1,1,63,0,1.424792," ","integrate(x**5*(a+b*atan(c*x)),x)","\begin{cases} \frac{a x^{6}}{6} + \frac{b x^{6} \operatorname{atan}{\left(c x \right)}}{6} - \frac{b x^{5}}{30 c} + \frac{b x^{3}}{18 c^{3}} - \frac{b x}{6 c^{5}} + \frac{b \operatorname{atan}{\left(c x \right)}}{6 c^{6}} & \text{for}\: c \neq 0 \\\frac{a x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**6/6 + b*x**6*atan(c*x)/6 - b*x**5/(30*c) + b*x**3/(18*c**3) - b*x/(6*c**5) + b*atan(c*x)/(6*c**6), Ne(c, 0)), (a*x**6/6, True))","A",0
2,1,60,0,1.041878," ","integrate(x**4*(a+b*atan(c*x)),x)","\begin{cases} \frac{a x^{5}}{5} + \frac{b x^{5} \operatorname{atan}{\left(c x \right)}}{5} - \frac{b x^{4}}{20 c} + \frac{b x^{2}}{10 c^{3}} - \frac{b \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10 c^{5}} & \text{for}\: c \neq 0 \\\frac{a x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**5/5 + b*x**5*atan(c*x)/5 - b*x**4/(20*c) + b*x**2/(10*c**3) - b*log(x**2 + c**(-2))/(10*c**5), Ne(c, 0)), (a*x**5/5, True))","A",0
3,1,53,0,0.817436," ","integrate(x**3*(a+b*atan(c*x)),x)","\begin{cases} \frac{a x^{4}}{4} + \frac{b x^{4} \operatorname{atan}{\left(c x \right)}}{4} - \frac{b x^{3}}{12 c} + \frac{b x}{4 c^{3}} - \frac{b \operatorname{atan}{\left(c x \right)}}{4 c^{4}} & \text{for}\: c \neq 0 \\\frac{a x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**4/4 + b*x**4*atan(c*x)/4 - b*x**3/(12*c) + b*x/(4*c**3) - b*atan(c*x)/(4*c**4), Ne(c, 0)), (a*x**4/4, True))","A",0
4,1,49,0,0.576514," ","integrate(x**2*(a+b*atan(c*x)),x)","\begin{cases} \frac{a x^{3}}{3} + \frac{b x^{3} \operatorname{atan}{\left(c x \right)}}{3} - \frac{b x^{2}}{6 c} + \frac{b \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\\frac{a x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**3/3 + b*x**3*atan(c*x)/3 - b*x**2/(6*c) + b*log(x**2 + c**(-2))/(6*c**3), Ne(c, 0)), (a*x**3/3, True))","A",0
5,1,42,0,0.422727," ","integrate(x*(a+b*atan(c*x)),x)","\begin{cases} \frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{atan}{\left(c x \right)}}{2} - \frac{b x}{2 c} + \frac{b \operatorname{atan}{\left(c x \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\\frac{a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**2/2 + b*x**2*atan(c*x)/2 - b*x/(2*c) + b*atan(c*x)/(2*c**2), Ne(c, 0)), (a*x**2/2, True))","A",0
6,1,26,0,0.205341," ","integrate(a+b*atan(c*x),x)","a x + b \left(\begin{cases} x \operatorname{atan}{\left(c x \right)} - \frac{\log{\left(c^{2} x^{2} + 1 \right)}}{2 c} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x*atan(c*x) - log(c**2*x**2 + 1)/(2*c), Ne(c, 0)), (0, True))","A",0
7,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x,x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))/x, x)","F",0
8,1,37,0,0.631461," ","integrate((a+b*atan(c*x))/x**2,x)","\begin{cases} - \frac{a}{x} + b c \log{\left(x \right)} - \frac{b c \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b \operatorname{atan}{\left(c x \right)}}{x} & \text{for}\: c \neq 0 \\- \frac{a}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x + b*c*log(x) - b*c*log(x**2 + c**(-2))/2 - b*atan(c*x)/x, Ne(c, 0)), (-a/x, True))","A",0
9,1,37,0,0.527807," ","integrate((a+b*atan(c*x))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{b c^{2} \operatorname{atan}{\left(c x \right)}}{2} - \frac{b c}{2 x} - \frac{b \operatorname{atan}{\left(c x \right)}}{2 x^{2}}"," ",0,"-a/(2*x**2) - b*c**2*atan(c*x)/2 - b*c/(2*x) - b*atan(c*x)/(2*x**2)","A",0
10,1,61,0,1.059318," ","integrate((a+b*atan(c*x))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} - \frac{b c^{3} \log{\left(x \right)}}{3} + \frac{b c^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6} - \frac{b c}{6 x^{2}} - \frac{b \operatorname{atan}{\left(c x \right)}}{3 x^{3}} & \text{for}\: c \neq 0 \\- \frac{a}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3) - b*c**3*log(x)/3 + b*c**3*log(x**2 + c**(-2))/6 - b*c/(6*x**2) - b*atan(c*x)/(3*x**3), Ne(c, 0)), (-a/(3*x**3), True))","A",0
11,1,46,0,0.827310," ","integrate((a+b*atan(c*x))/x**5,x)","- \frac{a}{4 x^{4}} + \frac{b c^{4} \operatorname{atan}{\left(c x \right)}}{4} + \frac{b c^{3}}{4 x} - \frac{b c}{12 x^{3}} - \frac{b \operatorname{atan}{\left(c x \right)}}{4 x^{4}}"," ",0,"-a/(4*x**4) + b*c**4*atan(c*x)/4 + b*c**3/(4*x) - b*c/(12*x**3) - b*atan(c*x)/(4*x**4)","A",0
12,1,71,0,1.673069," ","integrate((a+b*atan(c*x))/x**6,x)","\begin{cases} - \frac{a}{5 x^{5}} + \frac{b c^{5} \log{\left(x \right)}}{5} - \frac{b c^{5} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10} + \frac{b c^{3}}{10 x^{2}} - \frac{b c}{20 x^{4}} - \frac{b \operatorname{atan}{\left(c x \right)}}{5 x^{5}} & \text{for}\: c \neq 0 \\- \frac{a}{5 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(5*x**5) + b*c**5*log(x)/5 - b*c**5*log(x**2 + c**(-2))/10 + b*c**3/(10*x**2) - b*c/(20*x**4) - b*atan(c*x)/(5*x**5), Ne(c, 0)), (-a/(5*x**5), True))","A",0
13,1,199,0,2.393242," ","integrate(x**5*(a+b*atan(c*x))**2,x)","\begin{cases} \frac{a^{2} x^{6}}{6} + \frac{a b x^{6} \operatorname{atan}{\left(c x \right)}}{3} - \frac{a b x^{5}}{15 c} + \frac{a b x^{3}}{9 c^{3}} - \frac{a b x}{3 c^{5}} + \frac{a b \operatorname{atan}{\left(c x \right)}}{3 c^{6}} + \frac{b^{2} x^{6} \operatorname{atan}^{2}{\left(c x \right)}}{6} - \frac{b^{2} x^{5} \operatorname{atan}{\left(c x \right)}}{15 c} + \frac{b^{2} x^{4}}{60 c^{2}} + \frac{b^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{9 c^{3}} - \frac{4 b^{2} x^{2}}{45 c^{4}} - \frac{b^{2} x \operatorname{atan}{\left(c x \right)}}{3 c^{5}} + \frac{23 b^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{90 c^{6}} + \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{6 c^{6}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**6/6 + a*b*x**6*atan(c*x)/3 - a*b*x**5/(15*c) + a*b*x**3/(9*c**3) - a*b*x/(3*c**5) + a*b*atan(c*x)/(3*c**6) + b**2*x**6*atan(c*x)**2/6 - b**2*x**5*atan(c*x)/(15*c) + b**2*x**4/(60*c**2) + b**2*x**3*atan(c*x)/(9*c**3) - 4*b**2*x**2/(45*c**4) - b**2*x*atan(c*x)/(3*c**5) + 23*b**2*log(x**2 + c**(-2))/(90*c**6) + b**2*atan(c*x)**2/(6*c**6), Ne(c, 0)), (a**2*x**6/6, True))","A",0
14,0,0,0,0.000000," ","integrate(x**4*(a+b*atan(c*x))**2,x)","\int x^{4} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**4*(a + b*atan(c*x))**2, x)","F",0
15,1,155,0,1.444412," ","integrate(x**3*(a+b*atan(c*x))**2,x)","\begin{cases} \frac{a^{2} x^{4}}{4} + \frac{a b x^{4} \operatorname{atan}{\left(c x \right)}}{2} - \frac{a b x^{3}}{6 c} + \frac{a b x}{2 c^{3}} - \frac{a b \operatorname{atan}{\left(c x \right)}}{2 c^{4}} + \frac{b^{2} x^{4} \operatorname{atan}^{2}{\left(c x \right)}}{4} - \frac{b^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{6 c} + \frac{b^{2} x^{2}}{12 c^{2}} + \frac{b^{2} x \operatorname{atan}{\left(c x \right)}}{2 c^{3}} - \frac{b^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3 c^{4}} - \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{4 c^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**4/4 + a*b*x**4*atan(c*x)/2 - a*b*x**3/(6*c) + a*b*x/(2*c**3) - a*b*atan(c*x)/(2*c**4) + b**2*x**4*atan(c*x)**2/4 - b**2*x**3*atan(c*x)/(6*c) + b**2*x**2/(12*c**2) + b**2*x*atan(c*x)/(2*c**3) - b**2*log(x**2 + c**(-2))/(3*c**4) - b**2*atan(c*x)**2/(4*c**4), Ne(c, 0)), (a**2*x**4/4, True))","A",0
16,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**2,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))**2, x)","F",0
17,1,107,0,0.734342," ","integrate(x*(a+b*atan(c*x))**2,x)","\begin{cases} \frac{a^{2} x^{2}}{2} + a b x^{2} \operatorname{atan}{\left(c x \right)} - \frac{a b x}{c} + \frac{a b \operatorname{atan}{\left(c x \right)}}{c^{2}} + \frac{b^{2} x^{2} \operatorname{atan}^{2}{\left(c x \right)}}{2} - \frac{b^{2} x \operatorname{atan}{\left(c x \right)}}{c} + \frac{b^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{2}} + \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**2/2 + a*b*x**2*atan(c*x) - a*b*x/c + a*b*atan(c*x)/c**2 + b**2*x**2*atan(c*x)**2/2 - b**2*x*atan(c*x)/c + b**2*log(x**2 + c**(-2))/(2*c**2) + b**2*atan(c*x)**2/(2*c**2), Ne(c, 0)), (a**2*x**2/2, True))","A",0
18,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atan(c*x))**2, x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/x, x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/x**2, x)","F",0
21,1,119,0,1.015148," ","integrate((a+b*atan(c*x))**2/x**3,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} - a b c^{2} \operatorname{atan}{\left(c x \right)} - \frac{a b c}{x} - \frac{a b \operatorname{atan}{\left(c x \right)}}{x^{2}} + b^{2} c^{2} \log{\left(x \right)} - \frac{b^{2} c^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b^{2} c^{2} \operatorname{atan}^{2}{\left(c x \right)}}{2} - \frac{b^{2} c \operatorname{atan}{\left(c x \right)}}{x} - \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{2 x^{2}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2) - a*b*c**2*atan(c*x) - a*b*c/x - a*b*atan(c*x)/x**2 + b**2*c**2*log(x) - b**2*c**2*log(x**2 + c**(-2))/2 - b**2*c**2*atan(c*x)**2/2 - b**2*c*atan(c*x)/x - b**2*atan(c*x)**2/(2*x**2), Ne(c, 0)), (-a**2/(2*x**2), True))","A",0
22,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/x**4, x)","F",0
23,1,170,0,1.778385," ","integrate((a+b*atan(c*x))**2/x**5,x)","\begin{cases} - \frac{a^{2}}{4 x^{4}} + \frac{a b c^{4} \operatorname{atan}{\left(c x \right)}}{2} + \frac{a b c^{3}}{2 x} - \frac{a b c}{6 x^{3}} - \frac{a b \operatorname{atan}{\left(c x \right)}}{2 x^{4}} - \frac{2 b^{2} c^{4} \log{\left(x \right)}}{3} + \frac{b^{2} c^{4} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3} + \frac{b^{2} c^{4} \operatorname{atan}^{2}{\left(c x \right)}}{4} + \frac{b^{2} c^{3} \operatorname{atan}{\left(c x \right)}}{2 x} - \frac{b^{2} c^{2}}{12 x^{2}} - \frac{b^{2} c \operatorname{atan}{\left(c x \right)}}{6 x^{3}} - \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(4*x**4) + a*b*c**4*atan(c*x)/2 + a*b*c**3/(2*x) - a*b*c/(6*x**3) - a*b*atan(c*x)/(2*x**4) - 2*b**2*c**4*log(x)/3 + b**2*c**4*log(x**2 + c**(-2))/3 + b**2*c**4*atan(c*x)**2/4 + b**2*c**3*atan(c*x)/(2*x) - b**2*c**2/(12*x**2) - b**2*c*atan(c*x)/(6*x**3) - b**2*atan(c*x)**2/(4*x**4), Ne(c, 0)), (-a**2/(4*x**4), True))","A",0
24,0,0,0,0.000000," ","integrate(x**5*(a+b*atan(c*x))**3,x)","\int x^{5} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**5*(a + b*atan(c*x))**3, x)","F",0
25,0,0,0,0.000000," ","integrate(x**4*(a+b*atan(c*x))**3,x)","\int x^{4} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**4*(a + b*atan(c*x))**3, x)","F",0
26,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))**3,x)","\int x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))**3, x)","F",0
27,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**3,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))**3, x)","F",0
28,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))**3,x)","\int x \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))**3, x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*atan(c*x))**3, x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))**3/x, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))**3/x**2, x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))**3/x**3, x)","F",0
33,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x))**3/x**4, x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x**5,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}}{x^{5}}\, dx"," ",0,"Integral((a + b*atan(c*x))**3/x**5, x)","F",0
35,0,0,0,0.000000," ","integrate(x/atan(a*x),x)","\int \frac{x}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x/atan(a*x), x)","F",0
36,0,0,0,0.000000," ","integrate(1/atan(a*x),x)","\int \frac{1}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/atan(a*x), x)","F",0
37,0,0,0,0.000000," ","integrate(1/x/atan(a*x),x)","\int \frac{1}{x \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*atan(a*x)), x)","F",0
38,0,0,0,0.000000," ","integrate(x/atan(a*x)**2,x)","\int \frac{x}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/atan(a*x)**2, x)","F",0
39,0,0,0,0.000000," ","integrate(1/atan(a*x)**2,x)","\int \frac{1}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(atan(a*x)**(-2), x)","F",0
40,0,0,0,0.000000," ","integrate(1/x/atan(a*x)**2,x)","\int \frac{1}{x \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*atan(a*x)**2), x)","F",0
41,0,0,0,0.000000," ","integrate(x*atan(a*x)**(1/2),x)","\int x \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(atan(a*x)), x)","F",0
42,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2),x)","\int \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(atan(a*x)), x)","F",0
43,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x,x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x}\, dx"," ",0,"Integral(sqrt(atan(a*x))/x, x)","F",0
44,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2),x)","\int x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx"," ",0,"Integral(x*atan(a*x)**(3/2), x)","F",0
45,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2),x)","\int \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx"," ",0,"Integral(atan(a*x)**(3/2), x)","F",0
46,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x,x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/x, x)","F",0
47,0,0,0,0.000000," ","integrate(x/atan(a*x)**(1/2),x)","\int \frac{x}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x/sqrt(atan(a*x)), x)","F",0
48,0,0,0,0.000000," ","integrate(1/atan(a*x)**(1/2),x)","\int \frac{1}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/sqrt(atan(a*x)), x)","F",0
49,0,0,0,0.000000," ","integrate(1/x/atan(a*x)**(1/2),x)","\int \frac{1}{x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x*sqrt(atan(a*x))), x)","F",0
50,0,0,0,0.000000," ","integrate(x/atan(a*x)**(3/2),x)","\int \frac{x}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x/atan(a*x)**(3/2), x)","F",0
51,0,0,0,0.000000," ","integrate(1/atan(a*x)**(3/2),x)","\int \frac{1}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(atan(a*x)**(-3/2), x)","F",0
52,0,0,0,0.000000," ","integrate(1/x/atan(a*x)**(3/2),x)","\int \frac{1}{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*atan(a*x)**(3/2)), x)","F",0
53,1,104,0,3.224133," ","integrate(atan(x)*x**(1/2),x)","\frac{2 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{3} - \frac{4 \sqrt{x}}{3} - \frac{\sqrt{2} \log{\left(- \sqrt{2} \sqrt{x} + x + 1 \right)}}{6} + \frac{\sqrt{2} \log{\left(\sqrt{2} \sqrt{x} + x + 1 \right)}}{6} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{3} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{3}"," ",0,"2*x**(3/2)*atan(x)/3 - 4*sqrt(x)/3 - sqrt(2)*log(-sqrt(2)*sqrt(x) + x + 1)/6 + sqrt(2)*log(sqrt(2)*sqrt(x) + x + 1)/6 + sqrt(2)*atan(sqrt(2)*sqrt(x) - 1)/3 + sqrt(2)*atan(sqrt(2)*sqrt(x) + 1)/3","A",0
54,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x))**3,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral((d*x)**m*(a + b*atan(c*x))**3, x)","F",0
55,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x))**2,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((d*x)**m*(a + b*atan(c*x))**2, x)","F",0
56,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x)),x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right)\, dx"," ",0,"Integral((d*x)**m*(a + b*atan(c*x)), x)","F",0
57,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*atan(c*x)),x)","\int \frac{\left(d x\right)^{m}}{a + b \operatorname{atan}{\left(c x \right)}}\, dx"," ",0,"Integral((d*x)**m/(a + b*atan(c*x)), x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**p,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*atan(c*x))**p, x)","F",0
59,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,1,58,0,65.098490," ","integrate(x**7*(a+b*atan(c*x**2)),x)","\begin{cases} \frac{a x^{8}}{8} + \frac{b x^{8} \operatorname{atan}{\left(c x^{2} \right)}}{8} - \frac{b x^{6}}{24 c} + \frac{b x^{2}}{8 c^{3}} - \frac{b \operatorname{atan}{\left(c x^{2} \right)}}{8 c^{4}} & \text{for}\: c \neq 0 \\\frac{a x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**8/8 + b*x**8*atan(c*x**2)/8 - b*x**6/(24*c) + b*x**2/(8*c**3) - b*atan(c*x**2)/(8*c**4), Ne(c, 0)), (a*x**8/8, True))","A",0
61,1,80,0,46.372243," ","integrate(x**5*(a+b*atan(c*x**2)),x)","\begin{cases} \frac{a x^{6}}{6} + \frac{b x^{6} \operatorname{atan}{\left(c x^{2} \right)}}{6} - \frac{b x^{4}}{12 c} + \frac{i b \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{6 c^{2}} + \frac{b \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\\frac{a x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**6/6 + b*x**6*atan(c*x**2)/6 - b*x**4/(12*c) + I*b*sqrt(c**(-2))*atan(c*x**2)/(6*c**2) + b*log(x**2 + I*sqrt(c**(-2)))/(6*c**3), Ne(c, 0)), (a*x**6/6, True))","A",0
62,1,48,0,23.237245," ","integrate(x**3*(a+b*atan(c*x**2)),x)","\begin{cases} \frac{a x^{4}}{4} + \frac{b x^{4} \operatorname{atan}{\left(c x^{2} \right)}}{4} - \frac{b x^{2}}{4 c} + \frac{b \operatorname{atan}{\left(c x^{2} \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\\frac{a x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**4/4 + b*x**4*atan(c*x**2)/4 - b*x**2/(4*c) + b*atan(c*x**2)/(4*c**2), Ne(c, 0)), (a*x**4/4, True))","A",0
63,1,66,0,13.502434," ","integrate(x*(a+b*atan(c*x**2)),x)","\begin{cases} \frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{atan}{\left(c x^{2} \right)}}{2} - \frac{i b \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{2} - \frac{b \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2 c} & \text{for}\: c \neq 0 \\\frac{a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**2/2 + b*x**2*atan(c*x**2)/2 - I*b*sqrt(c**(-2))*atan(c*x**2)/2 - b*log(x**2 + I*sqrt(c**(-2)))/(2*c), Ne(c, 0)), (a*x**2/2, True))","A",0
64,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))/x,x)","\int \frac{a + b \operatorname{atan}{\left(c x^{2} \right)}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x**2))/x, x)","F",0
65,1,75,0,30.284698," ","integrate((a+b*atan(c*x**2))/x**3,x)","\begin{cases} - \frac{a}{2 x^{2}} + b c \log{\left(x \right)} - \frac{b c \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2} - \frac{i b \operatorname{atan}{\left(c x^{2} \right)}}{2 \sqrt{\frac{1}{c^{2}}}} - \frac{b \operatorname{atan}{\left(c x^{2} \right)}}{2 x^{2}} & \text{for}\: c \neq 0 \\- \frac{a}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) + b*c*log(x) - b*c*log(x**2 + I*sqrt(c**(-2)))/2 - I*b*atan(c*x**2)/(2*sqrt(c**(-2))) - b*atan(c*x**2)/(2*x**2), Ne(c, 0)), (-a/(2*x**2), True))","A",0
66,1,42,0,24.119689," ","integrate((a+b*atan(c*x**2))/x**5,x)","- \frac{a}{4 x^{4}} - \frac{b c^{2} \operatorname{atan}{\left(c x^{2} \right)}}{4} - \frac{b c}{4 x^{2}} - \frac{b \operatorname{atan}{\left(c x^{2} \right)}}{4 x^{4}}"," ",0,"-a/(4*x**4) - b*c**2*atan(c*x**2)/4 - b*c/(4*x**2) - b*atan(c*x**2)/(4*x**4)","A",0
67,1,92,0,81.386292," ","integrate((a+b*atan(c*x**2))/x**7,x)","\begin{cases} - \frac{a}{6 x^{6}} - \frac{b c^{3} \log{\left(x \right)}}{3} + \frac{b c^{3} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{6} + \frac{i b c^{2} \operatorname{atan}{\left(c x^{2} \right)}}{6 \sqrt{\frac{1}{c^{2}}}} - \frac{b c}{12 x^{4}} - \frac{b \operatorname{atan}{\left(c x^{2} \right)}}{6 x^{6}} & \text{for}\: c \neq 0 \\- \frac{a}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(6*x**6) - b*c**3*log(x)/3 + b*c**3*log(x**2 + I*sqrt(c**(-2)))/6 + I*b*c**2*atan(c*x**2)/(6*sqrt(c**(-2))) - b*c/(12*x**4) - b*atan(c*x**2)/(6*x**6), Ne(c, 0)), (-a/(6*x**6), True))","A",0
68,1,184,0,33.026096," ","integrate(x**4*(a+b*atan(c*x**2)),x)","\begin{cases} \frac{a x^{5}}{5} + \frac{b x^{5} \operatorname{atan}{\left(c x^{2} \right)}}{5} - \frac{2 b x^{3}}{15 c} - \frac{\left(-1\right)^{\frac{3}{4}} b \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{5 c^{3} \sqrt[4]{\frac{1}{c^{2}}}} + \frac{\left(-1\right)^{\frac{3}{4}} b \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{10 c^{3} \sqrt[4]{\frac{1}{c^{2}}}} + \frac{\left(-1\right)^{\frac{3}{4}} b \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{5 c^{3} \sqrt[4]{\frac{1}{c^{2}}}} - \frac{\sqrt[4]{-1} b \operatorname{atan}{\left(c x^{2} \right)}}{5 c^{6} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} & \text{for}\: c \neq 0 \\\frac{a x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**5/5 + b*x**5*atan(c*x**2)/5 - 2*b*x**3/(15*c) - (-1)**(3/4)*b*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(5*c**3*(c**(-2))**(1/4)) + (-1)**(3/4)*b*log(x**2 + I*sqrt(c**(-2)))/(10*c**3*(c**(-2))**(1/4)) + (-1)**(3/4)*b*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(5*c**3*(c**(-2))**(1/4)) - (-1)**(1/4)*b*atan(c*x**2)/(5*c**6*(c**(-2))**(7/4)), Ne(c, 0)), (a*x**5/5, True))","A",0
69,1,173,0,17.683713," ","integrate(x**2*(a+b*atan(c*x**2)),x)","\begin{cases} \frac{a x^{3}}{3} + \frac{b x^{3} \operatorname{atan}{\left(c x^{2} \right)}}{3} + \frac{\left(-1\right)^{\frac{3}{4}} b \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}} \operatorname{atan}{\left(c x^{2} \right)}}{3} - \frac{2 b x}{3 c} - \frac{\sqrt[4]{-1} b \sqrt[4]{\frac{1}{c^{2}}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{3 c} + \frac{\sqrt[4]{-1} b \sqrt[4]{\frac{1}{c^{2}}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{6 c} - \frac{\sqrt[4]{-1} b \sqrt[4]{\frac{1}{c^{2}}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{3 c} & \text{for}\: c \neq 0 \\\frac{a x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**3/3 + b*x**3*atan(c*x**2)/3 + (-1)**(3/4)*b*(c**(-2))**(3/4)*atan(c*x**2)/3 - 2*b*x/(3*c) - (-1)**(1/4)*b*(c**(-2))**(1/4)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(3*c) + (-1)**(1/4)*b*(c**(-2))**(1/4)*log(x**2 + I*sqrt(c**(-2)))/(6*c) - (-1)**(1/4)*b*(c**(-2))**(1/4)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(3*c), Ne(c, 0)), (a*x**3/3, True))","A",0
70,1,930,0,10.228053," ","integrate(a+b*atan(c*x**2),x)","a x + b \left(\begin{cases} - x \operatorname{atan}{\left(\frac{1}{\left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \right)} & \text{for}\: c = - \frac{1}{x^{2} \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \\- x \operatorname{atan}{\left(\frac{1}{\left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \right)} & \text{for}\: c = - \frac{1}{x^{2} \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \\- x \operatorname{atan}{\left(\frac{1}{\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \right)} & \text{for}\: c = - \frac{1}{x^{2} \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)^{2}} \\- x \operatorname{atan}{\left(\frac{1}{\left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \right)} & \text{for}\: c = - \frac{1}{x^{2} \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)^{2}} \\0 & \text{for}\: c = 0 \\- \frac{2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{5} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} \operatorname{atan}{\left(c x^{2} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} + \frac{2 i c^{4} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} - \frac{i c^{4} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} - \frac{2 i c^{4} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} - \frac{2 \left(-1\right)^{\frac{3}{4}} c^{3} x \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} \operatorname{atan}{\left(c x^{2} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} + \frac{2 i c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} - \frac{i c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} - \frac{2 i c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{3}{2}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} + \frac{2 c x^{4} \operatorname{atan}{\left(c x^{2} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{5} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} + \frac{2 \operatorname{atan}{\left(c x^{2} \right)}}{- 2 \left(-1\right)^{\frac{3}{4}} c^{6} x^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}} - 2 \left(-1\right)^{\frac{3}{4}} c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{7}{4}}} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-x*atan((-sqrt(2)/2 - sqrt(2)*I/2)**(-2)), Eq(c, -1/(x**2*(-sqrt(2)/2 - sqrt(2)*I/2)**2))), (-x*atan((-sqrt(2)/2 + sqrt(2)*I/2)**(-2)), Eq(c, -1/(x**2*(-sqrt(2)/2 + sqrt(2)*I/2)**2))), (-x*atan((sqrt(2)/2 - sqrt(2)*I/2)**(-2)), Eq(c, -1/(x**2*(sqrt(2)/2 - sqrt(2)*I/2)**2))), (-x*atan((sqrt(2)/2 + sqrt(2)*I/2)**(-2)), Eq(c, -1/(x**2*(sqrt(2)/2 + sqrt(2)*I/2)**2))), (0, Eq(c, 0)), (-2*(-1)**(3/4)*c**5*x**5*(c**(-2))**(7/4)*atan(c*x**2)/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) + 2*I*c**4*x**4*(c**(-2))**(3/2)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) - I*c**4*x**4*(c**(-2))**(3/2)*log(x**2 + I*sqrt(c**(-2)))/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) - 2*I*c**4*x**4*(c**(-2))**(3/2)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) - 2*(-1)**(3/4)*c**3*x*(c**(-2))**(7/4)*atan(c*x**2)/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) + 2*I*c**2*(c**(-2))**(3/2)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) - I*c**2*(c**(-2))**(3/2)*log(x**2 + I*sqrt(c**(-2)))/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) - 2*I*c**2*(c**(-2))**(3/2)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) + 2*c*x**4*atan(c*x**2)/(-2*(-1)**(3/4)*c**5*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**3*(c**(-2))**(7/4)) + 2*atan(c*x**2)/(-2*(-1)**(3/4)*c**6*x**4*(c**(-2))**(7/4) - 2*(-1)**(3/4)*c**4*(c**(-2))**(7/4)), True))","A",0
71,1,151,0,20.442914," ","integrate((a+b*atan(c*x**2))/x**2,x)","\begin{cases} - \frac{a}{x} - \sqrt[4]{-1} b c \sqrt[4]{\frac{1}{c^{2}}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)} + \frac{\sqrt[4]{-1} b c \sqrt[4]{\frac{1}{c^{2}}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2} - \sqrt[4]{-1} b c \sqrt[4]{\frac{1}{c^{2}}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)} + \frac{\left(-1\right)^{\frac{3}{4}} b \operatorname{atan}{\left(c x^{2} \right)}}{\sqrt[4]{\frac{1}{c^{2}}}} - \frac{b \operatorname{atan}{\left(c x^{2} \right)}}{x} & \text{for}\: c \neq 0 \\- \frac{a}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x - (-1)**(1/4)*b*c*(c**(-2))**(1/4)*log(x - (-1)**(1/4)*(c**(-2))**(1/4)) + (-1)**(1/4)*b*c*(c**(-2))**(1/4)*log(x**2 + I*sqrt(c**(-2)))/2 - (-1)**(1/4)*b*c*(c**(-2))**(1/4)*atan((-1)**(3/4)*x/(c**(-2))**(1/4)) + (-1)**(3/4)*b*atan(c*x**2)/(c**(-2))**(1/4) - b*atan(c*x**2)/x, Ne(c, 0)), (-a/x, True))","A",0
72,1,590,0,38.521142," ","integrate((a+b*atan(c*x**2))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} & \text{for}\: c = 0 \\- \frac{a - \infty i b}{3 x^{3}} & \text{for}\: c = - \frac{i}{x^{2}} \\- \frac{a + \infty i b}{3 x^{3}} & \text{for}\: c = \frac{i}{x^{2}} \\- \frac{2 a x^{4}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{2 a}{6 c^{2} x^{7} + 6 x^{3}} + \frac{2 \left(-1\right)^{\frac{3}{4}} b c^{3} x^{7} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{\left(-1\right)^{\frac{3}{4}} b c^{3} x^{7} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{2 \left(-1\right)^{\frac{3}{4}} b c^{3} x^{7} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} + \frac{2 \sqrt[4]{-1} b c^{2} x^{7} \sqrt[4]{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{4 b c x^{6}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} + \frac{2 \left(-1\right)^{\frac{3}{4}} b c x^{3} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{\left(-1\right)^{\frac{3}{4}} b c x^{3} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{2 \left(-1\right)^{\frac{3}{4}} b c x^{3} \left(\frac{1}{c^{2}}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{2 b x^{4} \operatorname{atan}{\left(c x^{2} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} + \frac{2 \sqrt[4]{-1} b x^{3} \sqrt[4]{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{6 x^{7} + \frac{6 x^{3}}{c^{2}}} - \frac{4 b x^{2}}{6 c x^{7} + \frac{6 x^{3}}{c}} - \frac{2 b \operatorname{atan}{\left(c x^{2} \right)}}{6 c^{2} x^{7} + 6 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3), Eq(c, 0)), (-(a - oo*I*b)/(3*x**3), Eq(c, -I/x**2)), (-(a + oo*I*b)/(3*x**3), Eq(c, I/x**2)), (-2*a*x**4/(6*x**7 + 6*x**3/c**2) - 2*a/(6*c**2*x**7 + 6*x**3) + 2*(-1)**(3/4)*b*c**3*x**7*(c**(-2))**(3/4)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(6*x**7 + 6*x**3/c**2) - (-1)**(3/4)*b*c**3*x**7*(c**(-2))**(3/4)*log(x**2 + I*sqrt(c**(-2)))/(6*x**7 + 6*x**3/c**2) - 2*(-1)**(3/4)*b*c**3*x**7*(c**(-2))**(3/4)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(6*x**7 + 6*x**3/c**2) + 2*(-1)**(1/4)*b*c**2*x**7*(c**(-2))**(1/4)*atan(c*x**2)/(6*x**7 + 6*x**3/c**2) - 4*b*c*x**6/(6*x**7 + 6*x**3/c**2) + 2*(-1)**(3/4)*b*c*x**3*(c**(-2))**(3/4)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/(6*x**7 + 6*x**3/c**2) - (-1)**(3/4)*b*c*x**3*(c**(-2))**(3/4)*log(x**2 + I*sqrt(c**(-2)))/(6*x**7 + 6*x**3/c**2) - 2*(-1)**(3/4)*b*c*x**3*(c**(-2))**(3/4)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/(6*x**7 + 6*x**3/c**2) - 2*b*x**4*atan(c*x**2)/(6*x**7 + 6*x**3/c**2) + 2*(-1)**(1/4)*b*x**3*(c**(-2))**(1/4)*atan(c*x**2)/(6*x**7 + 6*x**3/c**2) - 4*b*x**2/(6*c*x**7 + 6*x**3/c) - 2*b*atan(c*x**2)/(6*c**2*x**7 + 6*x**3), True))","A",0
73,1,185,0,63.233600," ","integrate((a+b*atan(c*x**2))/x**6,x)","\begin{cases} - \frac{a}{5 x^{5}} + \frac{\sqrt[4]{-1} b c^{3} \sqrt[4]{\frac{1}{c^{2}}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{c^{2}}} \right)}}{5} - \frac{\sqrt[4]{-1} b c^{3} \sqrt[4]{\frac{1}{c^{2}}} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{10} + \frac{\sqrt[4]{-1} b c^{3} \sqrt[4]{\frac{1}{c^{2}}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{c^{2}}}} \right)}}{5} - \frac{\left(-1\right)^{\frac{3}{4}} b c^{2} \operatorname{atan}{\left(c x^{2} \right)}}{5 \sqrt[4]{\frac{1}{c^{2}}}} - \frac{2 b c}{15 x^{3}} - \frac{b \operatorname{atan}{\left(c x^{2} \right)}}{5 x^{5}} & \text{for}\: c \neq 0 \\- \frac{a}{5 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(5*x**5) + (-1)**(1/4)*b*c**3*(c**(-2))**(1/4)*log(x - (-1)**(1/4)*(c**(-2))**(1/4))/5 - (-1)**(1/4)*b*c**3*(c**(-2))**(1/4)*log(x**2 + I*sqrt(c**(-2)))/10 + (-1)**(1/4)*b*c**3*(c**(-2))**(1/4)*atan((-1)**(3/4)*x/(c**(-2))**(1/4))/5 - (-1)**(3/4)*b*c**2*atan(c*x**2)/(5*(c**(-2))**(1/4)) - 2*b*c/(15*x**3) - b*atan(c*x**2)/(5*x**5), Ne(c, 0)), (-a/(5*x**5), True))","A",0
74,1,199,0,98.996270," ","integrate(x**7*(a+b*atan(c*x**2))**2,x)","\begin{cases} \frac{a^{2} x^{8}}{8} + \frac{a b x^{8} \operatorname{atan}{\left(c x^{2} \right)}}{4} - \frac{a b x^{6}}{12 c} + \frac{a b x^{2}}{4 c^{3}} - \frac{a b \operatorname{atan}{\left(c x^{2} \right)}}{4 c^{4}} + \frac{b^{2} x^{8} \operatorname{atan}^{2}{\left(c x^{2} \right)}}{8} - \frac{b^{2} x^{6} \operatorname{atan}{\left(c x^{2} \right)}}{12 c} + \frac{b^{2} x^{4}}{24 c^{2}} + \frac{b^{2} x^{2} \operatorname{atan}{\left(c x^{2} \right)}}{4 c^{3}} - \frac{i b^{2} \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{3 c^{3}} - \frac{b^{2} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{3 c^{4}} - \frac{b^{2} \operatorname{atan}^{2}{\left(c x^{2} \right)}}{8 c^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**8/8 + a*b*x**8*atan(c*x**2)/4 - a*b*x**6/(12*c) + a*b*x**2/(4*c**3) - a*b*atan(c*x**2)/(4*c**4) + b**2*x**8*atan(c*x**2)**2/8 - b**2*x**6*atan(c*x**2)/(12*c) + b**2*x**4/(24*c**2) + b**2*x**2*atan(c*x**2)/(4*c**3) - I*b**2*sqrt(c**(-2))*atan(c*x**2)/(3*c**3) - b**2*log(x**2 + I*sqrt(c**(-2)))/(3*c**4) - b**2*atan(c*x**2)**2/(8*c**4), Ne(c, 0)), (a**2*x**8/8, True))","A",0
75,0,0,0,0.000000," ","integrate(x**5*(a+b*atan(c*x**2))**2,x)","\int x^{5} \left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral(x**5*(a + b*atan(c*x**2))**2, x)","F",0
76,1,155,0,34.914121," ","integrate(x**3*(a+b*atan(c*x**2))**2,x)","\begin{cases} \frac{a^{2} x^{4}}{4} + \frac{a b x^{4} \operatorname{atan}{\left(c x^{2} \right)}}{2} - \frac{a b x^{2}}{2 c} + \frac{a b \operatorname{atan}{\left(c x^{2} \right)}}{2 c^{2}} + \frac{b^{2} x^{4} \operatorname{atan}^{2}{\left(c x^{2} \right)}}{4} - \frac{b^{2} x^{2} \operatorname{atan}{\left(c x^{2} \right)}}{2 c} + \frac{i b^{2} \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{2} \right)}}{2 c} + \frac{b^{2} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2 c^{2}} + \frac{b^{2} \operatorname{atan}^{2}{\left(c x^{2} \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**4/4 + a*b*x**4*atan(c*x**2)/2 - a*b*x**2/(2*c) + a*b*atan(c*x**2)/(2*c**2) + b**2*x**4*atan(c*x**2)**2/4 - b**2*x**2*atan(c*x**2)/(2*c) + I*b**2*sqrt(c**(-2))*atan(c*x**2)/(2*c) + b**2*log(x**2 + I*sqrt(c**(-2)))/(2*c**2) + b**2*atan(c*x**2)**2/(4*c**2), Ne(c, 0)), (a**2*x**4/4, True))","A",0
77,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x**2))**2,x)","\int x \left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*atan(c*x**2))**2, x)","F",0
78,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**2/x, x)","F",0
79,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**2/x**3, x)","F",0
80,1,167,0,52.407726," ","integrate((a+b*atan(c*x**2))**2/x**5,x)","\begin{cases} - \frac{a^{2}}{4 x^{4}} - \frac{a b c^{2} \operatorname{atan}{\left(c x^{2} \right)}}{2} - \frac{a b c}{2 x^{2}} - \frac{a b \operatorname{atan}{\left(c x^{2} \right)}}{2 x^{4}} + b^{2} c^{2} \log{\left(x \right)} - \frac{b^{2} c^{2} \log{\left(x^{2} + i \sqrt{\frac{1}{c^{2}}} \right)}}{2} - \frac{b^{2} c^{2} \operatorname{atan}^{2}{\left(c x^{2} \right)}}{4} - \frac{i b^{2} c \operatorname{atan}{\left(c x^{2} \right)}}{2 \sqrt{\frac{1}{c^{2}}}} - \frac{b^{2} c \operatorname{atan}{\left(c x^{2} \right)}}{2 x^{2}} - \frac{b^{2} \operatorname{atan}^{2}{\left(c x^{2} \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(4*x**4) - a*b*c**2*atan(c*x**2)/2 - a*b*c/(2*x**2) - a*b*atan(c*x**2)/(2*x**4) + b**2*c**2*log(x) - b**2*c**2*log(x**2 + I*sqrt(c**(-2)))/2 - b**2*c**2*atan(c*x**2)**2/4 - I*b**2*c*atan(c*x**2)/(2*sqrt(c**(-2))) - b**2*c*atan(c*x**2)/(2*x**2) - b**2*atan(c*x**2)**2/(4*x**4), Ne(c, 0)), (-a**2/(4*x**4), True))","A",0
81,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x**2))**2,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x**2))**2, x)","F",0
82,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**2, x)","F",0
83,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**2/x**2, x)","F",0
84,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**2/x**4, x)","F",0
85,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**2/x**6,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{2}}{x^{6}}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**2/x**6, x)","F",0
86,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x**2))**3,x)","\int x^{3} \left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x**2))**3, x)","F",0
87,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x**2))**3,x)","\int x \left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*atan(c*x**2))**3, x)","F",0
88,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**3/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**3/x, x)","F",0
89,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**3/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**3/x**3, x)","F",0
90,0,0,0,0.000000," ","integrate((a+b*atan(c*x**2))**3/x**5,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{2} \right)}\right)^{3}}{x^{5}}\, dx"," ",0,"Integral((a + b*atan(c*x**2))**3/x**5, x)","F",0
91,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x**2))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x**2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x**2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atan(c*x**2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atan(c*x**2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(x**11*(a+b*atan(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,1,133,0,177.260081," ","integrate(x**8*(a+b*atan(c*x**3)),x)","\begin{cases} \frac{a x^{9}}{9} + \frac{b x^{9} \operatorname{atan}{\left(c x^{3} \right)}}{9} - \frac{b x^{6}}{18 c} - \frac{i b \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{3} \right)}}{9 c^{2}} + \frac{b \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{9 c^{3}} + \frac{b \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{9 c^{3}} & \text{for}\: c \neq 0 \\\frac{a x^{9}}{9} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**9/9 + b*x**9*atan(c*x**3)/9 - b*x**6/(18*c) - I*b*sqrt(c**(-2))*atan(c*x**3)/(9*c**2) + b*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(9*c**3) + b*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(9*c**3), Ne(c, 0)), (a*x**9/9, True))","A",0
98,1,48,0,89.852705," ","integrate(x**5*(a+b*atan(c*x**3)),x)","\begin{cases} \frac{a x^{6}}{6} + \frac{b x^{6} \operatorname{atan}{\left(c x^{3} \right)}}{6} - \frac{b x^{3}}{6 c} + \frac{b \operatorname{atan}{\left(c x^{3} \right)}}{6 c^{2}} & \text{for}\: c \neq 0 \\\frac{a x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**6/6 + b*x**6*atan(c*x**3)/6 - b*x**3/(6*c) + b*atan(c*x**3)/(6*c**2), Ne(c, 0)), (a*x**6/6, True))","A",0
99,1,117,0,47.589390," ","integrate(x**2*(a+b*atan(c*x**3)),x)","\begin{cases} \frac{a x^{3}}{3} + \frac{b x^{3} \operatorname{atan}{\left(c x^{3} \right)}}{3} + \frac{i b \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{3} \right)}}{3} - \frac{b \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{3 c} - \frac{b \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{3 c} & \text{for}\: c \neq 0 \\\frac{a x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**3/3 + b*x**3*atan(c*x**3)/3 + I*b*sqrt(c**(-2))*atan(c*x**3)/3 - b*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(3*c) - b*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(3*c), Ne(c, 0)), (a*x**3/3, True))","A",0
100,0,0,0,0.000000," ","integrate((a+b*atan(c*x**3))/x,x)","\int \frac{a + b \operatorname{atan}{\left(c x^{3} \right)}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x**3))/x, x)","F",0
101,1,126,0,96.086149," ","integrate((a+b*atan(c*x**3))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} + b c \log{\left(x \right)} - \frac{b c \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{3} - \frac{b c \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{3} + \frac{i b \operatorname{atan}{\left(c x^{3} \right)}}{3 \sqrt{\frac{1}{c^{2}}}} - \frac{b \operatorname{atan}{\left(c x^{3} \right)}}{3 x^{3}} & \text{for}\: c \neq 0 \\- \frac{a}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3) + b*c*log(x) - b*c*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/3 - b*c*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/3 + I*b*atan(c*x**3)/(3*sqrt(c**(-2))) - b*atan(c*x**3)/(3*x**3), Ne(c, 0)), (-a/(3*x**3), True))","A",0
102,1,42,0,88.004939," ","integrate((a+b*atan(c*x**3))/x**7,x)","- \frac{a}{6 x^{6}} - \frac{b c^{2} \operatorname{atan}{\left(c x^{3} \right)}}{6} - \frac{b c}{6 x^{3}} - \frac{b \operatorname{atan}{\left(c x^{3} \right)}}{6 x^{6}}"," ",0,"-a/(6*x**6) - b*c**2*atan(c*x**3)/6 - b*c/(6*x**3) - b*atan(c*x**3)/(6*x**6)","A",0
103,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**3))/x**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,1,311,0,58.102568," ","integrate(x**3*(a+b*atan(c*x**3)),x)","\begin{cases} \frac{a x^{4}}{4} + \frac{b x^{4} \operatorname{atan}{\left(c x^{3} \right)}}{4} - \frac{3 b x}{4 c} - \frac{3 \sqrt[6]{-1} b \sqrt[6]{\frac{1}{c^{2}}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{16 c} + \frac{3 \sqrt[6]{-1} b \sqrt[6]{\frac{1}{c^{2}}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{16 c} - \frac{\sqrt[6]{-1} \sqrt{3} b \sqrt[6]{\frac{1}{c^{2}}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{8 c} - \frac{\sqrt[6]{-1} \sqrt{3} b \sqrt[6]{\frac{1}{c^{2}}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{8 c} - \frac{\left(-1\right)^{\frac{2}{3}} b \operatorname{atan}{\left(c x^{3} \right)}}{4 c^{2} \sqrt[3]{\frac{1}{c^{2}}}} & \text{for}\: c \neq 0 \\\frac{a x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**4/4 + b*x**4*atan(c*x**3)/4 - 3*b*x/(4*c) - 3*(-1)**(1/6)*b*(c**(-2))**(1/6)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(16*c) + 3*(-1)**(1/6)*b*(c**(-2))**(1/6)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(16*c) - (-1)**(1/6)*sqrt(3)*b*(c**(-2))**(1/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(8*c) - (-1)**(1/6)*sqrt(3)*b*(c**(-2))**(1/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(8*c) - (-1)**(2/3)*b*atan(c*x**3)/(4*c**2*(c**(-2))**(1/3)), Ne(c, 0)), (a*x**4/4, True))","A",0
105,1,898,0,31.243430," ","integrate(a+b*atan(c*x**3),x)","a x + b \left(\begin{cases} 0 & \text{for}\: c = 0 \\- \infty i x & \text{for}\: c = - \frac{i}{x^{3}} \\\infty i x & \text{for}\: c = \frac{i}{x^{3}} \\\frac{4 \left(-1\right)^{\frac{2}{3}} c^{4} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{4 c x^{6} + \frac{4}{c}} - \frac{3 \left(-1\right)^{\frac{2}{3}} c^{4} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{\left(-1\right)^{\frac{2}{3}} c^{4} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} c^{4} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{4 c x^{6} + \frac{4}{c}} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} c^{4} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{4 \left(-1\right)^{\frac{2}{3}} c^{4} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(2 \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{4 \sqrt[6]{-1} c^{3} x^{6} \left(\frac{1}{c^{2}}\right)^{\frac{7}{6}} \operatorname{atan}{\left(c x^{3} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{4 \left(-1\right)^{\frac{2}{3}} c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{4 c x^{6} + \frac{4}{c}} - \frac{3 \left(-1\right)^{\frac{2}{3}} c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{\left(-1\right)^{\frac{2}{3}} c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{4 c x^{6} + \frac{4}{c}} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{4 \left(-1\right)^{\frac{2}{3}} c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{5}{3}} \log{\left(2 \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{4 c x^{7} \operatorname{atan}{\left(c x^{3} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{4 \sqrt[6]{-1} c \left(\frac{1}{c^{2}}\right)^{\frac{7}{6}} \operatorname{atan}{\left(c x^{3} \right)}}{4 c x^{6} + \frac{4}{c}} + \frac{4 x \operatorname{atan}{\left(c x^{3} \right)}}{4 c^{2} x^{6} + 4} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((0, Eq(c, 0)), (-oo*I*x, Eq(c, -I/x**3)), (oo*I*x, Eq(c, I/x**3)), (4*(-1)**(2/3)*c**4*x**6*(c**(-2))**(5/3)*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(4*c*x**6 + 4/c) - 3*(-1)**(2/3)*c**4*x**6*(c**(-2))**(5/3)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(4*c*x**6 + 4/c) + (-1)**(2/3)*c**4*x**6*(c**(-2))**(5/3)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(4*c*x**6 + 4/c) + 2*(-1)**(2/3)*sqrt(3)*c**4*x**6*(c**(-2))**(5/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(4*c*x**6 + 4/c) - 2*(-1)**(2/3)*sqrt(3)*c**4*x**6*(c**(-2))**(5/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(4*c*x**6 + 4/c) + 4*(-1)**(2/3)*c**4*x**6*(c**(-2))**(5/3)*log(2)/(4*c*x**6 + 4/c) + 4*(-1)**(1/6)*c**3*x**6*(c**(-2))**(7/6)*atan(c*x**3)/(4*c*x**6 + 4/c) + 4*(-1)**(2/3)*c**2*(c**(-2))**(5/3)*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(4*c*x**6 + 4/c) - 3*(-1)**(2/3)*c**2*(c**(-2))**(5/3)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(4*c*x**6 + 4/c) + (-1)**(2/3)*c**2*(c**(-2))**(5/3)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(4*c*x**6 + 4/c) + 2*(-1)**(2/3)*sqrt(3)*c**2*(c**(-2))**(5/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(4*c*x**6 + 4/c) - 2*(-1)**(2/3)*sqrt(3)*c**2*(c**(-2))**(5/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(4*c*x**6 + 4/c) + 4*(-1)**(2/3)*c**2*(c**(-2))**(5/3)*log(2)/(4*c*x**6 + 4/c) + 4*c*x**7*atan(c*x**3)/(4*c*x**6 + 4/c) + 4*(-1)**(1/6)*c*(c**(-2))**(7/6)*atan(c*x**3)/(4*c*x**6 + 4/c) + 4*x*atan(c*x**3)/(4*c**2*x**6 + 4), True))","A",0
106,1,301,0,73.747209," ","integrate((a+b*atan(c*x**3))/x**3,x)","\begin{cases} - \frac{a}{2 x^{2}} - \frac{\left(-1\right)^{\frac{2}{3}} b \operatorname{atan}{\left(c x^{3} \right)}}{2 \sqrt[3]{\frac{1}{c^{2}}}} - \frac{b \operatorname{atan}{\left(c x^{3} \right)}}{2 x^{2}} - \frac{3 \sqrt[6]{-1} b \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 c \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}}} + \frac{3 \sqrt[6]{-1} b \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 c \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}}} - \frac{\sqrt[6]{-1} \sqrt{3} b \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}}} - \frac{\sqrt[6]{-1} \sqrt{3} b \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}}} & \text{for}\: c \neq 0 \\- \frac{a}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) - (-1)**(2/3)*b*atan(c*x**3)/(2*(c**(-2))**(1/3)) - b*atan(c*x**3)/(2*x**2) - 3*(-1)**(1/6)*b*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*c*(c**(-2))**(5/6)) + 3*(-1)**(1/6)*b*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*c*(c**(-2))**(5/6)) - (-1)**(1/6)*sqrt(3)*b*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(4*c*(c**(-2))**(5/6)) - (-1)**(1/6)*sqrt(3)*b*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(4*c*(c**(-2))**(5/6)), Ne(c, 0)), (-a/(2*x**2), True))","A",0
107,1,352,0,144.506331," ","integrate((a+b*atan(c*x**3))/x**6,x)","\begin{cases} - \frac{a}{5 x^{5}} + \frac{\sqrt[6]{-1} b c^{2} \sqrt[6]{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{3} \right)}}{5} + \frac{\left(-1\right)^{\frac{2}{3}} b c \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{5 \sqrt[3]{\frac{1}{c^{2}}}} - \frac{3 \left(-1\right)^{\frac{2}{3}} b c \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{20 \sqrt[3]{\frac{1}{c^{2}}}} + \frac{\left(-1\right)^{\frac{2}{3}} b c \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{20 \sqrt[3]{\frac{1}{c^{2}}}} + \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} b c \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{10 \sqrt[3]{\frac{1}{c^{2}}}} - \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} b c \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{10 \sqrt[3]{\frac{1}{c^{2}}}} - \frac{3 b c}{10 x^{2}} - \frac{b \operatorname{atan}{\left(c x^{3} \right)}}{5 x^{5}} & \text{for}\: c \neq 0 \\- \frac{a}{5 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(5*x**5) + (-1)**(1/6)*b*c**2*(c**(-2))**(1/6)*atan(c*x**3)/5 + (-1)**(2/3)*b*c*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(5*(c**(-2))**(1/3)) - 3*(-1)**(2/3)*b*c*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(20*(c**(-2))**(1/3)) + (-1)**(2/3)*b*c*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(20*(c**(-2))**(1/3)) + (-1)**(2/3)*sqrt(3)*b*c*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(10*(c**(-2))**(1/3)) - (-1)**(2/3)*sqrt(3)*b*c*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(10*(c**(-2))**(1/3)) - 3*b*c/(10*x**2) - b*atan(c*x**3)/(5*x**5), Ne(c, 0)), (-a/(5*x**5), True))","A",0
108,1,320,0,149.055937," ","integrate(x**7*(a+b*atan(c*x**3)),x)","\begin{cases} \frac{a x^{8}}{8} + \frac{b x^{8} \operatorname{atan}{\left(c x^{3} \right)}}{8} - \frac{3 b x^{5}}{40 c} - \frac{3 \left(-1\right)^{\frac{5}{6}} b \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{32 c^{3} \sqrt[6]{\frac{1}{c^{2}}}} + \frac{3 \left(-1\right)^{\frac{5}{6}} b \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{32 c^{3} \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\left(-1\right)^{\frac{5}{6}} \sqrt{3} b \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{16 c^{3} \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\left(-1\right)^{\frac{5}{6}} \sqrt{3} b \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{16 c^{3} \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt[3]{-1} b \operatorname{atan}{\left(c x^{3} \right)}}{8 c^{4} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}} & \text{for}\: c \neq 0 \\\frac{a x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**8/8 + b*x**8*atan(c*x**3)/8 - 3*b*x**5/(40*c) - 3*(-1)**(5/6)*b*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(32*c**3*(c**(-2))**(1/6)) + 3*(-1)**(5/6)*b*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(32*c**3*(c**(-2))**(1/6)) + (-1)**(5/6)*sqrt(3)*b*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(16*c**3*(c**(-2))**(1/6)) + (-1)**(5/6)*sqrt(3)*b*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(16*c**3*(c**(-2))**(1/6)) + (-1)**(1/3)*b*atan(c*x**3)/(8*c**4*(c**(-2))**(2/3)), Ne(c, 0)), (a*x**8/8, True))","A",0
109,1,359,0,71.604572," ","integrate(x**4*(a+b*atan(c*x**3)),x)","\begin{cases} \frac{a x^{5}}{5} - \frac{\sqrt[3]{-1} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{3}} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{5} + \frac{3 \sqrt[3]{-1} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{3}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{20} - \frac{\sqrt[3]{-1} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{3}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{20} + \frac{\sqrt[3]{-1} \sqrt{3} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{3}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{10} - \frac{\sqrt[3]{-1} \sqrt{3} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{7}{3}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{10} + \frac{\left(-1\right)^{\frac{5}{6}} b c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{11}{6}} \operatorname{atan}{\left(c x^{3} \right)}}{5} + \frac{b x^{5} \operatorname{atan}{\left(c x^{3} \right)}}{5} - \frac{3 b x^{2}}{10 c} & \text{for}\: c \neq 0 \\\frac{a x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**5/5 - (-1)**(1/3)*b*c**3*(c**(-2))**(7/3)*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/5 + 3*(-1)**(1/3)*b*c**3*(c**(-2))**(7/3)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/20 - (-1)**(1/3)*b*c**3*(c**(-2))**(7/3)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/20 + (-1)**(1/3)*sqrt(3)*b*c**3*(c**(-2))**(7/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/10 - (-1)**(1/3)*sqrt(3)*b*c**3*(c**(-2))**(7/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/10 + (-1)**(5/6)*b*c**2*(c**(-2))**(11/6)*atan(c*x**3)/5 + b*x**5*atan(c*x**3)/5 - 3*b*x**2/(10*c), Ne(c, 0)), (a*x**5/5, True))","A",0
110,1,303,0,39.659746," ","integrate(x*(a+b*atan(c*x**3)),x)","\begin{cases} \frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{atan}{\left(c x^{3} \right)}}{2} + \frac{3 \left(-1\right)^{\frac{5}{6}} b \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 c \sqrt[6]{\frac{1}{c^{2}}}} - \frac{3 \left(-1\right)^{\frac{5}{6}} b \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{8 c \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\left(-1\right)^{\frac{5}{6}} \sqrt{3} b \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{4 c \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\left(-1\right)^{\frac{5}{6}} \sqrt{3} b \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{4 c \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt[3]{-1} b \operatorname{atan}{\left(c x^{3} \right)}}{2 c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}} & \text{for}\: c \neq 0 \\\frac{a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**2/2 + b*x**2*atan(c*x**3)/2 + 3*(-1)**(5/6)*b*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*c*(c**(-2))**(1/6)) - 3*(-1)**(5/6)*b*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(8*c*(c**(-2))**(1/6)) - (-1)**(5/6)*sqrt(3)*b*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/(4*c*(c**(-2))**(1/6)) - (-1)**(5/6)*sqrt(3)*b*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/(4*c*(c**(-2))**(1/6)) - (-1)**(1/3)*b*atan(c*x**3)/(2*c**2*(c**(-2))**(2/3)), Ne(c, 0)), (a*x**2/2, True))","A",0
111,1,328,0,58.274258," ","integrate((a+b*atan(c*x**3))/x**2,x)","\begin{cases} - \frac{a}{x} + \left(-1\right)^{\frac{5}{6}} b c^{2} \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \operatorname{atan}{\left(c x^{3} \right)} - \sqrt[3]{-1} b c \sqrt[3]{\frac{1}{c^{2}}} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)} + \frac{3 \sqrt[3]{-1} b c \sqrt[3]{\frac{1}{c^{2}}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{4} - \frac{\sqrt[3]{-1} b c \sqrt[3]{\frac{1}{c^{2}}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{4} + \frac{\sqrt[3]{-1} \sqrt{3} b c \sqrt[3]{\frac{1}{c^{2}}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{2} - \frac{\sqrt[3]{-1} \sqrt{3} b c \sqrt[3]{\frac{1}{c^{2}}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{2} - \frac{b \operatorname{atan}{\left(c x^{3} \right)}}{x} & \text{for}\: c \neq 0 \\- \frac{a}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x + (-1)**(5/6)*b*c**2*(c**(-2))**(5/6)*atan(c*x**3) - (-1)**(1/3)*b*c*(c**(-2))**(1/3)*log(x - (-1)**(1/6)*(c**(-2))**(1/6)) + 3*(-1)**(1/3)*b*c*(c**(-2))**(1/3)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/4 - (-1)**(1/3)*b*c*(c**(-2))**(1/3)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/4 + (-1)**(1/3)*sqrt(3)*b*c*(c**(-2))**(1/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/2 - (-1)**(1/3)*sqrt(3)*b*c*(c**(-2))**(1/3)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/2 - b*atan(c*x**3)/x, Ne(c, 0)), (-a/x, True))","A",0
112,1,320,0,109.837682," ","integrate((a+b*atan(c*x**3))/x**5,x)","\begin{cases} - \frac{a}{4 x^{4}} + \frac{3 \left(-1\right)^{\frac{5}{6}} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \log{\left(4 x^{2} - 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{16} - \frac{3 \left(-1\right)^{\frac{5}{6}} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{16} - \frac{\left(-1\right)^{\frac{5}{6}} \sqrt{3} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} - \frac{\sqrt{3}}{3} \right)}}{8} - \frac{\left(-1\right)^{\frac{5}{6}} \sqrt{3} b c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \left(-1\right)^{\frac{5}{6}} \sqrt{3} x}{3 \sqrt[6]{\frac{1}{c^{2}}}} + \frac{\sqrt{3}}{3} \right)}}{8} - \frac{\sqrt[3]{-1} b c^{2} \sqrt[3]{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{3} \right)}}{4} - \frac{3 b c}{4 x} - \frac{b \operatorname{atan}{\left(c x^{3} \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(4*x**4) + 3*(-1)**(5/6)*b*c**3*(c**(-2))**(5/6)*log(4*x**2 - 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/16 - 3*(-1)**(5/6)*b*c**3*(c**(-2))**(5/6)*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/16 - (-1)**(5/6)*sqrt(3)*b*c**3*(c**(-2))**(5/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) - sqrt(3)/3)/8 - (-1)**(5/6)*sqrt(3)*b*c**3*(c**(-2))**(5/6)*atan(2*(-1)**(5/6)*sqrt(3)*x/(3*(c**(-2))**(1/6)) + sqrt(3)/3)/8 - (-1)**(1/3)*b*c**2*(c**(-2))**(1/3)*atan(c*x**3)/4 - 3*b*c/(4*x) - b*atan(c*x**3)/(4*x**4), Ne(c, 0)), (-a/(4*x**4), True))","A",0
113,-1,0,0,0.000000," ","integrate(x**11*(a+b*atan(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(x**8*(a+b*atan(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,1,209,0,122.135228," ","integrate(x**5*(a+b*atan(c*x**3))**2,x)","\begin{cases} \frac{a^{2} x^{6}}{6} + \frac{a b x^{6} \operatorname{atan}{\left(c x^{3} \right)}}{3} - \frac{a b x^{3}}{3 c} + \frac{a b \operatorname{atan}{\left(c x^{3} \right)}}{3 c^{2}} + \frac{b^{2} x^{6} \operatorname{atan}^{2}{\left(c x^{3} \right)}}{6} - \frac{b^{2} x^{3} \operatorname{atan}{\left(c x^{3} \right)}}{3 c} - \frac{i b^{2} \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{3} \right)}}{3 c} + \frac{b^{2} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{3 c^{2}} + \frac{b^{2} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{3 c^{2}} + \frac{b^{2} \operatorname{atan}^{2}{\left(c x^{3} \right)}}{6 c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**6/6 + a*b*x**6*atan(c*x**3)/3 - a*b*x**3/(3*c) + a*b*atan(c*x**3)/(3*c**2) + b**2*x**6*atan(c*x**3)**2/6 - b**2*x**3*atan(c*x**3)/(3*c) - I*b**2*sqrt(c**(-2))*atan(c*x**3)/(3*c) + b**2*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/(3*c**2) + b**2*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/(3*c**2) + b**2*atan(c*x**3)**2/(6*c**2), Ne(c, 0)), (a**2*x**6/6, True))","A",0
116,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x**3))**2,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x**3))**2, x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*atan(c*x**3))**2/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x**3))**2/x, x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*atan(c*x**3))**2/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x**3))**2/x**4, x)","F",0
119,1,223,0,173.365668," ","integrate((a+b*atan(c*x**3))**2/x**7,x)","\begin{cases} - \frac{a^{2}}{6 x^{6}} - \frac{a b c^{2} \operatorname{atan}{\left(c x^{3} \right)}}{3} - \frac{a b c}{3 x^{3}} - \frac{a b \operatorname{atan}{\left(c x^{3} \right)}}{3 x^{6}} + \frac{i b^{2} c^{3} \sqrt{\frac{1}{c^{2}}} \operatorname{atan}{\left(c x^{3} \right)}}{3} + b^{2} c^{2} \log{\left(x \right)} - \frac{b^{2} c^{2} \log{\left(x - \sqrt[6]{-1} \sqrt[6]{\frac{1}{c^{2}}} \right)}}{3} - \frac{b^{2} c^{2} \log{\left(4 x^{2} + 4 \sqrt[6]{-1} x \sqrt[6]{\frac{1}{c^{2}}} + 4 \sqrt[3]{-1} \sqrt[3]{\frac{1}{c^{2}}} \right)}}{3} - \frac{b^{2} c^{2} \operatorname{atan}^{2}{\left(c x^{3} \right)}}{6} - \frac{b^{2} c \operatorname{atan}{\left(c x^{3} \right)}}{3 x^{3}} - \frac{b^{2} \operatorname{atan}^{2}{\left(c x^{3} \right)}}{6 x^{6}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(6*x**6) - a*b*c**2*atan(c*x**3)/3 - a*b*c/(3*x**3) - a*b*atan(c*x**3)/(3*x**6) + I*b**2*c**3*sqrt(c**(-2))*atan(c*x**3)/3 + b**2*c**2*log(x) - b**2*c**2*log(x - (-1)**(1/6)*(c**(-2))**(1/6))/3 - b**2*c**2*log(4*x**2 + 4*(-1)**(1/6)*x*(c**(-2))**(1/6) + 4*(-1)**(1/3)*(c**(-2))**(1/3))/3 - b**2*c**2*atan(c*x**3)**2/6 - b**2*c*atan(c*x**3)/(3*x**3) - b**2*atan(c*x**3)**2/(6*x**6), Ne(c, 0)), (-a**2/(6*x**6), True))","A",0
120,-1,0,0,0.000000," ","integrate((a+b*atan(c*x**3))**2/x**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(x**8*(a+b*atan(c*x**3))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,0,0,0,0.000000," ","integrate(x**5*(a+b*atan(c*x**3))**3,x)","\int x^{5} \left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{3}\, dx"," ",0,"Integral(x**5*(a + b*atan(c*x**3))**3, x)","F",0
123,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x**3))**3,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x**3))**3, x)","F",0
124,0,0,0,0.000000," ","integrate((a+b*atan(c*x**3))**3/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x**3))**3/x, x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*atan(c*x**3))**3/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{3}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x**3))**3/x**4, x)","F",0
126,0,0,0,0.000000," ","integrate((a+b*atan(c*x**3))**3/x**7,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x^{3} \right)}\right)^{3}}{x^{7}}\, dx"," ",0,"Integral((a + b*atan(c*x**3))**3/x**7, x)","F",0
127,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x**3))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atan(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atan(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atan(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,1,46,0,0.495284," ","integrate(x**3*(a+b*atan(c/x)),x)","\frac{a x^{4}}{4} - \frac{b c^{4} \operatorname{atan}{\left(\frac{c}{x} \right)}}{4} - \frac{b c^{3} x}{4} + \frac{b c x^{3}}{12} + \frac{b x^{4} \operatorname{atan}{\left(\frac{c}{x} \right)}}{4}"," ",0,"a*x**4/4 - b*c**4*atan(c/x)/4 - b*c**3*x/4 + b*c*x**3/12 + b*x**4*atan(c/x)/4","A",0
133,1,41,0,0.367777," ","integrate(x**2*(a+b*atan(c/x)),x)","\frac{a x^{3}}{3} - \frac{b c^{3} \log{\left(c^{2} + x^{2} \right)}}{6} + \frac{b c x^{2}}{6} + \frac{b x^{3} \operatorname{atan}{\left(\frac{c}{x} \right)}}{3}"," ",0,"a*x**3/3 - b*c**3*log(c**2 + x**2)/6 + b*c*x**2/6 + b*x**3*atan(c/x)/3","A",0
134,1,36,0,0.288594," ","integrate(x*(a+b*atan(c/x)),x)","\frac{a x^{2}}{2} + \frac{b c^{2} \operatorname{atan}{\left(\frac{c}{x} \right)}}{2} + \frac{b c x}{2} + \frac{b x^{2} \operatorname{atan}{\left(\frac{c}{x} \right)}}{2}"," ",0,"a*x**2/2 + b*c**2*atan(c/x)/2 + b*c*x/2 + b*x**2*atan(c/x)/2","A",0
135,1,22,0,0.178405," ","integrate(a+b*atan(c/x),x)","a x + b \left(\frac{c \log{\left(c^{2} + x^{2} \right)}}{2} + x \operatorname{atan}{\left(\frac{c}{x} \right)}\right)"," ",0,"a*x + b*(c*log(c**2 + x**2)/2 + x*atan(c/x))","A",0
136,0,0,0,0.000000," ","integrate((a+b*atan(c/x))/x,x)","\int \frac{a + b \operatorname{atan}{\left(\frac{c}{x} \right)}}{x}\, dx"," ",0,"Integral((a + b*atan(c/x))/x, x)","F",0
137,1,36,0,0.645643," ","integrate((a+b*atan(c/x))/x**2,x)","\begin{cases} - \frac{a}{x} - \frac{b \operatorname{atan}{\left(\frac{c}{x} \right)}}{x} - \frac{b \log{\left(x \right)}}{c} + \frac{b \log{\left(c^{2} + x^{2} \right)}}{2 c} & \text{for}\: c \neq 0 \\- \frac{a}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x - b*atan(c/x)/x - b*log(x)/c + b*log(c**2 + x**2)/(2*c), Ne(c, 0)), (-a/x, True))","A",0
138,1,44,0,0.851348," ","integrate((a+b*atan(c/x))/x**3,x)","\begin{cases} - \frac{a}{2 x^{2}} - \frac{b \operatorname{atan}{\left(\frac{c}{x} \right)}}{2 x^{2}} + \frac{b}{2 c x} - \frac{b \operatorname{atan}{\left(\frac{c}{x} \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\- \frac{a}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) - b*atan(c/x)/(2*x**2) + b/(2*c*x) - b*atan(c/x)/(2*c**2), Ne(c, 0)), (-a/(2*x**2), True))","A",0
139,1,60,0,1.094907," ","integrate((a+b*atan(c/x))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} - \frac{b \operatorname{atan}{\left(\frac{c}{x} \right)}}{3 x^{3}} + \frac{b}{6 c x^{2}} + \frac{b \log{\left(x \right)}}{3 c^{3}} - \frac{b \log{\left(c^{2} + x^{2} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\- \frac{a}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3) - b*atan(c/x)/(3*x**3) + b/(6*c*x**2) + b*log(x)/(3*c**3) - b*log(c**2 + x**2)/(6*c**3), Ne(c, 0)), (-a/(3*x**3), True))","A",0
140,1,144,0,0.813590," ","integrate(x**3*(a+b*atan(c/x))**2,x)","\frac{a^{2} x^{4}}{4} - \frac{a b c^{4} \operatorname{atan}{\left(\frac{c}{x} \right)}}{2} - \frac{a b c^{3} x}{2} + \frac{a b c x^{3}}{6} + \frac{a b x^{4} \operatorname{atan}{\left(\frac{c}{x} \right)}}{2} - \frac{b^{2} c^{4} \log{\left(c^{2} + x^{2} \right)}}{3} - \frac{b^{2} c^{4} \operatorname{atan}^{2}{\left(\frac{c}{x} \right)}}{4} - \frac{b^{2} c^{3} x \operatorname{atan}{\left(\frac{c}{x} \right)}}{2} + \frac{b^{2} c^{2} x^{2}}{12} + \frac{b^{2} c x^{3} \operatorname{atan}{\left(\frac{c}{x} \right)}}{6} + \frac{b^{2} x^{4} \operatorname{atan}^{2}{\left(\frac{c}{x} \right)}}{4}"," ",0,"a**2*x**4/4 - a*b*c**4*atan(c/x)/2 - a*b*c**3*x/2 + a*b*c*x**3/6 + a*b*x**4*atan(c/x)/2 - b**2*c**4*log(c**2 + x**2)/3 - b**2*c**4*atan(c/x)**2/4 - b**2*c**3*x*atan(c/x)/2 + b**2*c**2*x**2/12 + b**2*c*x**3*atan(c/x)/6 + b**2*x**4*atan(c/x)**2/4","A",0
141,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c/x))**2,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atan(c/x))**2, x)","F",0
142,1,97,0,0.444997," ","integrate(x*(a+b*atan(c/x))**2,x)","\frac{a^{2} x^{2}}{2} + a b c^{2} \operatorname{atan}{\left(\frac{c}{x} \right)} + a b c x + a b x^{2} \operatorname{atan}{\left(\frac{c}{x} \right)} + \frac{b^{2} c^{2} \log{\left(c^{2} + x^{2} \right)}}{2} + \frac{b^{2} c^{2} \operatorname{atan}^{2}{\left(\frac{c}{x} \right)}}{2} + b^{2} c x \operatorname{atan}{\left(\frac{c}{x} \right)} + \frac{b^{2} x^{2} \operatorname{atan}^{2}{\left(\frac{c}{x} \right)}}{2}"," ",0,"a**2*x**2/2 + a*b*c**2*atan(c/x) + a*b*c*x + a*b*x**2*atan(c/x) + b**2*c**2*log(c**2 + x**2)/2 + b**2*c**2*atan(c/x)**2/2 + b**2*c*x*atan(c/x) + b**2*x**2*atan(c/x)**2/2","A",0
143,0,0,0,0.000000," ","integrate((a+b*atan(c/x))**2,x)","\int \left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atan(c/x))**2, x)","F",0
144,0,0,0,0.000000," ","integrate((a+b*atan(c/x))**2/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atan(c/x))**2/x, x)","F",0
145,0,0,0,0.000000," ","integrate((a+b*atan(c/x))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c/x))**2/x**2, x)","F",0
146,1,117,0,1.043777," ","integrate((a+b*atan(c/x))**2/x**3,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} - \frac{a b \operatorname{atan}{\left(\frac{c}{x} \right)}}{x^{2}} + \frac{a b}{c x} - \frac{a b \operatorname{atan}{\left(\frac{c}{x} \right)}}{c^{2}} - \frac{b^{2} \operatorname{atan}^{2}{\left(\frac{c}{x} \right)}}{2 x^{2}} + \frac{b^{2} \operatorname{atan}{\left(\frac{c}{x} \right)}}{c x} + \frac{b^{2} \log{\left(x \right)}}{c^{2}} - \frac{b^{2} \log{\left(c^{2} + x^{2} \right)}}{2 c^{2}} - \frac{b^{2} \operatorname{atan}^{2}{\left(\frac{c}{x} \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2) - a*b*atan(c/x)/x**2 + a*b/(c*x) - a*b*atan(c/x)/c**2 - b**2*atan(c/x)**2/(2*x**2) + b**2*atan(c/x)/(c*x) + b**2*log(x)/c**2 - b**2*log(c**2 + x**2)/(2*c**2) - b**2*atan(c/x)**2/(2*c**2), Ne(c, 0)), (-a**2/(2*x**2), True))","A",0
147,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c/x))**3,x)","\int x^{3} \left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*atan(c/x))**3, x)","F",0
148,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c/x))**3,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*atan(c/x))**3, x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*atan(c/x))**3,x)","\int x \left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*atan(c/x))**3, x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*atan(c/x))**3,x)","\int \left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*atan(c/x))**3, x)","F",0
151,0,0,0,0.000000," ","integrate((a+b*atan(c/x))**3/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atan(c/x))**3/x, x)","F",0
152,0,0,0,0.000000," ","integrate((a+b*atan(c/x))**3/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c/x))**3/x**2, x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*atan(c/x))**3/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(\frac{c}{x} \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c/x))**3/x**3, x)","F",0
154,1,39,0,1.969411," ","integrate(x**2*atan(x**(1/2)),x)","- \frac{x^{\frac{5}{2}}}{15} + \frac{x^{\frac{3}{2}}}{9} - \frac{\sqrt{x}}{3} + \frac{x^{3} \operatorname{atan}{\left(\sqrt{x} \right)}}{3} + \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{3}"," ",0,"-x**(5/2)/15 + x**(3/2)/9 - sqrt(x)/3 + x**3*atan(sqrt(x))/3 + atan(sqrt(x))/3","A",0
155,1,32,0,1.260511," ","integrate(x*atan(x**(1/2)),x)","- \frac{x^{\frac{3}{2}}}{6} + \frac{\sqrt{x}}{2} + \frac{x^{2} \operatorname{atan}{\left(\sqrt{x} \right)}}{2} - \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2}"," ",0,"-x**(3/2)/6 + sqrt(x)/2 + x**2*atan(sqrt(x))/2 - atan(sqrt(x))/2","A",0
156,1,19,0,1.147039," ","integrate(atan(x**(1/2)),x)","- \sqrt{x} + x \operatorname{atan}{\left(\sqrt{x} \right)} + \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"-sqrt(x) + x*atan(sqrt(x)) + atan(sqrt(x))","A",0
157,0,0,0,0.000000," ","integrate(atan(x**(1/2))/x,x)","\int \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{x}\, dx"," ",0,"Integral(atan(sqrt(x))/x, x)","F",0
158,1,94,0,1.917047," ","integrate(atan(x**(1/2))/x**2,x)","- \frac{x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} - \frac{2 x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} - \frac{\sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} - \frac{x^{2}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} - \frac{x}{x^{\frac{5}{2}} + x^{\frac{3}{2}}}"," ",0,"-x**(5/2)*atan(sqrt(x))/(x**(5/2) + x**(3/2)) - 2*x**(3/2)*atan(sqrt(x))/(x**(5/2) + x**(3/2)) - sqrt(x)*atan(sqrt(x))/(x**(5/2) + x**(3/2)) - x**2/(x**(5/2) + x**(3/2)) - x/(x**(5/2) + x**(3/2))","B",0
159,1,160,0,4.918977," ","integrate(atan(x**(1/2))/x**3,x)","\frac{3 x^{\frac{7}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} + \frac{3 x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} - \frac{3 x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} - \frac{3 \sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} + \frac{3 x^{3}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} + \frac{2 x^{2}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} - \frac{x}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}}"," ",0,"3*x**(7/2)*atan(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) + 3*x**(5/2)*atan(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) - 3*x**(3/2)*atan(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) - 3*sqrt(x)*atan(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) + 3*x**3/(6*x**(7/2) + 6*x**(5/2)) + 2*x**2/(6*x**(7/2) + 6*x**(5/2)) - x/(6*x**(7/2) + 6*x**(5/2))","B",0
160,1,85,0,4.793329," ","integrate(x**(3/2)*atan(x**(1/2)),x)","\frac{4 x^{\frac{7}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{10 x + 10} + \frac{4 x^{\frac{5}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{10 x + 10} - \frac{x^{3}}{10 x + 10} + \frac{x^{2}}{10 x + 10} - \frac{2 x \log{\left(x + 1 \right)}}{10 x + 10} - \frac{2 \log{\left(x + 1 \right)}}{10 x + 10} - \frac{2}{10 x + 10}"," ",0,"4*x**(7/2)*atan(sqrt(x))/(10*x + 10) + 4*x**(5/2)*atan(sqrt(x))/(10*x + 10) - x**3/(10*x + 10) + x**2/(10*x + 10) - 2*x*log(x + 1)/(10*x + 10) - 2*log(x + 1)/(10*x + 10) - 2/(10*x + 10)","B",0
161,1,24,0,1.238605," ","integrate(x**(1/2)*atan(x**(1/2)),x)","\frac{2 x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{3} - \frac{x}{3} + \frac{\log{\left(x + 1 \right)}}{3}"," ",0,"2*x**(3/2)*atan(sqrt(x))/3 - x/3 + log(x + 1)/3","A",0
162,1,17,0,0.325329," ","integrate(atan(x**(1/2))/x**(1/2),x)","2 \sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)} - \log{\left(x + 1 \right)}"," ",0,"2*sqrt(x)*atan(sqrt(x)) - log(x + 1)","A",0
163,1,20,0,1.155011," ","integrate(atan(x**(1/2))/x**(3/2),x)","\log{\left(x \right)} - \log{\left(x + 1 \right)} - \frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{\sqrt{x}}"," ",0,"log(x) - log(x + 1) - 2*atan(sqrt(x))/sqrt(x)","A",0
164,1,143,0,4.896606," ","integrate(atan(x**(1/2))/x**(5/2),x)","- \frac{2 x^{\frac{3}{2}} \operatorname{atan}{\left(\sqrt{x} \right)}}{3 x^{3} + 3 x^{2}} - \frac{2 \sqrt{x} \operatorname{atan}{\left(\sqrt{x} \right)}}{3 x^{3} + 3 x^{2}} - \frac{x^{3} \log{\left(x \right)}}{3 x^{3} + 3 x^{2}} + \frac{x^{3} \log{\left(x + 1 \right)}}{3 x^{3} + 3 x^{2}} - \frac{x^{2} \log{\left(x \right)}}{3 x^{3} + 3 x^{2}} + \frac{x^{2} \log{\left(x + 1 \right)}}{3 x^{3} + 3 x^{2}} - \frac{x^{2}}{3 x^{3} + 3 x^{2}} - \frac{x}{3 x^{3} + 3 x^{2}}"," ",0,"-2*x**(3/2)*atan(sqrt(x))/(3*x**3 + 3*x**2) - 2*sqrt(x)*atan(sqrt(x))/(3*x**3 + 3*x**2) - x**3*log(x)/(3*x**3 + 3*x**2) + x**3*log(x + 1)/(3*x**3 + 3*x**2) - x**2*log(x)/(3*x**3 + 3*x**2) + x**2*log(x + 1)/(3*x**3 + 3*x**2) - x**2/(3*x**3 + 3*x**2) - x/(3*x**3 + 3*x**2)","B",0
165,0,0,0,0.000000," ","integrate(atan(a*x**5)/x,x)","\int \frac{\operatorname{atan}{\left(a x^{5} \right)}}{x}\, dx"," ",0,"Integral(atan(a*x**5)/x, x)","F",0
166,0,0,0,0.000000," ","integrate(atan(a*x**n)/x,x)","\int \frac{\operatorname{atan}{\left(a x^{n} \right)}}{x}\, dx"," ",0,"Integral(atan(a*x**n)/x, x)","F",0
