1,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3,0,0,0,0.000000," ","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
4,0,0,0,0.000000," ","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
5,0,0,0,0.000000," ","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
6,0,0,0,0.000000," ","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
7,0,0,0,0.000000," ","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
8,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(4/3),x)","\int \left(a \cos{\left(c + d x \right)} + a\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(4/3), x)","F",0
9,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(2/3),x)","\int \left(a \cos{\left(c + d x \right)} + a\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(2/3), x)","F",0
10,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**(1/3),x)","\int \sqrt[3]{a \cos{\left(c + d x \right)} + a}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(1/3), x)","F",0
11,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{a \cos{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(-1/3), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(2/3),x)","\int \frac{1}{\left(a \cos{\left(c + d x \right)} + a\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(-2/3), x)","F",0
13,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))**(4/3),x)","\int \frac{1}{\left(a \cos{\left(c + d x \right)} + a\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**(-4/3), x)","F",0
14,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))**n,x)","\int \left(a \cos{\left(c + d x \right)} + a\right)^{n}\, dx"," ",0,"Integral((a*cos(c + d*x) + a)**n, x)","F",0
15,0,0,0,0.000000," ","integrate((a-a*cos(d*x+c))**n,x)","\int \left(- a \cos{\left(c + d x \right)} + a\right)^{n}\, dx"," ",0,"Integral((-a*cos(c + d*x) + a)**n, x)","F",0
16,0,0,0,0.000000," ","integrate((2+2*cos(d*x+c))**n,x)","2^{n} \int \left(\cos{\left(c + d x \right)} + 1\right)^{n}\, dx"," ",0,"2**n*Integral((cos(c + d*x) + 1)**n, x)","F",0
17,0,0,0,0.000000," ","integrate((2-2*cos(d*x+c))**n,x)","\int \left(2 - 2 \cos{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((2 - 2*cos(c + d*x))**n, x)","F",0
18,1,41,0,0.582987," ","integrate(1/(5+3*cos(d*x+c)),x)","\begin{cases} \frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{2 d} & \text{for}\: d \neq 0 \\\frac{x}{3 \cos{\left(c \right)} + 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(3*cos(c) + 5), True))","A",0
19,1,187,0,1.559579," ","integrate(1/(5+3*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(5 + 3 \cosh{\left(2 \operatorname{atanh}{\left(2 \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(2 \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(2 \right)} \\\frac{x}{\left(3 \cos{\left(c \right)} + 5\right)^{2}} & \text{for}\: d = 0 \\\frac{5 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 128 d} + \frac{20 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{32 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 128 d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 128 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 + 3*cosh(2*atanh(2)))**2, Eq(c, -d*x - 2*I*atanh(2)) | Eq(c, -d*x + 2*I*atanh(2))), (x/(3*cos(c) + 5)**2, Eq(d, 0)), (5*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(32*d*tan(c/2 + d*x/2)**2 + 128*d) + 20*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(32*d*tan(c/2 + d*x/2)**2 + 128*d) - 6*tan(c/2 + d*x/2)/(32*d*tan(c/2 + d*x/2)**2 + 128*d), True))","A",0
20,1,359,0,2.990933," ","integrate(1/(5+3*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(5 + 3 \cosh{\left(2 \operatorname{atanh}{\left(2 \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(2 \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(2 \right)} \\\frac{x}{\left(3 \cos{\left(c \right)} + 5\right)^{3}} & \text{for}\: d = 0 \\\frac{59 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{472 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{944 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} - \frac{138 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} - \frac{408 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 + 3*cosh(2*atanh(2)))**3, Eq(c, -d*x - 2*I*atanh(2)) | Eq(c, -d*x + 2*I*atanh(2))), (x/(3*cos(c) + 5)**3, Eq(d, 0)), (59*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) + 472*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) + 944*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) - 138*tan(c/2 + d*x/2)**3/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) - 408*tan(c/2 + d*x/2)/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d), True))","A",0
21,1,592,0,6.290984," ","integrate(1/(5+3*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(5 + 3 \cosh{\left(2 \operatorname{atanh}{\left(2 \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(2 \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(2 \right)} \\\frac{x}{\left(3 \cos{\left(c \right)} + 5\right)^{4}} & \text{for}\: d = 0 \\\frac{385 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} + \frac{4620 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} + \frac{18480 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} + \frac{24640 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} - \frac{1278 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} - \frac{7488 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} - \frac{11808 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 + 3*cosh(2*atanh(2)))**4, Eq(c, -d*x - 2*I*atanh(2)) | Eq(c, -d*x + 2*I*atanh(2))), (x/(3*cos(c) + 5)**4, Eq(d, 0)), (385*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) + 4620*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) + 18480*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) + 24640*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) - 1278*tan(c/2 + d*x/2)**5/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) - 7488*tan(c/2 + d*x/2)**3/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) - 11808*tan(c/2 + d*x/2)/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d), True))","A",0
22,1,41,0,0.597160," ","integrate(1/(5-3*cos(d*x+c)),x)","\begin{cases} \frac{\operatorname{atan}{\left(2 \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}{2 d} & \text{for}\: d \neq 0 \\\frac{x}{5 - 3 \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(5 - 3*cos(c)), True))","A",0
23,1,192,0,1.367567," ","integrate(1/(5-3*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(5 - 3 \cosh{\left(2 \operatorname{atanh}{\left(\frac{1}{2} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(5 - 3 \cos{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{20 \left(\operatorname{atan}{\left(2 \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) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{128 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 d} + \frac{5 \left(\operatorname{atan}{\left(2 \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)}{128 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{128 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*cosh(2*atanh(1/2)))**2, Eq(c, -d*x - 2*I*atanh(1/2)) | Eq(c, -d*x + 2*I*atanh(1/2))), (x/(5 - 3*cos(c))**2, Eq(d, 0)), (20*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(128*d*tan(c/2 + d*x/2)**2 + 32*d) + 5*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(128*d*tan(c/2 + d*x/2)**2 + 32*d) + 6*tan(c/2 + d*x/2)/(128*d*tan(c/2 + d*x/2)**2 + 32*d), True))","A",0
24,1,364,0,2.804249," ","integrate(1/(5-3*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(5 - 3 \cosh{\left(2 \operatorname{atanh}{\left(\frac{1}{2} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(5 - 3 \cos{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\\frac{944 \left(\operatorname{atan}{\left(2 \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) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} + \frac{472 \left(\operatorname{atan}{\left(2 \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) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} + \frac{59 \left(\operatorname{atan}{\left(2 \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)}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} + \frac{408 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} + \frac{138 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*cosh(2*atanh(1/2)))**3, Eq(c, -d*x - 2*I*atanh(1/2)) | Eq(c, -d*x + 2*I*atanh(1/2))), (x/(5 - 3*cos(c))**3, Eq(d, 0)), (944*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) + 472*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) + 59*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) + 408*tan(c/2 + d*x/2)**3/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) + 138*tan(c/2 + d*x/2)/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d), True))","A",0
25,1,597,0,6.064051," ","integrate(1/(5-3*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(5 - 3 \cosh{\left(2 \operatorname{atanh}{\left(\frac{1}{2} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(5 - 3 \cos{\left(c \right)}\right)^{4}} & \text{for}\: d = 0 \\\frac{24640 \left(\operatorname{atan}{\left(2 \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) \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{18480 \left(\operatorname{atan}{\left(2 \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) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{4620 \left(\operatorname{atan}{\left(2 \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) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{385 \left(\operatorname{atan}{\left(2 \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)}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{11808 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{7488 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{1278 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*cosh(2*atanh(1/2)))**4, Eq(c, -d*x - 2*I*atanh(1/2)) | Eq(c, -d*x + 2*I*atanh(1/2))), (x/(5 - 3*cos(c))**4, Eq(d, 0)), (24640*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 18480*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 4620*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 385*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 11808*tan(c/2 + d*x/2)**5/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 7488*tan(c/2 + d*x/2)**3/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 1278*tan(c/2 + d*x/2)/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d), True))","A",0
26,1,42,0,0.589686," ","integrate(1/(-5+3*cos(d*x+c)),x)","\begin{cases} - \frac{\operatorname{atan}{\left(2 \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}{2 d} & \text{for}\: d \neq 0 \\\frac{x}{3 \cos{\left(c \right)} - 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(3*cos(c) - 5), True))","A",0
27,1,192,0,1.371937," ","integrate(1/(-5+3*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-5 + 3 \cosh{\left(2 \operatorname{atanh}{\left(\frac{1}{2} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(3 \cos{\left(c \right)} - 5\right)^{2}} & \text{for}\: d = 0 \\\frac{20 \left(\operatorname{atan}{\left(2 \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) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{128 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 d} + \frac{5 \left(\operatorname{atan}{\left(2 \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)}{128 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{128 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*cosh(2*atanh(1/2)))**2, Eq(c, -d*x - 2*I*atanh(1/2)) | Eq(c, -d*x + 2*I*atanh(1/2))), (x/(3*cos(c) - 5)**2, Eq(d, 0)), (20*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(128*d*tan(c/2 + d*x/2)**2 + 32*d) + 5*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(128*d*tan(c/2 + d*x/2)**2 + 32*d) + 6*tan(c/2 + d*x/2)/(128*d*tan(c/2 + d*x/2)**2 + 32*d), True))","A",0
28,1,366,0,2.801357," ","integrate(1/(-5+3*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-5 + 3 \cosh{\left(2 \operatorname{atanh}{\left(\frac{1}{2} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(3 \cos{\left(c \right)} - 5\right)^{3}} & \text{for}\: d = 0 \\- \frac{944 \left(\operatorname{atan}{\left(2 \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) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} - \frac{472 \left(\operatorname{atan}{\left(2 \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) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} - \frac{59 \left(\operatorname{atan}{\left(2 \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)}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} - \frac{408 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} - \frac{138 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1024 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*cosh(2*atanh(1/2)))**3, Eq(c, -d*x - 2*I*atanh(1/2)) | Eq(c, -d*x + 2*I*atanh(1/2))), (x/(3*cos(c) - 5)**3, Eq(d, 0)), (-944*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) - 472*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) - 59*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) - 408*tan(c/2 + d*x/2)**3/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d) - 138*tan(c/2 + d*x/2)/(16384*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 1024*d), True))","A",0
29,1,597,0,6.060066," ","integrate(1/(-5+3*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-5 + 3 \cosh{\left(2 \operatorname{atanh}{\left(\frac{1}{2} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(3 \cos{\left(c \right)} - 5\right)^{4}} & \text{for}\: d = 0 \\\frac{24640 \left(\operatorname{atan}{\left(2 \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) \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{18480 \left(\operatorname{atan}{\left(2 \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) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{4620 \left(\operatorname{atan}{\left(2 \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) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{385 \left(\operatorname{atan}{\left(2 \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)}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{11808 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{7488 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{1278 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1048576 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*cosh(2*atanh(1/2)))**4, Eq(c, -d*x - 2*I*atanh(1/2)) | Eq(c, -d*x + 2*I*atanh(1/2))), (x/(3*cos(c) - 5)**4, Eq(d, 0)), (24640*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 18480*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 4620*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 385*(atan(2*tan(c/2 + d*x/2)) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 11808*tan(c/2 + d*x/2)**5/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 7488*tan(c/2 + d*x/2)**3/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d) + 1278*tan(c/2 + d*x/2)/(1048576*d*tan(c/2 + d*x/2)**6 + 786432*d*tan(c/2 + d*x/2)**4 + 196608*d*tan(c/2 + d*x/2)**2 + 16384*d), True))","A",0
30,1,44,0,0.591234," ","integrate(1/(-5-3*cos(d*x+c)),x)","\begin{cases} - \frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{2 d} & \text{for}\: d \neq 0 \\\frac{x}{- 3 \cos{\left(c \right)} - 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(-3*cos(c) - 5), True))","A",0
31,1,190,0,1.570742," ","integrate(1/(-5-3*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-5 - 3 \cosh{\left(2 \operatorname{atanh}{\left(2 \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(2 \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(2 \right)} \\\frac{x}{\left(- 3 \cos{\left(c \right)} - 5\right)^{2}} & \text{for}\: d = 0 \\\frac{5 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 128 d} + \frac{20 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{32 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 128 d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 128 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 - 3*cosh(2*atanh(2)))**2, Eq(c, -d*x - 2*I*atanh(2)) | Eq(c, -d*x + 2*I*atanh(2))), (x/(-3*cos(c) - 5)**2, Eq(d, 0)), (5*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(32*d*tan(c/2 + d*x/2)**2 + 128*d) + 20*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(32*d*tan(c/2 + d*x/2)**2 + 128*d) - 6*tan(c/2 + d*x/2)/(32*d*tan(c/2 + d*x/2)**2 + 128*d), True))","A",0
32,1,362,0,3.050979," ","integrate(1/(-5-3*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-5 - 3 \cosh{\left(2 \operatorname{atanh}{\left(2 \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(2 \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(2 \right)} \\\frac{x}{\left(- 3 \cos{\left(c \right)} - 5\right)^{3}} & \text{for}\: d = 0 \\- \frac{59 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} - \frac{472 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} - \frac{944 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{138 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} + \frac{408 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1024 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8192 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16384 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 - 3*cosh(2*atanh(2)))**3, Eq(c, -d*x - 2*I*atanh(2)) | Eq(c, -d*x + 2*I*atanh(2))), (x/(-3*cos(c) - 5)**3, Eq(d, 0)), (-59*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) - 472*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) - 944*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) + 138*tan(c/2 + d*x/2)**3/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d) + 408*tan(c/2 + d*x/2)/(1024*d*tan(c/2 + d*x/2)**4 + 8192*d*tan(c/2 + d*x/2)**2 + 16384*d), True))","A",0
33,1,595,0,6.286650," ","integrate(1/(-5-3*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-5 - 3 \cosh{\left(2 \operatorname{atanh}{\left(2 \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 i \operatorname{atanh}{\left(2 \right)} \vee c = - d x + 2 i \operatorname{atanh}{\left(2 \right)} \\\frac{x}{\left(- 3 \cos{\left(c \right)} - 5\right)^{4}} & \text{for}\: d = 0 \\\frac{385 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} + \frac{4620 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} + \frac{18480 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} + \frac{24640 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} - \frac{1278 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} - \frac{7488 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} - \frac{11808 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{16384 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 196608 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 786432 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1048576 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 - 3*cosh(2*atanh(2)))**4, Eq(c, -d*x - 2*I*atanh(2)) | Eq(c, -d*x + 2*I*atanh(2))), (x/(-3*cos(c) - 5)**4, Eq(d, 0)), (385*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) + 4620*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) + 18480*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) + 24640*(atan(tan(c/2 + d*x/2)/2) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) - 1278*tan(c/2 + d*x/2)**5/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) - 7488*tan(c/2 + d*x/2)**3/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d) - 11808*tan(c/2 + d*x/2)/(16384*d*tan(c/2 + d*x/2)**6 + 196608*d*tan(c/2 + d*x/2)**4 + 786432*d*tan(c/2 + d*x/2)**2 + 1048576*d), True))","A",0
34,1,41,0,0.545180," ","integrate(1/(3+5*cos(d*x+c)),x)","\begin{cases} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{4 d} + \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{5 \cos{\left(c \right)} + 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(c/2 + d*x/2) - 2)/(4*d) + log(tan(c/2 + d*x/2) + 2)/(4*d), Ne(d, 0)), (x/(5*cos(c) + 3), True))","A",0
35,1,228,0,1.233501," ","integrate(1/(3+5*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(5 \cos{\left(2 \operatorname{atan}{\left(2 \right)} \right)} + 3\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(2 \right)} \vee c = - d x + 2 \operatorname{atan}{\left(2 \right)} \\\frac{x}{\left(5 \cos{\left(c \right)} + 3\right)^{2}} & \text{for}\: d = 0 \\\frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} - \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} - \frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} + \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} - \frac{20 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5*cos(2*atan(2)) + 3)**2, Eq(c, -d*x - 2*atan(2)) | Eq(c, -d*x + 2*atan(2))), (x/(5*cos(c) + 3)**2, Eq(d, 0)), (3*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**2/(64*d*tan(c/2 + d*x/2)**2 - 256*d) - 12*log(tan(c/2 + d*x/2) - 2)/(64*d*tan(c/2 + d*x/2)**2 - 256*d) - 3*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**2/(64*d*tan(c/2 + d*x/2)**2 - 256*d) + 12*log(tan(c/2 + d*x/2) + 2)/(64*d*tan(c/2 + d*x/2)**2 - 256*d) - 20*tan(c/2 + d*x/2)/(64*d*tan(c/2 + d*x/2)**2 - 256*d), True))","A",0
36,1,474,0,2.464513," ","integrate(1/(3+5*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(5 \cos{\left(2 \operatorname{atan}{\left(2 \right)} \right)} + 3\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(2 \right)} \vee c = - d x + 2 \operatorname{atan}{\left(2 \right)} \\\frac{x}{\left(5 \cos{\left(c \right)} + 3\right)^{3}} & \text{for}\: d = 0 \\- \frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} + \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} - \frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} + \frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} - \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} + \frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} + \frac{340 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} - \frac{560 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5*cos(2*atan(2)) + 3)**3, Eq(c, -d*x - 2*atan(2)) | Eq(c, -d*x + 2*atan(2))), (x/(5*cos(c) + 3)**3, Eq(d, 0)), (-43*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**4/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) + 344*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**2/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) - 688*log(tan(c/2 + d*x/2) - 2)/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) + 43*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**4/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) - 344*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**2/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) + 688*log(tan(c/2 + d*x/2) + 2)/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) + 340*tan(c/2 + d*x/2)**3/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) - 560*tan(c/2 + d*x/2)/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d), True))","A",0
37,1,813,0,5.239172," ","integrate(1/(3+5*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(5 \cos{\left(2 \operatorname{atan}{\left(2 \right)} \right)} + 3\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(2 \right)} \vee c = - d x + 2 \operatorname{atan}{\left(2 \right)} \\\frac{x}{\left(5 \cos{\left(c \right)} + 3\right)^{4}} & \text{for}\: d = 0 \\\frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{8940 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{33920 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{56640 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5*cos(2*atan(2)) + 3)**4, Eq(c, -d*x - 2*atan(2)) | Eq(c, -d*x + 2*atan(2))), (x/(5*cos(c) + 3)**4, Eq(d, 0)), (837*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**6/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 10044*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**4/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 40176*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**2/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 53568*log(tan(c/2 + d*x/2) - 2)/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 837*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**6/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 10044*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**4/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 40176*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**2/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 53568*log(tan(c/2 + d*x/2) + 2)/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 8940*tan(c/2 + d*x/2)**5/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 33920*tan(c/2 + d*x/2)**3/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 56640*tan(c/2 + d*x/2)/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d), True))","A",0
38,1,44,0,0.569579," ","integrate(1/(3-5*cos(d*x+c)),x)","\begin{cases} \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{4 d} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{3 - 5 \cos{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(c/2 + d*x/2) - 1/2)/(4*d) - log(tan(c/2 + d*x/2) + 1/2)/(4*d), Ne(d, 0)), (x/(3 - 5*cos(c)), True))","A",0
39,1,240,0,1.250956," ","integrate(1/(3-5*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(3 - 5 \cos{\left(2 \operatorname{atan}{\left(\frac{1}{2} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(3 - 5 \cos{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} + \frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} + \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} - \frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} - \frac{20 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*cos(2*atan(1/2)))**2, Eq(c, -d*x - 2*atan(1/2)) | Eq(c, -d*x + 2*atan(1/2))), (x/(3 - 5*cos(c))**2, Eq(d, 0)), (-12*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**2/(256*d*tan(c/2 + d*x/2)**2 - 64*d) + 3*log(tan(c/2 + d*x/2) - 1/2)/(256*d*tan(c/2 + d*x/2)**2 - 64*d) + 12*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**2/(256*d*tan(c/2 + d*x/2)**2 - 64*d) - 3*log(tan(c/2 + d*x/2) + 1/2)/(256*d*tan(c/2 + d*x/2)**2 - 64*d) - 20*tan(c/2 + d*x/2)/(256*d*tan(c/2 + d*x/2)**2 - 64*d), True))","A",0
40,1,490,0,2.475279," ","integrate(1/(3-5*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(3 - 5 \cos{\left(2 \operatorname{atan}{\left(\frac{1}{2} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(3 - 5 \cos{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\\frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} - \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} + \frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} - \frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} + \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} - \frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} + \frac{560 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} - \frac{340 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*cos(2*atan(1/2)))**3, Eq(c, -d*x - 2*atan(1/2)) | Eq(c, -d*x + 2*atan(1/2))), (x/(3 - 5*cos(c))**3, Eq(d, 0)), (688*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**4/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) - 344*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**2/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) + 43*log(tan(c/2 + d*x/2) - 1/2)/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) - 688*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**4/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) + 344*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**2/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) - 43*log(tan(c/2 + d*x/2) + 1/2)/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) + 560*tan(c/2 + d*x/2)**3/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) - 340*tan(c/2 + d*x/2)/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d), True))","A",0
41,1,831,0,5.304441," ","integrate(1/(3-5*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(3 - 5 \cos{\left(2 \operatorname{atan}{\left(\frac{1}{2} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(3 - 5 \cos{\left(c \right)}\right)^{4}} & \text{for}\: d = 0 \\- \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{56640 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{33920 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{8940 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*cos(2*atan(1/2)))**4, Eq(c, -d*x - 2*atan(1/2)) | Eq(c, -d*x + 2*atan(1/2))), (x/(3 - 5*cos(c))**4, Eq(d, 0)), (-53568*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**6/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 40176*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**4/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 10044*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**2/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 837*log(tan(c/2 + d*x/2) - 1/2)/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 53568*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**6/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 40176*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**4/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 10044*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**2/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 837*log(tan(c/2 + d*x/2) + 1/2)/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 56640*tan(c/2 + d*x/2)**5/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 33920*tan(c/2 + d*x/2)**3/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 8940*tan(c/2 + d*x/2)/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d), True))","A",0
42,1,44,0,0.556797," ","integrate(1/(-3+5*cos(d*x+c)),x)","\begin{cases} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{4 d} + \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{5 \cos{\left(c \right)} - 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(c/2 + d*x/2) - 1/2)/(4*d) + log(tan(c/2 + d*x/2) + 1/2)/(4*d), Ne(d, 0)), (x/(5*cos(c) - 3), True))","A",0
43,1,240,0,1.242954," ","integrate(1/(-3+5*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-3 + 5 \cos{\left(2 \operatorname{atan}{\left(\frac{1}{2} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(5 \cos{\left(c \right)} - 3\right)^{2}} & \text{for}\: d = 0 \\- \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} + \frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} + \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} - \frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} - \frac{20 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 64 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*cos(2*atan(1/2)))**2, Eq(c, -d*x - 2*atan(1/2)) | Eq(c, -d*x + 2*atan(1/2))), (x/(5*cos(c) - 3)**2, Eq(d, 0)), (-12*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**2/(256*d*tan(c/2 + d*x/2)**2 - 64*d) + 3*log(tan(c/2 + d*x/2) - 1/2)/(256*d*tan(c/2 + d*x/2)**2 - 64*d) + 12*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**2/(256*d*tan(c/2 + d*x/2)**2 - 64*d) - 3*log(tan(c/2 + d*x/2) + 1/2)/(256*d*tan(c/2 + d*x/2)**2 - 64*d) - 20*tan(c/2 + d*x/2)/(256*d*tan(c/2 + d*x/2)**2 - 64*d), True))","A",0
44,1,490,0,2.476131," ","integrate(1/(-3+5*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-3 + 5 \cos{\left(2 \operatorname{atan}{\left(\frac{1}{2} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(5 \cos{\left(c \right)} - 3\right)^{3}} & \text{for}\: d = 0 \\- \frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} + \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} - \frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} + \frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} - \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} + \frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} - \frac{560 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} + \frac{340 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{32768 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2048 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*cos(2*atan(1/2)))**3, Eq(c, -d*x - 2*atan(1/2)) | Eq(c, -d*x + 2*atan(1/2))), (x/(5*cos(c) - 3)**3, Eq(d, 0)), (-688*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**4/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) + 344*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**2/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) - 43*log(tan(c/2 + d*x/2) - 1/2)/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) + 688*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**4/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) - 344*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**2/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) + 43*log(tan(c/2 + d*x/2) + 1/2)/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) - 560*tan(c/2 + d*x/2)**3/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d) + 340*tan(c/2 + d*x/2)/(32768*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 2048*d), True))","A",0
45,1,831,0,5.276791," ","integrate(1/(-3+5*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-3 + 5 \cos{\left(2 \operatorname{atan}{\left(\frac{1}{2} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \vee c = - d x + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} \\\frac{x}{\left(5 \cos{\left(c \right)} - 3\right)^{4}} & \text{for}\: d = 0 \\- \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{56640 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} + \frac{33920 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} - \frac{8940 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6291456 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4718592 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1179648 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 98304 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*cos(2*atan(1/2)))**4, Eq(c, -d*x - 2*atan(1/2)) | Eq(c, -d*x + 2*atan(1/2))), (x/(5*cos(c) - 3)**4, Eq(d, 0)), (-53568*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**6/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 40176*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**4/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 10044*log(tan(c/2 + d*x/2) - 1/2)*tan(c/2 + d*x/2)**2/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 837*log(tan(c/2 + d*x/2) - 1/2)/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 53568*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**6/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 40176*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**4/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 10044*log(tan(c/2 + d*x/2) + 1/2)*tan(c/2 + d*x/2)**2/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 837*log(tan(c/2 + d*x/2) + 1/2)/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 56640*tan(c/2 + d*x/2)**5/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) + 33920*tan(c/2 + d*x/2)**3/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d) - 8940*tan(c/2 + d*x/2)/(6291456*d*tan(c/2 + d*x/2)**6 - 4718592*d*tan(c/2 + d*x/2)**4 + 1179648*d*tan(c/2 + d*x/2)**2 - 98304*d), True))","A",0
46,1,42,0,0.559072," ","integrate(1/(-3-5*cos(d*x+c)),x)","\begin{cases} \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{4 d} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{- 5 \cos{\left(c \right)} - 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(c/2 + d*x/2) - 2)/(4*d) - log(tan(c/2 + d*x/2) + 2)/(4*d), Ne(d, 0)), (x/(-5*cos(c) - 3), True))","A",0
47,1,231,0,1.232026," ","integrate(1/(-3-5*cos(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-3 - 5 \cos{\left(2 \operatorname{atan}{\left(2 \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(2 \right)} \vee c = - d x + 2 \operatorname{atan}{\left(2 \right)} \\\frac{x}{\left(- 5 \cos{\left(c \right)} - 3\right)^{2}} & \text{for}\: d = 0 \\\frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} - \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} - \frac{3 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} + \frac{12 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} - \frac{20 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{64 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 256 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 - 5*cos(2*atan(2)))**2, Eq(c, -d*x - 2*atan(2)) | Eq(c, -d*x + 2*atan(2))), (x/(-5*cos(c) - 3)**2, Eq(d, 0)), (3*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**2/(64*d*tan(c/2 + d*x/2)**2 - 256*d) - 12*log(tan(c/2 + d*x/2) - 2)/(64*d*tan(c/2 + d*x/2)**2 - 256*d) - 3*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**2/(64*d*tan(c/2 + d*x/2)**2 - 256*d) + 12*log(tan(c/2 + d*x/2) + 2)/(64*d*tan(c/2 + d*x/2)**2 - 256*d) - 20*tan(c/2 + d*x/2)/(64*d*tan(c/2 + d*x/2)**2 - 256*d), True))","A",0
48,1,478,0,2.479822," ","integrate(1/(-3-5*cos(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-3 - 5 \cos{\left(2 \operatorname{atan}{\left(2 \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(2 \right)} \vee c = - d x + 2 \operatorname{atan}{\left(2 \right)} \\\frac{x}{\left(- 5 \cos{\left(c \right)} - 3\right)^{3}} & \text{for}\: d = 0 \\\frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} - \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} + \frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} - \frac{43 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} + \frac{344 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} - \frac{688 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} - \frac{340 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} + \frac{560 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16384 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32768 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 - 5*cos(2*atan(2)))**3, Eq(c, -d*x - 2*atan(2)) | Eq(c, -d*x + 2*atan(2))), (x/(-5*cos(c) - 3)**3, Eq(d, 0)), (43*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**4/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) - 344*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**2/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) + 688*log(tan(c/2 + d*x/2) - 2)/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) - 43*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**4/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) + 344*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**2/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) - 688*log(tan(c/2 + d*x/2) + 2)/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) - 340*tan(c/2 + d*x/2)**3/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d) + 560*tan(c/2 + d*x/2)/(2048*d*tan(c/2 + d*x/2)**4 - 16384*d*tan(c/2 + d*x/2)**2 + 32768*d), True))","A",0
49,1,816,0,5.250114," ","integrate(1/(-3-5*cos(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-3 - 5 \cos{\left(2 \operatorname{atan}{\left(2 \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(2 \right)} \vee c = - d x + 2 \operatorname{atan}{\left(2 \right)} \\\frac{x}{\left(- 5 \cos{\left(c \right)} - 3\right)^{4}} & \text{for}\: d = 0 \\\frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{837 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{10044 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{40176 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{53568 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{8940 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} + \frac{33920 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} - \frac{56640 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{98304 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1179648 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4718592 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6291456 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 - 5*cos(2*atan(2)))**4, Eq(c, -d*x - 2*atan(2)) | Eq(c, -d*x + 2*atan(2))), (x/(-5*cos(c) - 3)**4, Eq(d, 0)), (837*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**6/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 10044*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**4/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 40176*log(tan(c/2 + d*x/2) - 2)*tan(c/2 + d*x/2)**2/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 53568*log(tan(c/2 + d*x/2) - 2)/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 837*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**6/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 10044*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**4/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 40176*log(tan(c/2 + d*x/2) + 2)*tan(c/2 + d*x/2)**2/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 53568*log(tan(c/2 + d*x/2) + 2)/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 8940*tan(c/2 + d*x/2)**5/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) + 33920*tan(c/2 + d*x/2)**3/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d) - 56640*tan(c/2 + d*x/2)/(98304*d*tan(c/2 + d*x/2)**6 - 1179648*d*tan(c/2 + d*x/2)**4 + 4718592*d*tan(c/2 + d*x/2)**2 - 6291456*d), True))","A",0
50,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,0,0,0,0.000000," ","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
52,0,0,0,0.000000," ","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
53,0,0,0,0.000000," ","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
54,0,0,0,0.000000," ","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
55,0,0,0,0.000000," ","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
56,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(4/3),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(4/3), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(2/3),x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(2/3), x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**(1/3),x)","\int \sqrt[3]{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(1/3), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{a + b \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(-1/3), x)","F",0
60,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(2/3),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(-2/3), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**(4/3),x)","\int \frac{1}{\left(a + b \cos{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**(-4/3), x)","F",0
62,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**n,x)","\int \left(a + b \cos{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**n, x)","F",0
