos(d*x+c))**(1/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\sqrt{4 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(sec(c + d*x)/sqrt(4*cos(c + d*x) + 3), x)","F",0
552,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(3+4*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\sqrt{4 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(sec(c + d*x)**2/sqrt(4*cos(c + d*x) + 3), x)","F",0
553,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(3+4*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\sqrt{4 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(sec(c + d*x)**3/sqrt(4*cos(c + d*x) + 3), x)","F",0
554,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(3-4*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(3-4*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\sqrt{3 - 4 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/sqrt(3 - 4*cos(c + d*x)), x)","F",0
556,0,0,0,0.000000," ","integrate(cos(d*x+c)/(3-4*cos(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)}}{\sqrt{3 - 4 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)/sqrt(3 - 4*cos(c + d*x)), x)","F",0
557,0,0,0,0.000000," ","integrate(1/(3-4*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{3 - 4 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(3 - 4*cos(c + d*x)), x)","F",0
558,0,0,0,0.000000," ","integrate(sec(d*x+c)/(3-4*cos(d*x+c))**(1/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\sqrt{3 - 4 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)/sqrt(3 - 4*cos(c + d*x)), x)","F",0
559,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(3-4*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\sqrt{3 - 4 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/sqrt(3 - 4*cos(c + d*x)), x)","F",0
560,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(3-4*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\sqrt{3 - 4 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/sqrt(3 - 4*cos(c + d*x)), x)","F",0
561,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)**(1/2),x)","\int \left(A + B \cos{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sqrt(cos(c + d*x)), x)","F",0
564,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
565,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
566,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(9/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(3/2), x)","F",0
604,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x)), x)","F",0
605,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
606,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
607,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(5/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))/cos(c + d*x)**(5/2), x)","F",0
608,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(3/2),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2)*sqrt(cos(c + d*x)), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2)/sqrt(cos(c + d*x)), x)","F",0
613,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(3/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2)/cos(c + d*x)**(3/2), x)","F",0
614,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(5/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2)/cos(c + d*x)**(5/2), x)","F",0
615,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/sqrt(a + b*cos(c + d*x)), x)","F",0
627,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
628,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
629,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
630,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(5/2)), x)","F",0
631,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/(a + b*cos(c + d*x))**(3/2), x)","F",0
633,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(3/2), x)","F",0
634,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
635,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))**(3/2)*cos(c + d*x)**(3/2)), x)","F",0
636,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(7/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,0,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**(3/2)/(a + b*cos(c + d*x))**(5/2), x)","F",0
640,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/(a + b*cos(c + d*x))**(5/2), x)","F",0
641,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{5}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))**(5/2)*sqrt(cos(c + d*x))), x)","F",0
642,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(2+3*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{3 \cos{\left(c + d x \right)} + 2} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(3*cos(c + d*x) + 2)*sqrt(cos(c + d*x))), x)","F",0
645,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(-2+3*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{3 \cos{\left(c + d x \right)} - 2} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(3*cos(c + d*x) - 2)*sqrt(cos(c + d*x))), x)","F",0
646,0,0,0,0.000000," ","integrate(1/(2-3*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{2 - 3 \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(2 - 3*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
647,0,0,0,0.000000," ","integrate(1/(-2-3*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{- 3 \cos{\left(c + d x \right)} - 2} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-3*cos(c + d*x) - 2)*sqrt(cos(c + d*x))), x)","F",0
648,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(3+2*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{2 \cos{\left(c + d x \right)} + 3} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(2*cos(c + d*x) + 3)*sqrt(cos(c + d*x))), x)","F",0
649,0,0,0,0.000000," ","integrate(1/(3-2*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{3 - 2 \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(3 - 2*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
650,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/2)/(-3+2*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{2 \cos{\left(c + d x \right)} - 3} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(2*cos(c + d*x) - 3)*sqrt(cos(c + d*x))), x)","F",0
651,0,0,0,0.000000," ","integrate(1/(-3-2*cos(d*x+c))**(1/2)/cos(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{- 2 \cos{\left(c + d x \right)} - 3} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-2*cos(c + d*x) - 3)*sqrt(cos(c + d*x))), x)","F",0
652,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))**(1/2)/(2+3*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{3 \cos{\left(c + d x \right)} + 2}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(3*cos(c + d*x) + 2)), x)","F",0
653,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))**(1/2)/(-2+3*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{3 \cos{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(3*cos(c + d*x) - 2)), x)","F",0
654,0,0,0,0.000000," ","integrate(1/(2-3*cos(d*x+c))**(1/2)/(-cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{2 - 3 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(2 - 3*cos(c + d*x))), x)","F",0
655,0,0,0,0.000000," ","integrate(1/(-2-3*cos(d*x+c))**(1/2)/(-cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{- 3 \cos{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(-3*cos(c + d*x) - 2)), x)","F",0
656,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))**(1/2)/(3+2*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{2 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(2*cos(c + d*x) + 3)), x)","F",0
657,0,0,0,0.000000," ","integrate(1/(3-2*cos(d*x+c))**(1/2)/(-cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{3 - 2 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(3 - 2*cos(c + d*x))), x)","F",0
658,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))**(1/2)/(-3+2*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{2 \cos{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(2*cos(c + d*x) - 3)), x)","F",0
659,0,0,0,0.000000," ","integrate(1/(-3-2*cos(d*x+c))**(1/2)/(-cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(c + d x \right)}} \sqrt{- 2 \cos{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(1/(sqrt(-cos(c + d*x))*sqrt(-2*cos(c + d*x) - 3)), x)","F",0
660,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(2+3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{3 \cos{\left(c + d x \right)} + 2}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(3*cos(c + d*x) + 2), x)","F",0
661,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(-2+3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{3 \cos{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(3*cos(c + d*x) - 2), x)","F",0
662,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(2-3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{2 - 3 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(2 - 3*cos(c + d*x)), x)","F",0
663,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(-2-3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{- 3 \cos{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(-3*cos(c + d*x) - 2), x)","F",0
664,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(3+2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{2 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(2*cos(c + d*x) + 3), x)","F",0
665,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(3-2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{3 - 2 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(3 - 2*cos(c + d*x)), x)","F",0
666,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(-3+2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{2 \cos{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(2*cos(c + d*x) - 3), x)","F",0
667,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)/(-3-2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cos{\left(c + d x \right)}}}{\sqrt{- 2 \cos{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(sqrt(cos(c + d*x))/sqrt(-2*cos(c + d*x) - 3), x)","F",0
668,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(2+3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{3 \cos{\left(c + d x \right)} + 2}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(3*cos(c + d*x) + 2), x)","F",0
669,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(-2+3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{3 \cos{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(3*cos(c + d*x) - 2), x)","F",0
670,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(2-3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{2 - 3 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(2 - 3*cos(c + d*x)), x)","F",0
671,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(-2-3*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{- 3 \cos{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(-3*cos(c + d*x) - 2), x)","F",0
672,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(3+2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{2 \cos{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(2*cos(c + d*x) + 3), x)","F",0
673,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(3-2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{3 - 2 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(3 - 2*cos(c + d*x)), x)","F",0
674,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(-3+2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{2 \cos{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(2*cos(c + d*x) - 3), x)","F",0
675,0,0,0,0.000000," ","integrate((-cos(d*x+c))**(1/2)/(-3-2*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{- \cos{\left(c + d x \right)}}}{\sqrt{- 2 \cos{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(sqrt(-cos(c + d*x))/sqrt(-2*cos(c + d*x) - 3), x)","F",0
676,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(2/3)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/3)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/3)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
679,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(2/3)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
680,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/3)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
681,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/3)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
682,0,0,0,0.000000," ","integrate(cos(d*x+c)**(4/3)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{\frac{4}{3}}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**(4/3)/sqrt(a + b*cos(c + d*x)), x)","F",0
683,0,0,0,0.000000," ","integrate(cos(d*x+c)**(2/3)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\cos^{\frac{2}{3}}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**(2/3)/sqrt(a + b*cos(c + d*x)), x)","F",0
684,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/3)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt[3]{\cos{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**(1/3)/sqrt(a + b*cos(c + d*x)), x)","F",0
685,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(1/3)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt[3]{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(1/3)), x)","F",0
686,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(2/3)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{2}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(2/3)), x)","F",0
687,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(4/3)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{4}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(4/3)), x)","F",0
688,0,0,0,0.000000," ","integrate(1/cos(d*x+c)**(5/3)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \cos^{\frac{5}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*cos(c + d*x)**(5/3)), x)","F",0
689,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)**(7/3)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**(1/2),x)","\int \left(A + B \cos{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sqrt(sec(c + d*x)), x)","F",0
694,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/sqrt(sec(c + d*x)), x)","F",0
695,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/sec(c + d*x)**(3/2), x)","F",0
696,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
698,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
700,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
701,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**(1/2),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*sqrt(sec(c + d*x)), x)","F",0
702,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2/sqrt(sec(c + d*x)), x)","F",0
703,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2/sec(c + d*x)**(3/2), x)","F",0
704,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
709,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**(1/2),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{3} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3*sqrt(sec(c + d*x)), x)","F",0
710,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3/sqrt(sec(c + d*x)), x)","F",0
711,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3/sec(c + d*x)**(3/2), x)","F",0
712,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+b*cos(d*x+c)),x)","\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**(3/2)/(a + b*cos(c + d*x)), x)","F",0
714,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+b*cos(d*x+c)),x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/(a + b*cos(c + d*x)), x)","F",0
715,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right) \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
716,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)**(3/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right) \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))*sec(c + d*x)**(3/2)), x)","F",0
717,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**2,x)","\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**(3/2)/(a + b*cos(c + d*x))**2, x)","F",0
720,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**2,x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**2, x)","F",0
721,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2/sec(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{2} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))**2*sqrt(sec(c + d*x))), x)","F",0
722,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2/sec(d*x+c)**(3/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))**2*sec(c + d*x)**(3/2)), x)","F",0
723,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**3,x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**3, x)","F",0
727,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3/sec(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{3} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))**3*sqrt(sec(c + d*x))), x)","F",0
728,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(7/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)*(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)*sec(d*x+c)**(1/2),x)","\int \sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\sec{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x)), x)","F",0
734,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))/sqrt(sec(c + d*x)), x)","F",0
735,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(3/2),x)","\int \frac{\sqrt{a + b \cos{\left(c + d x \right)}}}{\sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(c + d*x))/sec(c + d*x)**(3/2), x)","F",0
736,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
737,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
738,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
739,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
741,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(3/2)/sqrt(sec(c + d*x)), x)","F",0
742,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)*sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**(3/2)/sqrt(a + b*cos(c + d*x)), x)","F",0
753,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\sqrt{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/sqrt(a + b*cos(c + d*x)), x)","F",0
754,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(1/2)/sec(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*sqrt(sec(c + d*x))), x)","F",0
755,0,0,0,0.000000," ","integrate(1/sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(c + d x \right)}} \sec^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*cos(c + d*x))*sec(c + d*x)**(3/2)), x)","F",0
756,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,0,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\sec^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**(3/2)/(a + b*cos(c + d*x))**(3/2), x)","F",0
759,0,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(3/2),x)","\int \frac{\sqrt{\sec{\left(c + d x \right)}}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(sec(c + d*x))/(a + b*cos(c + d*x))**(3/2), x)","F",0
760,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\sec{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*cos(c + d*x))**(3/2)*sqrt(sec(c + d*x))), x)","F",0
761,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(3/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(5/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(3/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,-1,0,0,0.000000," ","integrate(sec(d*x+c)**(1/2)/(a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
768,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(5/2)/sec(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
770,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
771,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c))**2,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \cos^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*cos(c + d*x)**m, x)","F",0
772,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a+b*cos(d*x+c)),x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \cos^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*cos(c + d*x)**m, x)","F",0
773,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
774,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
775,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*sec(d*x+c)**m,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{3} \sec^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3*sec(c + d*x)**m, x)","F",0
776,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*sec(d*x+c)**m,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{2} \sec^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2*sec(c + d*x)**m, x)","F",0
777,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)**m,x)","\int \left(a + b \cos{\left(c + d x \right)}\right) \sec^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*cos(c + d*x))*sec(c + d*x)**m, x)","F",0
778,0,0,0,0.000000," ","integrate((1-cos(x))**(1/2)/(a-cos(x))**(1/2),x)","\int \frac{\sqrt{1 - \cos{\left(x \right)}}}{\sqrt{a - \cos{\left(x \right)}}}\, dx"," ",0,"Integral(sqrt(1 - cos(x))/sqrt(a - cos(x)), x)","F",0
779,0,0,0,0.000000," ","integrate(((1-cos(x))/(a-cos(x)))**(1/2),x)","\int \sqrt{\frac{1 - \cos{\left(x \right)}}{a - \cos{\left(x \right)}}}\, dx"," ",0,"Integral(sqrt((1 - cos(x))/(a - cos(x))), x)","F",0
780,1,87,0,0.276545," ","integrate((a+a*cos(d*x+c))*(-1/2*B+B*cos(d*x+c)),x)","\begin{cases} \frac{B a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B a x \cos^{2}{\left(c + d x \right)}}{2} - \frac{B a x}{2} + \frac{B a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{B a \sin{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} - \frac{B}{2}\right) \left(a \cos{\left(c \right)} + a\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a*x*sin(c + d*x)**2/2 + B*a*x*cos(c + d*x)**2/2 - B*a*x/2 + B*a*sin(c + d*x)*cos(c + d*x)/(2*d) + B*a*sin(c + d*x)/(2*d), Ne(d, 0)), (x*(B*cos(c) - B/2)*(a*cos(c) + a), True))","A",0
781,1,333,0,2.458865," ","integrate((a+a*cos(d*x+c))**4*(-4/5*B+B*cos(d*x+c)),x)","\begin{cases} \frac{6 B a^{4} x \sin^{4}{\left(c + d x \right)}}{5} + \frac{12 B a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5} - \frac{2 B a^{4} x \sin^{2}{\left(c + d x \right)}}{5} + \frac{6 B a^{4} x \cos^{4}{\left(c + d x \right)}}{5} - \frac{2 B a^{4} x \cos^{2}{\left(c + d x \right)}}{5} - \frac{4 B a^{4} x}{5} + \frac{8 B a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 B a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{6 B a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{5 d} + \frac{28 B a^{4} \sin^{3}{\left(c + d x \right)}}{15 d} + \frac{B a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{2 B a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} + \frac{14 B a^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} - \frac{2 B a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{5 d} - \frac{11 B a^{4} \sin{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(B \cos{\left(c \right)} - \frac{4 B}{5}\right) \left(a \cos{\left(c \right)} + a\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*B*a**4*x*sin(c + d*x)**4/5 + 12*B*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/5 - 2*B*a**4*x*sin(c + d*x)**2/5 + 6*B*a**4*x*cos(c + d*x)**4/5 - 2*B*a**4*x*cos(c + d*x)**2/5 - 4*B*a**4*x/5 + 8*B*a**4*sin(c + d*x)**5/(15*d) + 4*B*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 6*B*a**4*sin(c + d*x)**3*cos(c + d*x)/(5*d) + 28*B*a**4*sin(c + d*x)**3/(15*d) + B*a**4*sin(c + d*x)*cos(c + d*x)**4/d + 2*B*a**4*sin(c + d*x)*cos(c + d*x)**3/d + 14*B*a**4*sin(c + d*x)*cos(c + d*x)**2/(5*d) - 2*B*a**4*sin(c + d*x)*cos(c + d*x)/(5*d) - 11*B*a**4*sin(c + d*x)/(5*d), Ne(d, 0)), (x*(B*cos(c) - 4*B/5)*(a*cos(c) + a)**4, True))","A",0
782,1,114,0,4.991610," ","integrate((a+a*cos(d*x+c))**n*(-B*n/(1+n)+B*cos(d*x+c)),x)","\begin{cases} \frac{2 B \left(a - \frac{a \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1} + \frac{a}{\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1}\right)^{n} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{d n \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + d n + d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + a\right)^{n} \left(- \frac{B n}{n + 1} + B \cos{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*B*(a - a*tan(c/2 + d*x/2)**2/(tan(c/2 + d*x/2)**2 + 1) + a/(tan(c/2 + d*x/2)**2 + 1))**n*tan(c/2 + d*x/2)/(d*n*tan(c/2 + d*x/2)**2 + d*n + d*tan(c/2 + d*x/2)**2 + d), Ne(d, 0)), (x*(a*cos(c) + a)**n*(-B*n/(n + 1) + B*cos(c)), True))","A",0
783,1,80,0,2.374542," ","integrate((-3/2*B+B*cos(d*x+c))/(a+a*cos(d*x+c))**3,x)","\begin{cases} - \frac{B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d} - \frac{B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4 a^{3} d} - \frac{B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \left(B \cos{\left(c \right)} - \frac{3 B}{2}\right)}{\left(a \cos{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*tan(c/2 + d*x/2)**5/(8*a**3*d) - B*tan(c/2 + d*x/2)**3/(4*a**3*d) - B*tan(c/2 + d*x/2)/(8*a**3*d), Ne(d, 0)), (x*(B*cos(c) - 3*B/2)/(a*cos(c) + a)**3, True))","A",0
784,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(3/2)*(-3/5*B+B*cos(d*x+c)),x)","\frac{B \left(\int \left(- 3 a \sqrt{a \cos{\left(c + d x \right)} + a}\right)\, dx + \int 2 a \sqrt{a \cos{\left(c + d x \right)} + a} \cos{\left(c + d x \right)}\, dx + \int 5 a \sqrt{a \cos{\left(c + d x \right)} + a} \cos^{2}{\left(c + d x \right)}\, dx\right)}{5}"," ",0,"B*(Integral(-3*a*sqrt(a*cos(c + d*x) + a), x) + Integral(2*a*sqrt(a*cos(c + d*x) + a)*cos(c + d*x), x) + Integral(5*a*sqrt(a*cos(c + d*x) + a)*cos(c + d*x)**2, x))/5","F",0
785,0,0,0,0.000000," ","integrate((B+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/2),x)","B \left(\int \frac{\cos{\left(c + d x \right)}}{\sqrt{a \cos{\left(c + d x \right)} + a}}\, dx + \int \frac{1}{\sqrt{a \cos{\left(c + d x \right)} + a}}\, dx\right)"," ",0,"B*(Integral(cos(c + d*x)/sqrt(a*cos(c + d*x) + a), x) + Integral(1/sqrt(a*cos(c + d*x) + a), x))","F",0
786,-1,0,0,0.000000," ","integrate((-5/3*B+B*cos(d*x+c))/(a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
787,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(2/3)*(A+B*cos(d*x+c)),x)","\int \left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{2}{3}} \left(A + B \cos{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(2/3)*(A + B*cos(c + d*x)), x)","F",0
788,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c)),x)","\int \sqrt[3]{a \left(\cos{\left(c + d x \right)} + 1\right)} \left(A + B \cos{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((a*(cos(c + d*x) + 1))**(1/3)*(A + B*cos(c + d*x)), x)","F",0
789,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(1/3),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt[3]{a \left(\cos{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(a*(cos(c + d*x) + 1))**(1/3), x)","F",0
790,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))**(2/3),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\left(a \left(\cos{\left(c + d x \right)} + 1\right)\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(a*(cos(c + d*x) + 1))**(2/3), x)","F",0
791,1,235,0,32.916209," ","integrate((b*B/a+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\begin{cases} \text{NaN} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{x \left(B \cos{\left(c \right)} + \frac{B b}{a}\right)}{a + b \cos{\left(c \right)}} & \text{for}\: d = 0 \\\frac{B x}{b} & \text{for}\: a = b \\\frac{B \sin{\left(c + d x \right)}}{a d} & \text{for}\: b = 0 \\\frac{B x}{b} & \text{for}\: a = - b \\\frac{B x}{b} - \frac{B \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{B \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{b d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{B \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{B \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{a d \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (x*(B*cos(c) + B*b/a)/(a + b*cos(c)), Eq(d, 0)), (B*x/b, Eq(a, b)), (B*sin(c + d*x)/(a*d), Eq(b, 0)), (B*x/b, Eq(a, -b)), (B*x/b - B*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(b*d*sqrt(-a/(a - b) - b/(a - b))) + B*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(b*d*sqrt(-a/(a - b) - b/(a - b))) - B*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*d*sqrt(-a/(a - b) - b/(a - b))) + B*log(sqrt(-a/(a - b) - b/(a - b)) + tan(c/2 + d*x/2))/(a*d*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
792,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(b+a*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
793,1,56,0,2.424481," ","integrate((3+cos(d*x+c))/(2-cos(d*x+c)),x)","\begin{cases} - x + \frac{10 \sqrt{3} \left(\operatorname{atan}{\left(\sqrt{3} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3 d} & \text{for}\: d \neq 0 \\\frac{x \left(\cos{\left(c \right)} + 3\right)}{2 - \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x + 10*sqrt(3)*(atan(sqrt(3)*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(3*d), Ne(d, 0)), (x*(cos(c) + 3)/(2 - cos(c)), True))","A",0
794,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/2),x)","B \int \sqrt{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sqrt(a + b*cos(c + d*x)), x)","F",0
795,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(2/3)*(A+B*cos(d*x+c)),x)","\int \left(A + B \cos{\left(c + d x \right)}\right) \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**(2/3), x)","F",0
796,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c)),x)","\int \left(A + B \cos{\left(c + d x \right)}\right) \sqrt[3]{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*(a + b*cos(c + d*x))**(1/3), x)","F",0
797,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(1/3),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt[3]{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(a + b*cos(c + d*x))**(1/3), x)","F",0
798,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))**(2/3),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(a + b*cos(c + d*x))**(2/3), x)","F",0
799,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
800,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
801,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\int \sqrt{b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(b*cos(c + d*x))*(A + B*cos(c + d*x)), x)","F",0
802,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\int \sqrt{b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(b*cos(c + d*x))*(A + B*cos(c + d*x))*sec(c + d*x), x)","F",0
803,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\int \sqrt{b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(b*cos(c + d*x))*(A + B*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
804,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
805,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
807,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
810,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
811,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
812,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
813,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
815,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt{b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/sqrt(b*cos(c + d*x)), x)","F",0
824,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\sqrt{b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)/sqrt(b*cos(c + d*x)), x)","F",0
825,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\sqrt{b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)**2/sqrt(b*cos(c + d*x)), x)","F",0
826,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(b*cos(d*x+c))**(1/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\sqrt{b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)**3/sqrt(b*cos(c + d*x)), x)","F",0
827,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
828,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)/(b*cos(c + d*x))**(3/2), x)","F",0
833,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)**2/(b*cos(c + d*x))**(3/2), x)","F",0
834,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
839,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
840,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
843,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,1,99,0,40.282667," ","integrate(cos(d*x+c)**(1/2)*(b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c)),x)","\begin{cases} \frac{A \sqrt{b} \sin{\left(c + d x \right)}}{d} + \frac{B \sqrt{b} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{B \sqrt{b} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{B \sqrt{b} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \sqrt{b \cos{\left(c \right)}} \left(A + B \cos{\left(c \right)}\right) \sqrt{\cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*sqrt(b)*sin(c + d*x)/d + B*sqrt(b)*x*sin(c + d*x)**2/2 + B*sqrt(b)*x*cos(c + d*x)**2/2 + B*sqrt(b)*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*sqrt(b*cos(c))*(A + B*cos(c))*sqrt(cos(c)), True))","A",0
845,1,46,0,12.092740," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\begin{cases} A \sqrt{b} x + \frac{B \sqrt{b} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \sqrt{b \cos{\left(c \right)}} \left(A + B \cos{\left(c \right)}\right)}{\sqrt{\cos{\left(c \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*sqrt(b)*x + B*sqrt(b)*sin(c + d*x)/d, Ne(d, 0)), (x*sqrt(b*cos(c))*(A + B*cos(c))/sqrt(cos(c)), True))","A",0
846,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\int \frac{\sqrt{b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)}\right)}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(b*cos(c + d*x))*(A + B*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
847,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
863,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
864,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,1,46,0,12.675967," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/2),x)","\begin{cases} \frac{A x}{\sqrt{b}} + \frac{B \sin{\left(c + d x \right)}}{\sqrt{b} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \cos{\left(c \right)}\right) \sqrt{\cos{\left(c \right)}}}{\sqrt{b \cos{\left(c \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*x/sqrt(b) + B*sin(c + d*x)/(sqrt(b)*d), Ne(d, 0)), (x*(A + B*cos(c))*sqrt(cos(c))/sqrt(b*cos(c)), True))","A",0
869,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt{b \cos{\left(c + d x \right)}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(sqrt(b*cos(c + d*x))*sqrt(cos(c + d*x))), x)","F",0
870,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(b*cos(d*x+c))**(1/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\sqrt{b \cos{\left(c + d x \right)}} \cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(sqrt(b*cos(c + d*x))*cos(c + d*x)**(3/2)), x)","F",0
871,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(7/2)/(b*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,0,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(3/2),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sqrt{\cos{\left(c + d x \right)}}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sqrt(cos(c + d*x))/(b*cos(c + d*x))**(3/2), x)","F",0
877,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(b*cos(d*x+c))**(3/2),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/((b*cos(c + d*x))**(3/2)*sqrt(cos(c + d*x))), x)","F",0
878,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(5/2)/(b*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(9/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(1/2)/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)**(3/2)/(b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\int \sqrt[3]{b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((b*cos(c + d*x))**(1/3)*(A + B*cos(c + d*x))*sec(c + d*x), x)","F",0
891,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(b*cos(d*x+c))**(4/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))**(4/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(4/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(4/3)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
899,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))**(2/3),x)","\int \frac{A + B \cos{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))/(b*cos(c + d*x))**(2/3), x)","F",0
902,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))**(2/3),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)/(b*cos(c + d*x))**(2/3), x)","F",0
903,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(b*cos(d*x+c))**(2/3),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)**2/(b*cos(c + d*x))**(2/3), x)","F",0
904,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(b*cos(d*x+c))**(2/3),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*sec(c + d*x)**3/(b*cos(c + d*x))**(2/3), x)","F",0
905,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**2/(b*cos(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)**3/(b*cos(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(b*cos(d*x+c))**n*(A+B*cos(d*x+c)),x)","\int \left(b \cos{\left(c + d x \right)}\right)^{n} \left(A + B \cos{\left(c + d x \right)}\right) \cos^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((b*cos(c + d*x))**n*(A + B*cos(c + d*x))*cos(c + d*x)**m, x)","F",0
912,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(b*cos(d*x+c))**n*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
913,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))**n*(A+B*cos(d*x+c)),x)","\int \left(b \cos{\left(c + d x \right)}\right)^{n} \left(A + B \cos{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((b*cos(c + d*x))**n*(A + B*cos(c + d*x))*cos(c + d*x), x)","F",0
914,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c)),x)","\int \left(b \cos{\left(c + d x \right)}\right)^{n} \left(A + B \cos{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((b*cos(c + d*x))**n*(A + B*cos(c + d*x)), x)","F",0
915,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))*sec(d*x+c),x)","\int \left(b \cos{\left(c + d x \right)}\right)^{n} \left(A + B \cos{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((b*cos(c + d*x))**n*(A + B*cos(c + d*x))*sec(c + d*x), x)","F",0
916,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))*sec(d*x+c)**2,x)","\int \left(b \cos{\left(c + d x \right)}\right)^{n} \left(A + B \cos{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((b*cos(c + d*x))**n*(A + B*cos(c + d*x))*sec(c + d*x)**2, x)","F",0
917,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))*sec(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
918,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))*sec(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(5/2)*(b*cos(d*x+c))**n*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,-1,0,0,0.000000," ","integrate(cos(d*x+c)**(3/2)*(b*cos(d*x+c))**n*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
921,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))*cos(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
922,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))/cos(d*x+c)**(1/2),x)","\int \frac{\left(b \cos{\left(c + d x \right)}\right)^{n} \left(A + B \cos{\left(c + d x \right)}\right)}{\sqrt{\cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((b*cos(c + d*x))**n*(A + B*cos(c + d*x))/sqrt(cos(c + d*x)), x)","F",0
923,0,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))/cos(d*x+c)**(3/2),x)","\int \frac{\left(b \cos{\left(c + d x \right)}\right)^{n} \left(A + B \cos{\left(c + d x \right)}\right)}{\cos^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((b*cos(c + d*x))**n*(A + B*cos(c + d*x))/cos(c + d*x)**(3/2), x)","F",0
924,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))/cos(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
925,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))/cos(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate((b*cos(d*x+c))**n*(A+B*cos(d*x+c))/cos(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(b*cos(d*x+c))**(4/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
928,-1,0,0,0.000000," ","integrate(cos(d*x+c)**m*(b*cos(d*x+c))**(2/3)*(A+B*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
929,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(b*cos(d*x+c))**(1/3)*(A+B*cos(d*x+c)),x)","\int \sqrt[3]{b \cos{\left(c + d x \right)}} \left(A + B \cos{\left(c + d x \right)}\right) \cos^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((b*cos(c + d*x))**(1/3)*(A + B*cos(c + d*x))*cos(c + d*x)**m, x)","F",0
930,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(1/3),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \cos^{m}{\left(c + d x \right)}}{\sqrt[3]{b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*cos(c + d*x)**m/(b*cos(c + d*x))**(1/3), x)","F",0
931,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(2/3),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \cos^{m}{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*cos(c + d*x)**m/(b*cos(c + d*x))**(2/3), x)","F",0
932,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(A+B*cos(d*x+c))/(b*cos(d*x+c))**(4/3),x)","\int \frac{\left(A + B \cos{\left(c + d x \right)}\right) \cos^{m}{\left(c + d x \right)}}{\left(b \cos{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((A + B*cos(c + d*x))*cos(c + d*x)**m/(b*cos(c + d*x))**(4/3), x)","F",0
