1,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(5/2), x)","F",0
3,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(3/2), x)","F",0
4,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \sin{\left(c + d x \right)} + a}\, dx"," ",0,"Integral(sqrt(a*sin(c + d*x) + a), x)","F",0
5,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \sin{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(a*sin(c + d*x) + a), x)","F",0
6,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + a\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-3/2), x)","F",0
7,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + a\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-5/2), x)","F",0
8,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(4/3),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(4/3), x)","F",0
9,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(2/3),x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(2/3), x)","F",0
10,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/3),x)","\int \sqrt[3]{a \sin{\left(c + d x \right)} + a}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(1/3), x)","F",0
11,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{a \sin{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-1/3), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(2/3),x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + a\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-2/3), x)","F",0
13,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(4/3),x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + a\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**(-4/3), x)","F",0
14,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**n,x)","\int \left(a \sin{\left(c + d x \right)} + a\right)^{n}\, dx"," ",0,"Integral((a*sin(c + d*x) + a)**n, x)","F",0
15,0,0,0,0.000000," ","integrate((a-a*sin(d*x+c))**n,x)","\int \left(- a \sin{\left(c + d x \right)} + a\right)^{n}\, dx"," ",0,"Integral((-a*sin(c + d*x) + a)**n, x)","F",0
16,0,0,0,0.000000," ","integrate((2+2*sin(d*x+c))**n,x)","2^{n} \int \left(\sin{\left(c + d x \right)} + 1\right)^{n}\, dx"," ",0,"2**n*Integral((sin(c + d*x) + 1)**n, x)","F",0
17,0,0,0,0.000000," ","integrate((2-2*sin(d*x+c))**n,x)","\int \left(2 - 2 \sin{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((2 - 2*sin(c + d*x))**n, x)","F",0
18,1,46,0,0.743240," ","integrate(1/(5+3*sin(d*x+c)),x)","\begin{cases} \frac{\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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 \sin{\left(c \right)} + 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(3*sin(c) + 5), True))","A",0
19,1,388,0,2.061946," ","integrate(1/(5+3*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(3 \sin{\left(c \right)} + 5\right)^{2}} & \text{for}\: d = 0 \\\frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{150 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{36 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{60}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*sin(2*atan(3/5 - 4*I/5)))**2, Eq(c, -d*x - 2*atan(3/5 - 4*I/5))), (x/(5 - 3*sin(2*atan(3/5 + 4*I/5)))**2, Eq(c, -d*x - 2*atan(3/5 + 4*I/5))), (x/(3*sin(c) + 5)**2, Eq(d, 0)), (125*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 150*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 125*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 36*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 60/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d), True))","A",0
20,1,918,0,4.720599," ","integrate(1/(5+3*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(3 \sin{\left(c \right)} + 5\right)^{3}} & \text{for}\: d = 0 \\\frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{126850 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{19260 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{46956 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{46260 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{27300}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*sin(2*atan(3/5 - 4*I/5)))**3, Eq(c, -d*x - 2*atan(3/5 - 4*I/5))), (x/(5 - 3*sin(2*atan(3/5 + 4*I/5)))**3, Eq(c, -d*x - 2*atan(3/5 + 4*I/5))), (x/(3*sin(c) + 5)**3, Eq(d, 0)), (36875*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 88500*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 126850*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 88500*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 36875*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 19260*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 46956*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 46260*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 27300/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d), True))","A",0
21,1,1693,0,10.831197," ","integrate(1/(5+3*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(3 \sin{\left(c \right)} + 5\right)^{4}} & \text{for}\: d = 0 \\\frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{53707500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{3993300 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{13454460 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{22960584 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{24195960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{14523300 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{5143500}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*sin(2*atan(3/5 - 4*I/5)))**4, Eq(c, -d*x - 2*atan(3/5 - 4*I/5))), (x/(5 - 3*sin(2*atan(3/5 + 4*I/5)))**4, Eq(c, -d*x - 2*atan(3/5 + 4*I/5))), (x/(3*sin(c) + 5)**4, Eq(d, 0)), (6015625*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 21656250*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 53707500*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 21656250*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 6015625*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 3993300*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 13454460*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 22960584*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 24195960*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 14523300*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 5143500/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d), True))","A",0
22,1,46,0,0.777098," ","integrate(1/(5-3*sin(d*x+c)),x)","\begin{cases} \frac{\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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 \sin{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(5 - 3*sin(c)), True))","A",0
23,1,384,0,2.050537," ","integrate(1/(5-3*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} - \frac{150 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{36 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} - \frac{60}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*sin(2*atan(3/5 - 4*I/5)))**2, Eq(c, -d*x + 2*atan(3/5 - 4*I/5))), (x/(5 - 3*sin(2*atan(3/5 + 4*I/5)))**2, Eq(c, -d*x + 2*atan(3/5 + 4*I/5))), (x/(5 - 3*sin(c))**2, Eq(d, 0)), (125*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) - 150*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) + 125*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) + 36*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) - 60/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d), True))","A",0
24,1,915,0,4.713276," ","integrate(1/(5-3*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\\frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{126850 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{19260 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{46956 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{46260 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{27300}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*sin(2*atan(3/5 - 4*I/5)))**3, Eq(c, -d*x + 2*atan(3/5 - 4*I/5))), (x/(5 - 3*sin(2*atan(3/5 + 4*I/5)))**3, Eq(c, -d*x + 2*atan(3/5 + 4*I/5))), (x/(5 - 3*sin(c))**3, Eq(d, 0)), (36875*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 88500*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 126850*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 88500*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 36875*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 19260*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 46956*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 46260*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 27300/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d), True))","A",0
25,1,1690,0,10.701925," ","integrate(1/(5-3*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(5 - 3 \sin{\left(c \right)}\right)^{4}} & \text{for}\: d = 0 \\\frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{53707500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{3993300 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{13454460 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{22960584 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{24195960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{14523300 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{5143500}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(5 - 3*sin(2*atan(3/5 - 4*I/5)))**4, Eq(c, -d*x + 2*atan(3/5 - 4*I/5))), (x/(5 - 3*sin(2*atan(3/5 + 4*I/5)))**4, Eq(c, -d*x + 2*atan(3/5 + 4*I/5))), (x/(5 - 3*sin(c))**4, Eq(d, 0)), (6015625*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 21656250*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 53707500*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 21656250*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 6015625*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 3993300*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 13454460*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 22960584*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 24195960*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 14523300*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 5143500/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d), True))","A",0
26,1,48,0,0.734269," ","integrate(1/(-5+3*sin(d*x+c)),x)","\begin{cases} - \frac{\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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 \sin{\left(c \right)} - 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(3*sin(c) - 5), True))","A",0
27,1,384,0,2.021176," ","integrate(1/(-5+3*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(3 \sin{\left(c \right)} - 5\right)^{2}} & \text{for}\: d = 0 \\\frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} - \frac{150 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{36 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} - \frac{60}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*sin(2*atan(3/5 - 4*I/5)))**2, Eq(c, -d*x + 2*atan(3/5 - 4*I/5))), (x/(-5 + 3*sin(2*atan(3/5 + 4*I/5)))**2, Eq(c, -d*x + 2*atan(3/5 + 4*I/5))), (x/(3*sin(c) - 5)**2, Eq(d, 0)), (125*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) - 150*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) + 125*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) + 36*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d) - 60/(800*d*tan(c/2 + d*x/2)**2 - 960*d*tan(c/2 + d*x/2) + 800*d), True))","A",0
28,1,915,0,4.728791," ","integrate(1/(-5+3*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(3 \sin{\left(c \right)} - 5\right)^{3}} & \text{for}\: d = 0 \\- \frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{126850 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{19260 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{46956 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{46260 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} + \frac{27300}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*sin(2*atan(3/5 - 4*I/5)))**3, Eq(c, -d*x + 2*atan(3/5 - 4*I/5))), (x/(-5 + 3*sin(2*atan(3/5 + 4*I/5)))**3, Eq(c, -d*x + 2*atan(3/5 + 4*I/5))), (x/(3*sin(c) - 5)**3, Eq(d, 0)), (-36875*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 88500*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 126850*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 88500*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 36875*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 19260*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 46956*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 46260*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d) + 27300/(640000*d*tan(c/2 + d*x/2)**4 - 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 - 1536000*d*tan(c/2 + d*x/2) + 640000*d), True))","A",0
29,1,1690,0,10.778844," ","integrate(1/(-5+3*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(3 \sin{\left(c \right)} - 5\right)^{4}} & \text{for}\: d = 0 \\\frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{53707500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} - \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{3993300 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{13454460 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{22960584 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{24195960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{14523300 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} - \frac{5143500}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*sin(2*atan(3/5 - 4*I/5)))**4, Eq(c, -d*x + 2*atan(3/5 - 4*I/5))), (x/(-5 + 3*sin(2*atan(3/5 + 4*I/5)))**4, Eq(c, -d*x + 2*atan(3/5 + 4*I/5))), (x/(3*sin(c) - 5)**4, Eq(d, 0)), (6015625*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 21656250*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 53707500*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 21656250*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 6015625*(atan(5*tan(c/2 + d*x/2)/4 - 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 3993300*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 13454460*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 22960584*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 24195960*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 14523300*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d) - 5143500/(256000000*d*tan(c/2 + d*x/2)**6 - 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 - 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 - 921600000*d*tan(c/2 + d*x/2) + 256000000*d), True))","A",0
30,1,49,0,0.751184," ","integrate(1/(-5-3*sin(d*x+c)),x)","\begin{cases} - \frac{\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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 \sin{\left(c \right)} - 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(2*d), Ne(d, 0)), (x/(-3*sin(c) - 5), True))","A",0
31,1,389,0,2.076063," ","integrate(1/(-5-3*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(- 3 \sin{\left(c \right)} - 5\right)^{2}} & \text{for}\: d = 0 \\\frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{150 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{125 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{36 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} + \frac{60}{800 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 960 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 800 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*sin(2*atan(3/5 - 4*I/5)))**2, Eq(c, -d*x - 2*atan(3/5 - 4*I/5))), (x/(-5 + 3*sin(2*atan(3/5 + 4*I/5)))**2, Eq(c, -d*x - 2*atan(3/5 + 4*I/5))), (x/(-3*sin(c) - 5)**2, Eq(d, 0)), (125*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 150*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 125*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 36*tan(c/2 + d*x/2)/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d) + 60/(800*d*tan(c/2 + d*x/2)**2 + 960*d*tan(c/2 + d*x/2) + 800*d), True))","A",0
32,1,921,0,4.750647," ","integrate(1/(-5-3*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(- 3 \sin{\left(c \right)} - 5\right)^{3}} & \text{for}\: d = 0 \\- \frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{126850 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{88500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{36875 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{19260 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{46956 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{46260 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} - \frac{27300}{640000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2201600 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1536000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 640000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*sin(2*atan(3/5 - 4*I/5)))**3, Eq(c, -d*x - 2*atan(3/5 - 4*I/5))), (x/(-5 + 3*sin(2*atan(3/5 + 4*I/5)))**3, Eq(c, -d*x - 2*atan(3/5 + 4*I/5))), (x/(-3*sin(c) - 5)**3, Eq(d, 0)), (-36875*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 88500*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 126850*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 88500*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 36875*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 19260*tan(c/2 + d*x/2)**3/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 46956*tan(c/2 + d*x/2)**2/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 46260*tan(c/2 + d*x/2)/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d) - 27300/(640000*d*tan(c/2 + d*x/2)**4 + 1536000*d*tan(c/2 + d*x/2)**3 + 2201600*d*tan(c/2 + d*x/2)**2 + 1536000*d*tan(c/2 + d*x/2) + 640000*d), True))","A",0
33,1,1695,0,10.875824," ","integrate(1/(-5-3*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} - \frac{4 i}{5} \right)} \\\frac{x}{\left(-5 + 3 \sin{\left(2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{3}{5} + \frac{4 i}{5} \right)} \\\frac{x}{\left(- 3 \sin{\left(c \right)} - 5\right)^{4}} & \text{for}\: d = 0 \\\frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{53707500 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{44034375 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \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)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{21656250 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{6015625 \left(\operatorname{atan}{\left(\frac{5 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4} + \frac{3}{4} \right)} + \pi \left\lfloor{\frac{\frac{c}{2} + \frac{d x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{3993300 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{13454460 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{22960584 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{24195960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{14523300 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} + \frac{5143500}{256000000 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2285568000 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1873920000 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 921600000 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 256000000 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-5 + 3*sin(2*atan(3/5 - 4*I/5)))**4, Eq(c, -d*x - 2*atan(3/5 - 4*I/5))), (x/(-5 + 3*sin(2*atan(3/5 + 4*I/5)))**4, Eq(c, -d*x - 2*atan(3/5 + 4*I/5))), (x/(-3*sin(c) - 5)**4, Eq(d, 0)), (6015625*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**6/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 21656250*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 53707500*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 44034375*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 21656250*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 6015625*(atan(5*tan(c/2 + d*x/2)/4 + 3/4) + pi*floor((c/2 + d*x/2 - pi/2)/pi))/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 3993300*tan(c/2 + d*x/2)**5/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 13454460*tan(c/2 + d*x/2)**4/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 22960584*tan(c/2 + d*x/2)**3/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 24195960*tan(c/2 + d*x/2)**2/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 14523300*tan(c/2 + d*x/2)/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d) + 5143500/(256000000*d*tan(c/2 + d*x/2)**6 + 921600000*d*tan(c/2 + d*x/2)**5 + 1873920000*d*tan(c/2 + d*x/2)**4 + 2285568000*d*tan(c/2 + d*x/2)**3 + 1873920000*d*tan(c/2 + d*x/2)**2 + 921600000*d*tan(c/2 + d*x/2) + 256000000*d), True))","A",0
34,1,42,0,0.657996," ","integrate(1/(3+5*sin(d*x+c)),x)","\begin{cases} \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{4 d} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{5 \sin{\left(c \right)} + 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(c/2 + d*x/2) + 1/3)/(4*d) - log(tan(c/2 + d*x/2) + 3)/(4*d), Ne(d, 0)), (x/(5*sin(c) + 3), True))","A",0
35,1,466,0,1.685345," ","integrate(1/(3+5*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(5 \sin{\left(c \right)} + 3\right)^{2}} & \text{for}\: d = 0 \\- \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{200 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{120}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*sin(2*atan(1/3)))**2, Eq(c, -d*x - 2*atan(1/3))), (x/(3 - 5*sin(2*atan(3)))**2, Eq(c, -d*x - 2*atan(3))), (x/(5*sin(c) + 3)**2, Eq(d, 0)), (-27*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 90*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 27*log(tan(c/2 + d*x/2) + 1/3)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) + 90*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) + 3)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 200*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 120/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d), True))","A",0
36,1,1227,0,3.544598," ","integrate(1/(3+5*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(5 \sin{\left(c \right)} + 3\right)^{3}} & \text{for}\: d = 0 \\\frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3000 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{25960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{29400 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3960}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*sin(2*atan(1/3)))**3, Eq(c, -d*x - 2*atan(1/3))), (x/(3 - 5*sin(2*atan(3)))**3, Eq(c, -d*x - 2*atan(3))), (x/(5*sin(c) + 3)**3, Eq(d, 0)), (3483*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 45666*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3483*log(tan(c/2 + d*x/2) + 1/3)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3483*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 45666*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3483*log(tan(c/2 + d*x/2) + 3)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3000*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 25960*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 29400*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3960/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d), True))","A",0
37,1,2356,0,7.995572," ","integrate(1/(3+5*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(5 \sin{\left(c \right)} + 3\right)^{4}} & \text{for}\: d = 0 \\- \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{3396600 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{19457640 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{48756400 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{42659280 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{13699800 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{1709640}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*sin(2*atan(1/3)))**4, Eq(c, -d*x - 2*atan(1/3))), (x/(3 - 5*sin(2*atan(3)))**4, Eq(c, -d*x - 2*atan(3))), (x/(5*sin(c) + 3)**4, Eq(d, 0)), (-610173*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 34802460*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 610173*log(tan(c/2 + d*x/2) + 1/3)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 34802460*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) + 3)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 3396600*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 19457640*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 48756400*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 42659280*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 13699800*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 1709640/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d), True))","A",0
38,1,42,0,0.662376," ","integrate(1/(3-5*sin(d*x+c)),x)","\begin{cases} \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{4 d} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{3 - 5 \sin{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(c/2 + d*x/2) - 3)/(4*d) - log(tan(c/2 + d*x/2) - 1/3)/(4*d), Ne(d, 0)), (x/(3 - 5*sin(c)), True))","A",0
39,1,462,0,1.685430," ","integrate(1/(3-5*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(3 - 5 \sin{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{200 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{120}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*sin(2*atan(1/3)))**2, Eq(c, -d*x + 2*atan(1/3))), (x/(3 - 5*sin(2*atan(3)))**2, Eq(c, -d*x + 2*atan(3))), (x/(3 - 5*sin(c))**2, Eq(d, 0)), (-27*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 90*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) - 27*log(tan(c/2 + d*x/2) - 3)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) - 90*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) - 1/3)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) - 200*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 120/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d), True))","A",0
40,1,1224,0,3.525550," ","integrate(1/(3-5*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(3 - 5 \sin{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\\frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3000 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{25960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{29400 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3960}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*sin(2*atan(1/3)))**3, Eq(c, -d*x + 2*atan(1/3))), (x/(3 - 5*sin(2*atan(3)))**3, Eq(c, -d*x + 2*atan(3))), (x/(3 - 5*sin(c))**3, Eq(d, 0)), (3483*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 45666*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3483*log(tan(c/2 + d*x/2) - 3)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3483*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 45666*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3483*log(tan(c/2 + d*x/2) - 1/3)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3000*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 25960*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 29400*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3960/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d), True))","A",0
41,1,2353,0,7.688097," ","integrate(1/(3-5*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(3 - 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(3 - 5 \sin{\left(c \right)}\right)^{4}} & \text{for}\: d = 0 \\- \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{3396600 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{19457640 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{48756400 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{42659280 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{13699800 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{1709640}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(3 - 5*sin(2*atan(1/3)))**4, Eq(c, -d*x + 2*atan(1/3))), (x/(3 - 5*sin(2*atan(3)))**4, Eq(c, -d*x + 2*atan(3))), (x/(3 - 5*sin(c))**4, Eq(d, 0)), (-610173*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 34802460*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 610173*log(tan(c/2 + d*x/2) - 3)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 34802460*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) - 1/3)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 3396600*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 19457640*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 48756400*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 42659280*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 13699800*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 1709640/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d), True))","A",0
42,1,42,0,0.633351," ","integrate(1/(-3+5*sin(d*x+c)),x)","\begin{cases} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{4 d} + \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{5 \sin{\left(c \right)} - 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(c/2 + d*x/2) - 3)/(4*d) + log(tan(c/2 + d*x/2) - 1/3)/(4*d), Ne(d, 0)), (x/(5*sin(c) - 3), True))","A",0
43,1,462,0,1.619838," ","integrate(1/(-3+5*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{2}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(5 \sin{\left(c \right)} - 3\right)^{2}} & \text{for}\: d = 0 \\- \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{200 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{120}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*sin(2*atan(1/3)))**2, Eq(c, -d*x + 2*atan(1/3))), (x/(-3 + 5*sin(2*atan(3)))**2, Eq(c, -d*x + 2*atan(3))), (x/(5*sin(c) - 3)**2, Eq(d, 0)), (-27*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 90*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) - 27*log(tan(c/2 + d*x/2) - 3)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) - 90*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) - 1/3)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) - 200*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d) + 120/(576*d*tan(c/2 + d*x/2)**2 - 1920*d*tan(c/2 + d*x/2) + 576*d), True))","A",0
44,1,1224,0,3.408201," ","integrate(1/(-3+5*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{3}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(5 \sin{\left(c \right)} - 3\right)^{3}} & \text{for}\: d = 0 \\- \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3000 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{25960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{29400 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3960}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*sin(2*atan(1/3)))**3, Eq(c, -d*x + 2*atan(1/3))), (x/(-3 + 5*sin(2*atan(3)))**3, Eq(c, -d*x + 2*atan(3))), (x/(5*sin(c) - 3)**3, Eq(d, 0)), (-3483*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 45666*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3483*log(tan(c/2 + d*x/2) - 3)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3483*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 45666*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3483*log(tan(c/2 + d*x/2) - 1/3)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3000*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 25960*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 29400*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3960/(165888*d*tan(c/2 + d*x/2)**4 - 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 - 1105920*d*tan(c/2 + d*x/2) + 165888*d), True))","A",0
45,1,2353,0,8.007906," ","integrate(1/(-3+5*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{4}} & \text{for}\: c = - d x + 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(5 \sin{\left(c \right)} - 3\right)^{4}} & \text{for}\: d = 0 \\- \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} - \frac{1}{3} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{3396600 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{19457640 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{48756400 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{42659280 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{13699800 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{1709640}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*sin(2*atan(1/3)))**4, Eq(c, -d*x + 2*atan(1/3))), (x/(-3 + 5*sin(2*atan(3)))**4, Eq(c, -d*x + 2*atan(3))), (x/(5*sin(c) - 3)**4, Eq(d, 0)), (-610173*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 34802460*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) - 3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 610173*log(tan(c/2 + d*x/2) - 3)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 34802460*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) - 1/3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) - 1/3)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 3396600*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 19457640*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 48756400*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 42659280*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 13699800*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 1709640/(71663616*d*tan(c/2 + d*x/2)**6 - 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 - 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 - 716636160*d*tan(c/2 + d*x/2) + 71663616*d), True))","A",0
46,1,44,0,0.652342," ","integrate(1/(-3-5*sin(d*x+c)),x)","\begin{cases} - \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{4 d} + \frac{\log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{4 d} & \text{for}\: d \neq 0 \\\frac{x}{- 5 \sin{\left(c \right)} - 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(c/2 + d*x/2) + 1/3)/(4*d) + log(tan(c/2 + d*x/2) + 3)/(4*d), Ne(d, 0)), (x/(-5*sin(c) - 3), True))","A",0
47,1,468,0,1.651552," ","integrate(1/(-3-5*sin(d*x+c))**2,x)","\begin{cases} \frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{2}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(- 5 \sin{\left(c \right)} - 3\right)^{2}} & \text{for}\: d = 0 \\- \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{90 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} + \frac{27 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{200 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} - \frac{120}{576 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 576 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*sin(2*atan(1/3)))**2, Eq(c, -d*x - 2*atan(1/3))), (x/(-3 + 5*sin(2*atan(3)))**2, Eq(c, -d*x - 2*atan(3))), (x/(-5*sin(c) - 3)**2, Eq(d, 0)), (-27*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 90*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 27*log(tan(c/2 + d*x/2) + 1/3)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**2/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) + 90*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) + 27*log(tan(c/2 + d*x/2) + 3)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 200*tan(c/2 + d*x/2)/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d) - 120/(576*d*tan(c/2 + d*x/2)**2 + 1920*d*tan(c/2 + d*x/2) + 576*d), True))","A",0
48,1,1229,0,3.448403," ","integrate(1/(-3-5*sin(d*x+c))**3,x)","\begin{cases} \frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{3}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(- 5 \sin{\left(c \right)} - 3\right)^{3}} & \text{for}\: d = 0 \\- \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{45666 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{23220 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3483 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} + \frac{3000 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{25960 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{29400 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} - \frac{3960}{165888 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2174976 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1105920 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 165888 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*sin(2*atan(1/3)))**3, Eq(c, -d*x - 2*atan(1/3))), (x/(-3 + 5*sin(2*atan(3)))**3, Eq(c, -d*x - 2*atan(3))), (x/(-5*sin(c) - 3)**3, Eq(d, 0)), (-3483*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 45666*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 23220*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3483*log(tan(c/2 + d*x/2) + 1/3)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3483*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**4/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 45666*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 23220*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3483*log(tan(c/2 + d*x/2) + 3)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) + 3000*tan(c/2 + d*x/2)**3/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 25960*tan(c/2 + d*x/2)**2/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 29400*tan(c/2 + d*x/2)/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d) - 3960/(165888*d*tan(c/2 + d*x/2)**4 + 1105920*d*tan(c/2 + d*x/2)**3 + 2174976*d*tan(c/2 + d*x/2)**2 + 1105920*d*tan(c/2 + d*x/2) + 165888*d), True))","A",0
49,1,2358,0,7.751956," ","integrate(1/(-3-5*sin(d*x+c))**4,x)","\begin{cases} \frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \\\frac{x}{\left(-3 + 5 \sin{\left(2 \operatorname{atan}{\left(3 \right)} \right)}\right)^{4}} & \text{for}\: c = - d x - 2 \operatorname{atan}{\left(3 \right)} \\\frac{x}{\left(- 5 \sin{\left(c \right)} - 3\right)^{4}} & \text{for}\: d = 0 \\- \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + \frac{1}{3} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{34802460 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{22169619 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{6101730 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} + \frac{610173 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{3396600 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{19457640 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{48756400 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{42659280 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{13699800 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} - \frac{1709640}{71663616 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4087480320 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2603778048 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 716636160 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 71663616 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(-3 + 5*sin(2*atan(1/3)))**4, Eq(c, -d*x - 2*atan(1/3))), (x/(-3 + 5*sin(2*atan(3)))**4, Eq(c, -d*x - 2*atan(3))), (x/(-5*sin(c) - 3)**4, Eq(d, 0)), (-610173*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 34802460*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 22169619*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 6101730*log(tan(c/2 + d*x/2) + 1/3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 610173*log(tan(c/2 + d*x/2) + 1/3)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**6/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 34802460*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 22169619*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 6101730*log(tan(c/2 + d*x/2) + 3)*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) + 610173*log(tan(c/2 + d*x/2) + 3)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 3396600*tan(c/2 + d*x/2)**5/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 19457640*tan(c/2 + d*x/2)**4/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 48756400*tan(c/2 + d*x/2)**3/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 42659280*tan(c/2 + d*x/2)**2/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 13699800*tan(c/2 + d*x/2)/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d) - 1709640/(71663616*d*tan(c/2 + d*x/2)**6 + 716636160*d*tan(c/2 + d*x/2)**5 + 2603778048*d*tan(c/2 + d*x/2)**4 + 4087480320*d*tan(c/2 + d*x/2)**3 + 2603778048*d*tan(c/2 + d*x/2)**2 + 716636160*d*tan(c/2 + d*x/2) + 71663616*d), True))","A",0
50,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**(5/2),x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(5/2), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**(3/2),x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x)), x)","F",0
54,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(c + d*x)), x)","F",0
55,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(-3/2), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(-5/2), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**(7/2),x)","\int \frac{1}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(-7/2), x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**(4/3),x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(4/3), x)","F",0
59,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**(2/3),x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(2/3), x)","F",0
60,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**(1/3),x)","\int \sqrt[3]{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(1/3), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(-1/3), x)","F",0
62,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**(2/3),x)","\int \frac{1}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(-2/3), x)","F",0
63,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**(4/3),x)","\int \frac{1}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(-4/3), x)","F",0
64,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**n,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**n, x)","F",0
65,0,0,0,0.000000," ","integrate((3+4*sin(d*x+c))**n,x)","\int \left(4 \sin{\left(c + d x \right)} + 3\right)^{n}\, dx"," ",0,"Integral((4*sin(c + d*x) + 3)**n, x)","F",0
66,0,0,0,0.000000," ","integrate((3-4*sin(d*x+c))**n,x)","\int \left(3 - 4 \sin{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((3 - 4*sin(c + d*x))**n, x)","F",0
67,0,0,0,0.000000," ","integrate((4+3*sin(d*x+c))**n,x)","\int \left(3 \sin{\left(c + d x \right)} + 4\right)^{n}\, dx"," ",0,"Integral((3*sin(c + d*x) + 4)**n, x)","F",0
68,0,0,0,0.000000," ","integrate((4-3*sin(d*x+c))**n,x)","\int \left(4 - 3 \sin{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((4 - 3*sin(c + d*x))**n, x)","F",0
69,0,0,0,0.000000," ","integrate((-3+4*sin(d*x+c))**n,x)","\int \left(4 \sin{\left(c + d x \right)} - 3\right)^{n}\, dx"," ",0,"Integral((4*sin(c + d*x) - 3)**n, x)","F",0
70,0,0,0,0.000000," ","integrate((-3-4*sin(d*x+c))**n,x)","\int \left(- 4 \sin{\left(c + d x \right)} - 3\right)^{n}\, dx"," ",0,"Integral((-4*sin(c + d*x) - 3)**n, x)","F",0
71,0,0,0,0.000000," ","integrate((-4+3*sin(d*x+c))**n,x)","\int \left(3 \sin{\left(c + d x \right)} - 4\right)^{n}\, dx"," ",0,"Integral((3*sin(c + d*x) - 4)**n, x)","F",0
72,0,0,0,0.000000," ","integrate((-4-3*sin(d*x+c))**n,x)","\int \left(- 3 \sin{\left(c + d x \right)} - 4\right)^{n}\, dx"," ",0,"Integral((-3*sin(c + d*x) - 4)**n, x)","F",0
