1,1,184,0,3.396596," ","integrate(x**3*(d+I*c*d*x)*(a+b*atan(c*x)),x)","\frac{i a c d x^{5}}{5} - \frac{b d x^{3}}{12 c} + \frac{i b d x^{2}}{10 c^{2}} + \frac{b d x}{4 c^{3}} + \frac{b d \left(\frac{i \log{\left(25 b c d x - 25 i b d \right)}}{40} - \frac{11 i \log{\left(25 b c d x + 25 i b d \right)}}{60}\right)}{c^{4}} + x^{4} \left(\frac{a d}{4} - \frac{i b d}{20}\right) + \left(\frac{b c d x^{5}}{10} - \frac{i b d x^{4}}{8}\right) \log{\left(i c x + 1 \right)} - \frac{\left(12 b c^{5} d x^{5} - 15 i b c^{4} d x^{4} + 5 i b d\right) \log{\left(- i c x + 1 \right)}}{120 c^{4}}"," ",0,"I*a*c*d*x**5/5 - b*d*x**3/(12*c) + I*b*d*x**2/(10*c**2) + b*d*x/(4*c**3) + b*d*(I*log(25*b*c*d*x - 25*I*b*d)/40 - 11*I*log(25*b*c*d*x + 25*I*b*d)/60)/c**4 + x**4*(a*d/4 - I*b*d/20) + (b*c*d*x**5/10 - I*b*d*x**4/8)*log(I*c*x + 1) - (12*b*c**5*d*x**5 - 15*I*b*c**4*d*x**4 + 5*I*b*d)*log(-I*c*x + 1)/(120*c**4)","A",0
2,1,167,0,3.081284," ","integrate(x**2*(d+I*c*d*x)*(a+b*atan(c*x)),x)","\frac{i a c d x^{4}}{4} - \frac{b d x^{2}}{6 c} + \frac{i b d x}{4 c^{2}} + \frac{b d \left(\frac{\log{\left(11 b c d x - 11 i b d \right)}}{24} + \frac{9 \log{\left(11 b c d x + 11 i b d \right)}}{40}\right)}{c^{3}} + x^{3} \left(\frac{a d}{3} - \frac{i b d}{12}\right) + \left(\frac{b c d x^{4}}{8} - \frac{i b d x^{3}}{6}\right) \log{\left(i c x + 1 \right)} - \frac{\left(15 b c^{4} d x^{4} - 20 i b c^{3} d x^{3} - 8 b d\right) \log{\left(- i c x + 1 \right)}}{120 c^{3}}"," ",0,"I*a*c*d*x**4/4 - b*d*x**2/(6*c) + I*b*d*x/(4*c**2) + b*d*(log(11*b*c*d*x - 11*I*b*d)/24 + 9*log(11*b*c*d*x + 11*I*b*d)/40)/c**3 + x**3*(a*d/3 - I*b*d/12) + (b*c*d*x**4/8 - I*b*d*x**3/6)*log(I*c*x + 1) - (15*b*c**4*d*x**4 - 20*I*b*c**3*d*x**3 - 8*b*d)*log(-I*c*x + 1)/(120*c**3)","A",0
3,1,158,0,2.889671," ","integrate(x*(d+I*c*d*x)*(a+b*atan(c*x)),x)","\frac{i a c d x^{3}}{3} - \frac{b d x}{2 c} + \frac{b d \left(- \frac{i \log{\left(9 b c d x - 9 i b d \right)}}{12} + \frac{7 i \log{\left(9 b c d x + 9 i b d \right)}}{24}\right)}{c^{2}} + x^{2} \left(\frac{a d}{2} - \frac{i b d}{6}\right) + \left(\frac{b c d x^{3}}{6} - \frac{i b d x^{2}}{4}\right) \log{\left(i c x + 1 \right)} - \frac{\left(4 b c^{3} d x^{3} - 6 i b c^{2} d x^{2} - 3 i b d\right) \log{\left(- i c x + 1 \right)}}{24 c^{2}}"," ",0,"I*a*c*d*x**3/3 - b*d*x/(2*c) + b*d*(-I*log(9*b*c*d*x - 9*I*b*d)/12 + 7*I*log(9*b*c*d*x + 9*I*b*d)/24)/c**2 + x**2*(a*d/2 - I*b*d/6) + (b*c*d*x**3/6 - I*b*d*x**2/4)*log(I*c*x + 1) - (4*b*c**3*d*x**3 - 6*I*b*c**2*d*x**2 - 3*I*b*d)*log(-I*c*x + 1)/(24*c**2)","A",0
4,1,128,0,2.576982," ","integrate((d+I*c*d*x)*(a+b*atan(c*x)),x)","\frac{i a c d x^{2}}{2} + \frac{b d \left(- \frac{\log{\left(b c d x - i b d \right)}}{4} - \frac{5 \log{\left(b c d x + i b d \right)}}{12}\right)}{c} + x \left(a d - \frac{i b d}{2}\right) + \left(\frac{b c d x^{2}}{4} - \frac{i b d x}{2}\right) \log{\left(i c x + 1 \right)} - \frac{\left(3 b c^{2} d x^{2} - 6 i b c d x + 4 b d\right) \log{\left(- i c x + 1 \right)}}{12 c}"," ",0,"I*a*c*d*x**2/2 + b*d*(-log(b*c*d*x - I*b*d)/4 - 5*log(b*c*d*x + I*b*d)/12)/c + x*(a*d - I*b*d/2) + (b*c*d*x**2/4 - I*b*d*x/2)*log(I*c*x + 1) - (3*b*c**2*d*x**2 - 6*I*b*c*d*x + 4*b*d)*log(-I*c*x + 1)/(12*c)","B",0
5,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))/x,x)","i d \left(\int a c\, dx + \int \left(- \frac{i a}{x}\right)\, dx + \int b c \operatorname{atan}{\left(c x \right)}\, dx + \int \left(- \frac{i b \operatorname{atan}{\left(c x \right)}}{x}\right)\, dx\right)"," ",0,"I*d*(Integral(a*c, x) + Integral(-I*a/x, x) + Integral(b*c*atan(c*x), x) + Integral(-I*b*atan(c*x)/x, x))","F",0
6,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))/x**2,x)","i d \left(\int \left(- \frac{i a}{x^{2}}\right)\, dx + \int \frac{a c}{x}\, dx + \int \left(- \frac{i b \operatorname{atan}{\left(c x \right)}}{x^{2}}\right)\, dx + \int \frac{b c \operatorname{atan}{\left(c x \right)}}{x}\, dx\right)"," ",0,"I*d*(Integral(-I*a/x**2, x) + Integral(a*c/x, x) + Integral(-I*b*atan(c*x)/x**2, x) + Integral(b*c*atan(c*x)/x, x))","F",0
7,1,182,0,3.472508," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))/x**3,x)","i b c^{2} d \log{\left(35 b^{2} c^{5} d^{2} x \right)} - \frac{i b c^{2} d \log{\left(35 b^{2} c^{5} d^{2} x - 35 i b^{2} c^{4} d^{2} \right)}}{4} - \frac{3 i b c^{2} d \log{\left(35 b^{2} c^{5} d^{2} x + 35 i b^{2} c^{4} d^{2} \right)}}{4} + \frac{- a d + x \left(- 2 i a c d - b c d\right)}{2 x^{2}} + \frac{\left(- 2 b c d x + i b d\right) \log{\left(i c x + 1 \right)}}{4 x^{2}} + \frac{\left(2 b c d x - i b d\right) \log{\left(- i c x + 1 \right)}}{4 x^{2}}"," ",0,"I*b*c**2*d*log(35*b**2*c**5*d**2*x) - I*b*c**2*d*log(35*b**2*c**5*d**2*x - 35*I*b**2*c**4*d**2)/4 - 3*I*b*c**2*d*log(35*b**2*c**5*d**2*x + 35*I*b**2*c**4*d**2)/4 + (-a*d + x*(-2*I*a*c*d - b*c*d))/(2*x**2) + (-2*b*c*d*x + I*b*d)*log(I*c*x + 1)/(4*x**2) + (2*b*c*d*x - I*b*d)*log(-I*c*x + 1)/(4*x**2)","B",0
8,1,197,0,4.628038," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))/x**4,x)","- \frac{b c^{3} d \log{\left(27 b^{2} c^{7} d^{2} x \right)}}{3} - \frac{b c^{3} d \log{\left(27 b^{2} c^{7} d^{2} x - 27 i b^{2} c^{6} d^{2} \right)}}{12} + \frac{5 b c^{3} d \log{\left(27 b^{2} c^{7} d^{2} x + 27 i b^{2} c^{6} d^{2} \right)}}{12} + \frac{\left(- 3 b c d x + 2 i b d\right) \log{\left(i c x + 1 \right)}}{12 x^{3}} + \frac{\left(3 b c d x - 2 i b d\right) \log{\left(- i c x + 1 \right)}}{12 x^{3}} + \frac{- 2 a d - 3 i b c^{2} d x^{2} + x \left(- 3 i a c d - b c d\right)}{6 x^{3}}"," ",0,"-b*c**3*d*log(27*b**2*c**7*d**2*x)/3 - b*c**3*d*log(27*b**2*c**7*d**2*x - 27*I*b**2*c**6*d**2)/12 + 5*b*c**3*d*log(27*b**2*c**7*d**2*x + 27*I*b**2*c**6*d**2)/12 + (-3*b*c*d*x + 2*I*b*d)*log(I*c*x + 1)/(12*x**3) + (3*b*c*d*x - 2*I*b*d)*log(-I*c*x + 1)/(12*x**3) + (-2*a*d - 3*I*b*c**2*d*x**2 + x*(-3*I*a*c*d - b*c*d))/(6*x**3)","A",0
9,1,214,0,7.154102," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))/x**5,x)","- \frac{i b c^{4} d \log{\left(135 b^{2} c^{9} d^{2} x \right)}}{3} + \frac{i b c^{4} d \log{\left(135 b^{2} c^{9} d^{2} x - 135 i b^{2} c^{8} d^{2} \right)}}{24} + \frac{7 i b c^{4} d \log{\left(135 b^{2} c^{9} d^{2} x + 135 i b^{2} c^{8} d^{2} \right)}}{24} + \frac{\left(- 4 b c d x + 3 i b d\right) \log{\left(i c x + 1 \right)}}{24 x^{4}} + \frac{\left(4 b c d x - 3 i b d\right) \log{\left(- i c x + 1 \right)}}{24 x^{4}} + \frac{- 3 a d + 3 b c^{3} d x^{3} - 2 i b c^{2} d x^{2} + x \left(- 4 i a c d - b c d\right)}{12 x^{4}}"," ",0,"-I*b*c**4*d*log(135*b**2*c**9*d**2*x)/3 + I*b*c**4*d*log(135*b**2*c**9*d**2*x - 135*I*b**2*c**8*d**2)/24 + 7*I*b*c**4*d*log(135*b**2*c**9*d**2*x + 135*I*b**2*c**8*d**2)/24 + (-4*b*c*d*x + 3*I*b*d)*log(I*c*x + 1)/(24*x**4) + (4*b*c*d*x - 3*I*b*d)*log(-I*c*x + 1)/(24*x**4) + (-3*a*d + 3*b*c**3*d*x**3 - 2*I*b*c**2*d*x**2 + x*(-4*I*a*c*d - b*c*d))/(12*x**4)","A",0
10,1,270,0,4.534150," ","integrate(x**3*(d+I*c*d*x)**2*(a+b*atan(c*x)),x)","- \frac{a c^{2} d^{2} x^{6}}{6} - \frac{5 b d^{2} x^{3}}{36 c} + \frac{i b d^{2} x^{2}}{5 c^{2}} + \frac{5 b d^{2} x}{12 c^{3}} - \frac{b d^{2} \left(- \frac{i \log{\left(291 b c d^{2} x - 291 i b d^{2} \right)}}{120} + \frac{71 i \log{\left(291 b c d^{2} x + 291 i b d^{2} \right)}}{210}\right)}{c^{4}} - x^{5} \left(- \frac{2 i a c d^{2}}{5} - \frac{b c d^{2}}{30}\right) - x^{4} \left(- \frac{a d^{2}}{4} + \frac{i b d^{2}}{10}\right) + \left(\frac{i b c^{2} d^{2} x^{6}}{12} + \frac{b c d^{2} x^{5}}{5} - \frac{i b d^{2} x^{4}}{8}\right) \log{\left(i c x + 1 \right)} - \frac{\left(70 i b c^{6} d^{2} x^{6} + 168 b c^{5} d^{2} x^{5} - 105 i b c^{4} d^{2} x^{4} + 59 i b d^{2}\right) \log{\left(- i c x + 1 \right)}}{840 c^{4}}"," ",0,"-a*c**2*d**2*x**6/6 - 5*b*d**2*x**3/(36*c) + I*b*d**2*x**2/(5*c**2) + 5*b*d**2*x/(12*c**3) - b*d**2*(-I*log(291*b*c*d**2*x - 291*I*b*d**2)/120 + 71*I*log(291*b*c*d**2*x + 291*I*b*d**2)/210)/c**4 - x**5*(-2*I*a*c*d**2/5 - b*c*d**2/30) - x**4*(-a*d**2/4 + I*b*d**2/10) + (I*b*c**2*d**2*x**6/12 + b*c*d**2*x**5/5 - I*b*d**2*x**4/8)*log(I*c*x + 1) - (70*I*b*c**6*d**2*x**6 + 168*b*c**5*d**2*x**5 - 105*I*b*c**4*d**2*x**4 + 59*I*b*d**2)*log(-I*c*x + 1)/(840*c**4)","A",0
11,1,250,0,4.128580," ","integrate(x**2*(d+I*c*d*x)**2*(a+b*atan(c*x)),x)","- \frac{a c^{2} d^{2} x^{5}}{5} - \frac{4 b d^{2} x^{2}}{15 c} + \frac{i b d^{2} x}{2 c^{2}} - \frac{b d^{2} \left(- \frac{\log{\left(47 b c d^{2} x - 47 i b d^{2} \right)}}{60} - \frac{49 \log{\left(47 b c d^{2} x + 47 i b d^{2} \right)}}{120}\right)}{c^{3}} - x^{4} \left(- \frac{i a c d^{2}}{2} - \frac{b c d^{2}}{20}\right) - x^{3} \left(- \frac{a d^{2}}{3} + \frac{i b d^{2}}{6}\right) + \left(\frac{i b c^{2} d^{2} x^{5}}{10} + \frac{b c d^{2} x^{4}}{4} - \frac{i b d^{2} x^{3}}{6}\right) \log{\left(i c x + 1 \right)} - \frac{\left(12 i b c^{5} d^{2} x^{5} + 30 b c^{4} d^{2} x^{4} - 20 i b c^{3} d^{2} x^{3} - 13 b d^{2}\right) \log{\left(- i c x + 1 \right)}}{120 c^{3}}"," ",0,"-a*c**2*d**2*x**5/5 - 4*b*d**2*x**2/(15*c) + I*b*d**2*x/(2*c**2) - b*d**2*(-log(47*b*c*d**2*x - 47*I*b*d**2)/60 - 49*log(47*b*c*d**2*x + 47*I*b*d**2)/120)/c**3 - x**4*(-I*a*c*d**2/2 - b*c*d**2/20) - x**3*(-a*d**2/3 + I*b*d**2/6) + (I*b*c**2*d**2*x**5/10 + b*c*d**2*x**4/4 - I*b*d**2*x**3/6)*log(I*c*x + 1) - (12*I*b*c**5*d**2*x**5 + 30*b*c**4*d**2*x**4 - 20*I*b*c**3*d**2*x**3 - 13*b*d**2)*log(-I*c*x + 1)/(120*c**3)","A",0
12,1,240,0,3.838814," ","integrate(x*(d+I*c*d*x)**2*(a+b*atan(c*x)),x)","- \frac{a c^{2} d^{2} x^{4}}{4} - \frac{3 b d^{2} x}{4 c} - \frac{b d^{2} \left(\frac{i \log{\left(67 b c d^{2} x - 67 i b d^{2} \right)}}{24} - \frac{31 i \log{\left(67 b c d^{2} x + 67 i b d^{2} \right)}}{60}\right)}{c^{2}} - x^{3} \left(- \frac{2 i a c d^{2}}{3} - \frac{b c d^{2}}{12}\right) - x^{2} \left(- \frac{a d^{2}}{2} + \frac{i b d^{2}}{3}\right) + \left(\frac{i b c^{2} d^{2} x^{4}}{8} + \frac{b c d^{2} x^{3}}{3} - \frac{i b d^{2} x^{2}}{4}\right) \log{\left(i c x + 1 \right)} - \frac{\left(15 i b c^{4} d^{2} x^{4} + 40 b c^{3} d^{2} x^{3} - 30 i b c^{2} d^{2} x^{2} - 23 i b d^{2}\right) \log{\left(- i c x + 1 \right)}}{120 c^{2}}"," ",0,"-a*c**2*d**2*x**4/4 - 3*b*d**2*x/(4*c) - b*d**2*(I*log(67*b*c*d**2*x - 67*I*b*d**2)/24 - 31*I*log(67*b*c*d**2*x + 67*I*b*d**2)/60)/c**2 - x**3*(-2*I*a*c*d**2/3 - b*c*d**2/12) - x**2*(-a*d**2/2 + I*b*d**2/3) + (I*b*c**2*d**2*x**4/8 + b*c*d**2*x**3/3 - I*b*d**2*x**2/4)*log(I*c*x + 1) - (15*I*b*c**4*d**2*x**4 + 40*b*c**3*d**2*x**3 - 30*I*b*c**2*d**2*x**2 - 23*I*b*d**2)*log(-I*c*x + 1)/(120*c**2)","A",0
13,1,206,0,3.228014," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x)),x)","- \frac{a c^{2} d^{2} x^{3}}{3} - \frac{b d^{2} \left(\frac{\log{\left(13 b c d^{2} x - 13 i b d^{2} \right)}}{6} + \frac{17 \log{\left(13 b c d^{2} x + 13 i b d^{2} \right)}}{24}\right)}{c} - x^{2} \left(- i a c d^{2} - \frac{b c d^{2}}{6}\right) - x \left(- a d^{2} + i b d^{2}\right) + \left(\frac{i b c^{2} d^{2} x^{3}}{6} + \frac{b c d^{2} x^{2}}{2} - \frac{i b d^{2} x}{2}\right) \log{\left(i c x + 1 \right)} - \frac{\left(4 i b c^{3} d^{2} x^{3} + 12 b c^{2} d^{2} x^{2} - 12 i b c d^{2} x + 11 b d^{2}\right) \log{\left(- i c x + 1 \right)}}{24 c}"," ",0,"-a*c**2*d**2*x**3/3 - b*d**2*(log(13*b*c*d**2*x - 13*I*b*d**2)/6 + 17*log(13*b*c*d**2*x + 13*I*b*d**2)/24)/c - x**2*(-I*a*c*d**2 - b*c*d**2/6) - x*(-a*d**2 + I*b*d**2) + (I*b*c**2*d**2*x**3/6 + b*c*d**2*x**2/2 - I*b*d**2*x/2)*log(I*c*x + 1) - (4*I*b*c**3*d**2*x**3 + 12*b*c**2*d**2*x**2 - 12*I*b*c*d**2*x + 11*b*d**2)*log(-I*c*x + 1)/(24*c)","B",0
14,0,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))/x,x)","- d^{2} \left(\int \left(- \frac{a}{x}\right)\, dx + \int \left(- 2 i a c\right)\, dx + \int a c^{2} x\, dx + \int \left(- \frac{b \operatorname{atan}{\left(c x \right)}}{x}\right)\, dx + \int \left(- 2 i b c \operatorname{atan}{\left(c x \right)}\right)\, dx + \int b c^{2} x \operatorname{atan}{\left(c x \right)}\, dx\right)"," ",0,"-d**2*(Integral(-a/x, x) + Integral(-2*I*a*c, x) + Integral(a*c**2*x, x) + Integral(-b*atan(c*x)/x, x) + Integral(-2*I*b*c*atan(c*x), x) + Integral(b*c**2*x*atan(c*x), x))","F",0
15,0,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))/x**2,x)","- d^{2} \left(\int a c^{2}\, dx + \int \left(- \frac{a}{x^{2}}\right)\, dx + \int b c^{2} \operatorname{atan}{\left(c x \right)}\, dx + \int \left(- \frac{b \operatorname{atan}{\left(c x \right)}}{x^{2}}\right)\, dx + \int \left(- \frac{2 i a c}{x}\right)\, dx + \int \left(- \frac{2 i b c \operatorname{atan}{\left(c x \right)}}{x}\right)\, dx\right)"," ",0,"-d**2*(Integral(a*c**2, x) + Integral(-a/x**2, x) + Integral(b*c**2*atan(c*x), x) + Integral(-b*atan(c*x)/x**2, x) + Integral(-2*I*a*c/x, x) + Integral(-2*I*b*c*atan(c*x)/x, x))","F",0
16,0,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))/x**3,x)","- d^{2} \left(\int \left(- \frac{a}{x^{3}}\right)\, dx + \int \frac{a c^{2}}{x}\, dx + \int \left(- \frac{b \operatorname{atan}{\left(c x \right)}}{x^{3}}\right)\, dx + \int \left(- \frac{2 i a c}{x^{2}}\right)\, dx + \int \frac{b c^{2} \operatorname{atan}{\left(c x \right)}}{x}\, dx + \int \left(- \frac{2 i b c \operatorname{atan}{\left(c x \right)}}{x^{2}}\right)\, dx\right)"," ",0,"-d**2*(Integral(-a/x**3, x) + Integral(a*c**2/x, x) + Integral(-b*atan(c*x)/x**3, x) + Integral(-2*I*a*c/x**2, x) + Integral(b*c**2*atan(c*x)/x, x) + Integral(-2*I*b*c*atan(c*x)/x**2, x))","F",0
17,1,253,0,9.279322," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))/x**4,x)","- \frac{4 b c^{3} d^{2} \log{\left(135 b^{2} c^{7} d^{4} x \right)}}{3} + \frac{b c^{3} d^{2} \log{\left(135 b^{2} c^{7} d^{4} x - 135 i b^{2} c^{6} d^{4} \right)}}{6} + \frac{7 b c^{3} d^{2} \log{\left(135 b^{2} c^{7} d^{4} x + 135 i b^{2} c^{6} d^{4} \right)}}{6} - \frac{2 a d^{2} + x^{2} \left(- 6 a c^{2} d^{2} + 6 i b c^{2} d^{2}\right) + x \left(6 i a c d^{2} + b c d^{2}\right)}{6 x^{3}} + \frac{\left(- 3 i b c^{2} d^{2} x^{2} - 3 b c d^{2} x + i b d^{2}\right) \log{\left(i c x + 1 \right)}}{6 x^{3}} + \frac{\left(3 i b c^{2} d^{2} x^{2} + 3 b c d^{2} x - i b d^{2}\right) \log{\left(- i c x + 1 \right)}}{6 x^{3}}"," ",0,"-4*b*c**3*d**2*log(135*b**2*c**7*d**4*x)/3 + b*c**3*d**2*log(135*b**2*c**7*d**4*x - 135*I*b**2*c**6*d**4)/6 + 7*b*c**3*d**2*log(135*b**2*c**7*d**4*x + 135*I*b**2*c**6*d**4)/6 - (2*a*d**2 + x**2*(-6*a*c**2*d**2 + 6*I*b*c**2*d**2) + x*(6*I*a*c*d**2 + b*c*d**2))/(6*x**3) + (-3*I*b*c**2*d**2*x**2 - 3*b*c*d**2*x + I*b*d**2)*log(I*c*x + 1)/(6*x**3) + (3*I*b*c**2*d**2*x**2 + 3*b*c*d**2*x - I*b*d**2)*log(-I*c*x + 1)/(6*x**3)","B",0
18,1,275,0,16.394978," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))/x**5,x)","- \frac{2 i b c^{4} d^{2} \log{\left(1485 b^{2} c^{9} d^{4} x \right)}}{3} - \frac{i b c^{4} d^{2} \log{\left(1485 b^{2} c^{9} d^{4} x - 1485 i b^{2} c^{8} d^{4} \right)}}{24} + \frac{17 i b c^{4} d^{2} \log{\left(1485 b^{2} c^{9} d^{4} x + 1485 i b^{2} c^{8} d^{4} \right)}}{24} + \frac{\left(- 6 i b c^{2} d^{2} x^{2} - 8 b c d^{2} x + 3 i b d^{2}\right) \log{\left(i c x + 1 \right)}}{24 x^{4}} + \frac{\left(6 i b c^{2} d^{2} x^{2} + 8 b c d^{2} x - 3 i b d^{2}\right) \log{\left(- i c x + 1 \right)}}{24 x^{4}} - \frac{3 a d^{2} - 9 b c^{3} d^{2} x^{3} + x^{2} \left(- 6 a c^{2} d^{2} + 4 i b c^{2} d^{2}\right) + x \left(8 i a c d^{2} + b c d^{2}\right)}{12 x^{4}}"," ",0,"-2*I*b*c**4*d**2*log(1485*b**2*c**9*d**4*x)/3 - I*b*c**4*d**2*log(1485*b**2*c**9*d**4*x - 1485*I*b**2*c**8*d**4)/24 + 17*I*b*c**4*d**2*log(1485*b**2*c**9*d**4*x + 1485*I*b**2*c**8*d**4)/24 + (-6*I*b*c**2*d**2*x**2 - 8*b*c*d**2*x + 3*I*b*d**2)*log(I*c*x + 1)/(24*x**4) + (6*I*b*c**2*d**2*x**2 + 8*b*c*d**2*x - 3*I*b*d**2)*log(-I*c*x + 1)/(24*x**4) - (3*a*d**2 - 9*b*c**3*d**2*x**3 + x**2*(-6*a*c**2*d**2 + 4*I*b*c**2*d**2) + x*(8*I*a*c*d**2 + b*c*d**2))/(12*x**4)","A",0
19,1,287,0,26.066950," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))/x**6,x)","\frac{8 b c^{5} d^{2} \log{\left(10395 b^{2} c^{11} d^{4} x \right)}}{15} - \frac{b c^{5} d^{2} \log{\left(10395 b^{2} c^{11} d^{4} x - 10395 i b^{2} c^{10} d^{4} \right)}}{60} - \frac{31 b c^{5} d^{2} \log{\left(10395 b^{2} c^{11} d^{4} x + 10395 i b^{2} c^{10} d^{4} \right)}}{60} + \frac{\left(- 10 i b c^{2} d^{2} x^{2} - 15 b c d^{2} x + 6 i b d^{2}\right) \log{\left(i c x + 1 \right)}}{60 x^{5}} + \frac{\left(10 i b c^{2} d^{2} x^{2} + 15 b c d^{2} x - 6 i b d^{2}\right) \log{\left(- i c x + 1 \right)}}{60 x^{5}} - \frac{12 a d^{2} - 30 i b c^{4} d^{2} x^{4} - 16 b c^{3} d^{2} x^{3} + x^{2} \left(- 20 a c^{2} d^{2} + 10 i b c^{2} d^{2}\right) + x \left(30 i a c d^{2} + 3 b c d^{2}\right)}{60 x^{5}}"," ",0,"8*b*c**5*d**2*log(10395*b**2*c**11*d**4*x)/15 - b*c**5*d**2*log(10395*b**2*c**11*d**4*x - 10395*I*b**2*c**10*d**4)/60 - 31*b*c**5*d**2*log(10395*b**2*c**11*d**4*x + 10395*I*b**2*c**10*d**4)/60 + (-10*I*b*c**2*d**2*x**2 - 15*b*c*d**2*x + 6*I*b*d**2)*log(I*c*x + 1)/(60*x**5) + (10*I*b*c**2*d**2*x**2 + 15*b*c*d**2*x - 6*I*b*d**2)*log(-I*c*x + 1)/(60*x**5) - (12*a*d**2 - 30*I*b*c**4*d**2*x**4 - 16*b*c**3*d**2*x**3 + x**2*(-20*a*c**2*d**2 + 10*I*b*c**2*d**2) + x*(30*I*a*c*d**2 + 3*b*c*d**2))/(60*x**5)","A",0
20,1,328,0,5.378634," ","integrate(x**3*(d+I*c*d*x)**3*(a+b*atan(c*x)),x)","- \frac{i a c^{3} d^{3} x^{7}}{7} - \frac{b d^{3} x^{3}}{4 c} + \frac{13 i b d^{3} x^{2}}{35 c^{2}} + \frac{3 b d^{3} x}{4 c^{3}} - \frac{b d^{3} \left(- \frac{i \log{\left(353 b c d^{3} x - 353 i b d^{3} \right)}}{280} + \frac{351 i \log{\left(353 b c d^{3} x + 353 i b d^{3} \right)}}{560}\right)}{c^{4}} - x^{6} \left(\frac{a c^{2} d^{3}}{2} - \frac{i b c^{2} d^{3}}{42}\right) - x^{5} \left(- \frac{3 i a c d^{3}}{5} - \frac{b c d^{3}}{10}\right) - x^{4} \left(- \frac{a d^{3}}{4} + \frac{13 i b d^{3}}{70}\right) + \left(- \frac{b c^{3} d^{3} x^{7}}{14} + \frac{i b c^{2} d^{3} x^{6}}{4} + \frac{3 b c d^{3} x^{5}}{10} - \frac{i b d^{3} x^{4}}{8}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 40 b c^{7} d^{3} x^{7} + 140 i b c^{6} d^{3} x^{6} + 168 b c^{5} d^{3} x^{5} - 70 i b c^{4} d^{3} x^{4} + 67 i b d^{3}\right) \log{\left(- i c x + 1 \right)}}{560 c^{4}}"," ",0,"-I*a*c**3*d**3*x**7/7 - b*d**3*x**3/(4*c) + 13*I*b*d**3*x**2/(35*c**2) + 3*b*d**3*x/(4*c**3) - b*d**3*(-I*log(353*b*c*d**3*x - 353*I*b*d**3)/280 + 351*I*log(353*b*c*d**3*x + 353*I*b*d**3)/560)/c**4 - x**6*(a*c**2*d**3/2 - I*b*c**2*d**3/42) - x**5*(-3*I*a*c*d**3/5 - b*c*d**3/10) - x**4*(-a*d**3/4 + 13*I*b*d**3/70) + (-b*c**3*d**3*x**7/14 + I*b*c**2*d**3*x**6/4 + 3*b*c*d**3*x**5/10 - I*b*d**3*x**4/8)*log(I*c*x + 1) - (-40*b*c**7*d**3*x**7 + 140*I*b*c**6*d**3*x**6 + 168*b*c**5*d**3*x**5 - 70*I*b*c**4*d**3*x**4 + 67*I*b*d**3)*log(-I*c*x + 1)/(560*c**4)","A",0
21,1,316,0,4.903731," ","integrate(x**2*(d+I*c*d*x)**3*(a+b*atan(c*x)),x)","- \frac{i a c^{3} d^{3} x^{6}}{6} - \frac{7 b d^{3} x^{2}}{15 c} + \frac{11 i b d^{3} x}{12 c^{2}} - \frac{b d^{3} \left(- \frac{\log{\left(310 b c d^{3} x - 310 i b d^{3} \right)}}{120} - \frac{209 \log{\left(310 b c d^{3} x + 310 i b d^{3} \right)}}{280}\right)}{c^{3}} - x^{5} \left(\frac{3 a c^{2} d^{3}}{5} - \frac{i b c^{2} d^{3}}{30}\right) - x^{4} \left(- \frac{3 i a c d^{3}}{4} - \frac{3 b c d^{3}}{20}\right) - x^{3} \left(- \frac{a d^{3}}{3} + \frac{11 i b d^{3}}{36}\right) + \left(- \frac{b c^{3} d^{3} x^{6}}{12} + \frac{3 i b c^{2} d^{3} x^{5}}{10} + \frac{3 b c d^{3} x^{4}}{8} - \frac{i b d^{3} x^{3}}{6}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 70 b c^{6} d^{3} x^{6} + 252 i b c^{5} d^{3} x^{5} + 315 b c^{4} d^{3} x^{4} - 140 i b c^{3} d^{3} x^{3} - 150 b d^{3}\right) \log{\left(- i c x + 1 \right)}}{840 c^{3}}"," ",0,"-I*a*c**3*d**3*x**6/6 - 7*b*d**3*x**2/(15*c) + 11*I*b*d**3*x/(12*c**2) - b*d**3*(-log(310*b*c*d**3*x - 310*I*b*d**3)/120 - 209*log(310*b*c*d**3*x + 310*I*b*d**3)/280)/c**3 - x**5*(3*a*c**2*d**3/5 - I*b*c**2*d**3/30) - x**4*(-3*I*a*c*d**3/4 - 3*b*c*d**3/20) - x**3*(-a*d**3/3 + 11*I*b*d**3/36) + (-b*c**3*d**3*x**6/12 + 3*I*b*c**2*d**3*x**5/10 + 3*b*c*d**3*x**4/8 - I*b*d**3*x**3/6)*log(I*c*x + 1) - (-70*b*c**6*d**3*x**6 + 252*I*b*c**5*d**3*x**5 + 315*b*c**4*d**3*x**4 - 140*I*b*c**3*d**3*x**3 - 150*b*d**3)*log(-I*c*x + 1)/(840*c**3)","A",0
22,1,296,0,4.589972," ","integrate(x*(d+I*c*d*x)**3*(a+b*atan(c*x)),x)","- \frac{i a c^{3} d^{3} x^{5}}{5} - \frac{5 b d^{3} x}{4 c} - \frac{b d^{3} \left(\frac{i \log{\left(19 b c d^{3} x - 19 i b d^{3} \right)}}{40} - \frac{37 i \log{\left(19 b c d^{3} x + 19 i b d^{3} \right)}}{40}\right)}{c^{2}} - x^{4} \left(\frac{3 a c^{2} d^{3}}{4} - \frac{i b c^{2} d^{3}}{20}\right) - x^{3} \left(- i a c d^{3} - \frac{b c d^{3}}{4}\right) - x^{2} \left(- \frac{a d^{3}}{2} + \frac{3 i b d^{3}}{5}\right) + \left(- \frac{b c^{3} d^{3} x^{5}}{10} + \frac{3 i b c^{2} d^{3} x^{4}}{8} + \frac{b c d^{3} x^{3}}{2} - \frac{i b d^{3} x^{2}}{4}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 4 b c^{5} d^{3} x^{5} + 15 i b c^{4} d^{3} x^{4} + 20 b c^{3} d^{3} x^{3} - 10 i b c^{2} d^{3} x^{2} - 12 i b d^{3}\right) \log{\left(- i c x + 1 \right)}}{40 c^{2}}"," ",0,"-I*a*c**3*d**3*x**5/5 - 5*b*d**3*x/(4*c) - b*d**3*(I*log(19*b*c*d**3*x - 19*I*b*d**3)/40 - 37*I*log(19*b*c*d**3*x + 19*I*b*d**3)/40)/c**2 - x**4*(3*a*c**2*d**3/4 - I*b*c**2*d**3/20) - x**3*(-I*a*c*d**3 - b*c*d**3/4) - x**2*(-a*d**3/2 + 3*I*b*d**3/5) + (-b*c**3*d**3*x**5/10 + 3*I*b*c**2*d**3*x**4/8 + b*c*d**3*x**3/2 - I*b*d**3*x**2/4)*log(I*c*x + 1) - (-4*b*c**5*d**3*x**5 + 15*I*b*c**4*d**3*x**4 + 20*b*c**3*d**3*x**3 - 10*I*b*c**2*d**3*x**2 - 12*I*b*d**3)*log(-I*c*x + 1)/(40*c**2)","B",0
23,1,267,0,4.097835," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x)),x)","- \frac{i a c^{3} d^{3} x^{4}}{4} - \frac{b d^{3} \left(\frac{\log{\left(22 b c d^{3} x - 22 i b d^{3} \right)}}{8} + \frac{49 \log{\left(22 b c d^{3} x + 22 i b d^{3} \right)}}{40}\right)}{c} - x^{3} \left(a c^{2} d^{3} - \frac{i b c^{2} d^{3}}{12}\right) - x^{2} \left(- \frac{3 i a c d^{3}}{2} - \frac{b c d^{3}}{2}\right) - x \left(- a d^{3} + \frac{7 i b d^{3}}{4}\right) + \left(- \frac{b c^{3} d^{3} x^{4}}{8} + \frac{i b c^{2} d^{3} x^{3}}{2} + \frac{3 b c d^{3} x^{2}}{4} - \frac{i b d^{3} x}{2}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 5 b c^{4} d^{3} x^{4} + 20 i b c^{3} d^{3} x^{3} + 30 b c^{2} d^{3} x^{2} - 20 i b c d^{3} x + 26 b d^{3}\right) \log{\left(- i c x + 1 \right)}}{40 c}"," ",0,"-I*a*c**3*d**3*x**4/4 - b*d**3*(log(22*b*c*d**3*x - 22*I*b*d**3)/8 + 49*log(22*b*c*d**3*x + 22*I*b*d**3)/40)/c - x**3*(a*c**2*d**3 - I*b*c**2*d**3/12) - x**2*(-3*I*a*c*d**3/2 - b*c*d**3/2) - x*(-a*d**3 + 7*I*b*d**3/4) + (-b*c**3*d**3*x**4/8 + I*b*c**2*d**3*x**3/2 + 3*b*c*d**3*x**2/4 - I*b*d**3*x/2)*log(I*c*x + 1) - (-5*b*c**4*d**3*x**4 + 20*I*b*c**3*d**3*x**3 + 30*b*c**2*d**3*x**2 - 20*I*b*c*d**3*x + 26*b*d**3)*log(-I*c*x + 1)/(40*c)","B",0
24,0,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))/x,x)","- i d^{3} \left(\int \left(- 3 a c\right)\, dx + \int \frac{i a}{x}\, dx + \int a c^{3} x^{2}\, dx + \int \left(- 3 b c \operatorname{atan}{\left(c x \right)}\right)\, dx + \int \left(- 3 i a c^{2} x\right)\, dx + \int \frac{i b \operatorname{atan}{\left(c x \right)}}{x}\, dx + \int b c^{3} x^{2} \operatorname{atan}{\left(c x \right)}\, dx + \int \left(- 3 i b c^{2} x \operatorname{atan}{\left(c x \right)}\right)\, dx\right)"," ",0,"-I*d**3*(Integral(-3*a*c, x) + Integral(I*a/x, x) + Integral(a*c**3*x**2, x) + Integral(-3*b*c*atan(c*x), x) + Integral(-3*I*a*c**2*x, x) + Integral(I*b*atan(c*x)/x, x) + Integral(b*c**3*x**2*atan(c*x), x) + Integral(-3*I*b*c**2*x*atan(c*x), x))","F",0
25,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,1,311,0,26.545613," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))/x**5,x)","- 2 i b c^{4} d^{3} \log{\left(3689 b^{2} c^{9} d^{6} x \right)} + \frac{i b c^{4} d^{3} \log{\left(3689 b^{2} c^{9} d^{6} x - 3689 i b^{2} c^{8} d^{6} \right)}}{8} + \frac{15 i b c^{4} d^{3} \log{\left(3689 b^{2} c^{9} d^{6} x + 3689 i b^{2} c^{8} d^{6} \right)}}{8} - \frac{3 a d^{3} + x^{3} \left(- 12 i a c^{3} d^{3} - 21 b c^{3} d^{3}\right) + x^{2} \left(- 18 a c^{2} d^{3} + 6 i b c^{2} d^{3}\right) + x \left(12 i a c d^{3} + b c d^{3}\right)}{12 x^{4}} + \frac{\left(- 4 b c^{3} d^{3} x^{3} + 6 i b c^{2} d^{3} x^{2} + 4 b c d^{3} x - i b d^{3}\right) \log{\left(- i c x + 1 \right)}}{8 x^{4}} + \frac{\left(4 b c^{3} d^{3} x^{3} - 6 i b c^{2} d^{3} x^{2} - 4 b c d^{3} x + i b d^{3}\right) \log{\left(i c x + 1 \right)}}{8 x^{4}}"," ",0,"-2*I*b*c**4*d**3*log(3689*b**2*c**9*d**6*x) + I*b*c**4*d**3*log(3689*b**2*c**9*d**6*x - 3689*I*b**2*c**8*d**6)/8 + 15*I*b*c**4*d**3*log(3689*b**2*c**9*d**6*x + 3689*I*b**2*c**8*d**6)/8 - (3*a*d**3 + x**3*(-12*I*a*c**3*d**3 - 21*b*c**3*d**3) + x**2*(-18*a*c**2*d**3 + 6*I*b*c**2*d**3) + x*(12*I*a*c*d**3 + b*c*d**3))/(12*x**4) + (-4*b*c**3*d**3*x**3 + 6*I*b*c**2*d**3*x**2 + 4*b*c*d**3*x - I*b*d**3)*log(-I*c*x + 1)/(8*x**4) + (4*b*c**3*d**3*x**3 - 6*I*b*c**2*d**3*x**2 - 4*b*c*d**3*x + I*b*d**3)*log(I*c*x + 1)/(8*x**4)","B",0
29,1,326,0,48.016619," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))/x**6,x)","\frac{6 b c^{5} d^{3} \log{\left(113975 b^{2} c^{11} d^{6} x \right)}}{5} + \frac{b c^{5} d^{3} \log{\left(113975 b^{2} c^{11} d^{6} x - 113975 i b^{2} c^{10} d^{6} \right)}}{40} - \frac{49 b c^{5} d^{3} \log{\left(113975 b^{2} c^{11} d^{6} x + 113975 i b^{2} c^{10} d^{6} \right)}}{40} + \frac{\left(- 10 b c^{3} d^{3} x^{3} + 20 i b c^{2} d^{3} x^{2} + 15 b c d^{3} x - 4 i b d^{3}\right) \log{\left(- i c x + 1 \right)}}{40 x^{5}} + \frac{\left(10 b c^{3} d^{3} x^{3} - 20 i b c^{2} d^{3} x^{2} - 15 b c d^{3} x + 4 i b d^{3}\right) \log{\left(i c x + 1 \right)}}{40 x^{5}} - \frac{4 a d^{3} - 25 i b c^{4} d^{3} x^{4} + x^{3} \left(- 10 i a c^{3} d^{3} - 12 b c^{3} d^{3}\right) + x^{2} \left(- 20 a c^{2} d^{3} + 5 i b c^{2} d^{3}\right) + x \left(15 i a c d^{3} + b c d^{3}\right)}{20 x^{5}}"," ",0,"6*b*c**5*d**3*log(113975*b**2*c**11*d**6*x)/5 + b*c**5*d**3*log(113975*b**2*c**11*d**6*x - 113975*I*b**2*c**10*d**6)/40 - 49*b*c**5*d**3*log(113975*b**2*c**11*d**6*x + 113975*I*b**2*c**10*d**6)/40 + (-10*b*c**3*d**3*x**3 + 20*I*b*c**2*d**3*x**2 + 15*b*c*d**3*x - 4*I*b*d**3)*log(-I*c*x + 1)/(40*x**5) + (10*b*c**3*d**3*x**3 - 20*I*b*c**2*d**3*x**2 - 15*b*c*d**3*x + 4*I*b*d**3)*log(I*c*x + 1)/(40*x**5) - (4*a*d**3 - 25*I*b*c**4*d**3*x**4 + x**3*(-10*I*a*c**3*d**3 - 12*b*c**3*d**3) + x**2*(-20*a*c**2*d**3 + 5*I*b*c**2*d**3) + x*(15*I*a*c*d**3 + b*c*d**3))/(20*x**5)","B",0
30,1,347,0,84.078223," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))/x**7,x)","\frac{14 i b c^{6} d^{3} \log{\left(1385945 b^{2} c^{13} d^{6} x \right)}}{15} - \frac{i b c^{6} d^{3} \log{\left(1385945 b^{2} c^{13} d^{6} x - 1385945 i b^{2} c^{12} d^{6} \right)}}{120} - \frac{37 i b c^{6} d^{3} \log{\left(1385945 b^{2} c^{13} d^{6} x + 1385945 i b^{2} c^{12} d^{6} \right)}}{40} + \frac{\left(- 20 b c^{3} d^{3} x^{3} + 45 i b c^{2} d^{3} x^{2} + 36 b c d^{3} x - 10 i b d^{3}\right) \log{\left(- i c x + 1 \right)}}{120 x^{6}} + \frac{\left(20 b c^{3} d^{3} x^{3} - 45 i b c^{2} d^{3} x^{2} - 36 b c d^{3} x + 10 i b d^{3}\right) \log{\left(i c x + 1 \right)}}{120 x^{6}} - \frac{30 a d^{3} + 165 b c^{5} d^{3} x^{5} - 84 i b c^{4} d^{3} x^{4} + x^{3} \left(- 60 i a c^{3} d^{3} - 55 b c^{3} d^{3}\right) + x^{2} \left(- 135 a c^{2} d^{3} + 27 i b c^{2} d^{3}\right) + x \left(108 i a c d^{3} + 6 b c d^{3}\right)}{180 x^{6}}"," ",0,"14*I*b*c**6*d**3*log(1385945*b**2*c**13*d**6*x)/15 - I*b*c**6*d**3*log(1385945*b**2*c**13*d**6*x - 1385945*I*b**2*c**12*d**6)/120 - 37*I*b*c**6*d**3*log(1385945*b**2*c**13*d**6*x + 1385945*I*b**2*c**12*d**6)/40 + (-20*b*c**3*d**3*x**3 + 45*I*b*c**2*d**3*x**2 + 36*b*c*d**3*x - 10*I*b*d**3)*log(-I*c*x + 1)/(120*x**6) + (20*b*c**3*d**3*x**3 - 45*I*b*c**2*d**3*x**2 - 36*b*c*d**3*x + 10*I*b*d**3)*log(I*c*x + 1)/(120*x**6) - (30*a*d**3 + 165*b*c**5*d**3*x**5 - 84*I*b*c**4*d**3*x**4 + x**3*(-60*I*a*c**3*d**3 - 55*b*c**3*d**3) + x**2*(-135*a*c**2*d**3 + 27*I*b*c**2*d**3) + x*(108*I*a*c*d**3 + 6*b*c*d**3))/(180*x**6)","A",0
31,1,389,0,6.702404," ","integrate(x**3*(d+I*c*d*x)**4*(a+b*atan(c*x)),x)","\frac{a c^{4} d^{4} x^{8}}{8} - \frac{11 b d^{4} x^{3}}{24 c} + \frac{24 i b d^{4} x^{2}}{35 c^{2}} + \frac{11 b d^{4} x}{8 c^{3}} + \frac{b d^{4} \left(\frac{i \log{\left(5893 b c d^{4} x - 5893 i b d^{4} \right)}}{560} - \frac{1471 i \log{\left(5893 b c d^{4} x + 5893 i b d^{4} \right)}}{1260}\right)}{c^{4}} + x^{7} \left(- \frac{4 i a c^{3} d^{4}}{7} - \frac{b c^{3} d^{4}}{56}\right) + x^{6} \left(- a c^{2} d^{4} + \frac{2 i b c^{2} d^{4}}{21}\right) + x^{5} \left(\frac{4 i a c d^{4}}{5} + \frac{9 b c d^{4}}{40}\right) + x^{4} \left(\frac{a d^{4}}{4} - \frac{12 i b d^{4}}{35}\right) + \left(- \frac{i b c^{4} d^{4} x^{8}}{16} - \frac{2 b c^{3} d^{4} x^{7}}{7} + \frac{i b c^{2} d^{4} x^{6}}{2} + \frac{2 b c d^{4} x^{5}}{5} - \frac{i b d^{4} x^{4}}{8}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 315 i b c^{8} d^{4} x^{8} - 1440 b c^{7} d^{4} x^{7} + 2520 i b c^{6} d^{4} x^{6} + 2016 b c^{5} d^{4} x^{5} - 630 i b c^{4} d^{4} x^{4} + 1037 i b d^{4}\right) \log{\left(- i c x + 1 \right)}}{5040 c^{4}}"," ",0,"a*c**4*d**4*x**8/8 - 11*b*d**4*x**3/(24*c) + 24*I*b*d**4*x**2/(35*c**2) + 11*b*d**4*x/(8*c**3) + b*d**4*(I*log(5893*b*c*d**4*x - 5893*I*b*d**4)/560 - 1471*I*log(5893*b*c*d**4*x + 5893*I*b*d**4)/1260)/c**4 + x**7*(-4*I*a*c**3*d**4/7 - b*c**3*d**4/56) + x**6*(-a*c**2*d**4 + 2*I*b*c**2*d**4/21) + x**5*(4*I*a*c*d**4/5 + 9*b*c*d**4/40) + x**4*(a*d**4/4 - 12*I*b*d**4/35) + (-I*b*c**4*d**4*x**8/16 - 2*b*c**3*d**4*x**7/7 + I*b*c**2*d**4*x**6/2 + 2*b*c*d**4*x**5/5 - I*b*d**4*x**4/8)*log(I*c*x + 1) - (-315*I*b*c**8*d**4*x**8 - 1440*b*c**7*d**4*x**7 + 2520*I*b*c**6*d**4*x**6 + 2016*b*c**5*d**4*x**5 - 630*I*b*c**4*d**4*x**4 + 1037*I*b*d**4)*log(-I*c*x + 1)/(5040*c**4)","A",0
32,1,367,0,5.985457," ","integrate(x**2*(d+I*c*d*x)**4*(a+b*atan(c*x)),x)","\frac{a c^{4} d^{4} x^{7}}{7} - \frac{88 b d^{4} x^{2}}{105 c} + \frac{5 i b d^{4} x}{3 c^{2}} + \frac{b d^{4} \left(\frac{\log{\left(2299 b c d^{4} x - 2299 i b d^{4} \right)}}{210} + \frac{769 \log{\left(2299 b c d^{4} x + 2299 i b d^{4} \right)}}{560}\right)}{c^{3}} + x^{6} \left(- \frac{2 i a c^{3} d^{4}}{3} - \frac{b c^{3} d^{4}}{42}\right) + x^{5} \left(- \frac{6 a c^{2} d^{4}}{5} + \frac{2 i b c^{2} d^{4}}{15}\right) + x^{4} \left(i a c d^{4} + \frac{47 b c d^{4}}{140}\right) + x^{3} \left(\frac{a d^{4}}{3} - \frac{5 i b d^{4}}{9}\right) + \left(- \frac{i b c^{4} d^{4} x^{7}}{14} - \frac{b c^{3} d^{4} x^{6}}{3} + \frac{3 i b c^{2} d^{4} x^{5}}{5} + \frac{b c d^{4} x^{4}}{2} - \frac{i b d^{4} x^{3}}{6}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 120 i b c^{7} d^{4} x^{7} - 560 b c^{6} d^{4} x^{6} + 1008 i b c^{5} d^{4} x^{5} + 840 b c^{4} d^{4} x^{4} - 280 i b c^{3} d^{4} x^{3} - 501 b d^{4}\right) \log{\left(- i c x + 1 \right)}}{1680 c^{3}}"," ",0,"a*c**4*d**4*x**7/7 - 88*b*d**4*x**2/(105*c) + 5*I*b*d**4*x/(3*c**2) + b*d**4*(log(2299*b*c*d**4*x - 2299*I*b*d**4)/210 + 769*log(2299*b*c*d**4*x + 2299*I*b*d**4)/560)/c**3 + x**6*(-2*I*a*c**3*d**4/3 - b*c**3*d**4/42) + x**5*(-6*a*c**2*d**4/5 + 2*I*b*c**2*d**4/15) + x**4*(I*a*c*d**4 + 47*b*c*d**4/140) + x**3*(a*d**4/3 - 5*I*b*d**4/9) + (-I*b*c**4*d**4*x**7/14 - b*c**3*d**4*x**6/3 + 3*I*b*c**2*d**4*x**5/5 + b*c*d**4*x**4/2 - I*b*d**4*x**3/6)*log(I*c*x + 1) - (-120*I*b*c**7*d**4*x**7 - 560*b*c**6*d**4*x**6 + 1008*I*b*c**5*d**4*x**5 + 840*b*c**4*d**4*x**4 - 280*I*b*c**3*d**4*x**3 - 501*b*d**4)*log(-I*c*x + 1)/(1680*c**3)","A",0
33,1,360,0,5.472466," ","integrate(x*(d+I*c*d*x)**4*(a+b*atan(c*x)),x)","\frac{a c^{4} d^{4} x^{6}}{6} - \frac{13 b d^{4} x}{6 c} + \frac{b d^{4} \left(- \frac{i \log{\left(709 b c d^{4} x - 709 i b d^{4} \right)}}{60} + \frac{117 i \log{\left(709 b c d^{4} x + 709 i b d^{4} \right)}}{70}\right)}{c^{2}} + x^{5} \left(- \frac{4 i a c^{3} d^{4}}{5} - \frac{b c^{3} d^{4}}{30}\right) + x^{4} \left(- \frac{3 a c^{2} d^{4}}{2} + \frac{i b c^{2} d^{4}}{5}\right) + x^{3} \left(\frac{4 i a c d^{4}}{3} + \frac{5 b c d^{4}}{9}\right) + x^{2} \left(\frac{a d^{4}}{2} - \frac{16 i b d^{4}}{15}\right) + \left(- \frac{i b c^{4} d^{4} x^{6}}{12} - \frac{2 b c^{3} d^{4} x^{5}}{5} + \frac{3 i b c^{2} d^{4} x^{4}}{4} + \frac{2 b c d^{4} x^{3}}{3} - \frac{i b d^{4} x^{2}}{4}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 35 i b c^{6} d^{4} x^{6} - 168 b c^{5} d^{4} x^{5} + 315 i b c^{4} d^{4} x^{4} + 280 b c^{3} d^{4} x^{3} - 105 i b c^{2} d^{4} x^{2} - 201 i b d^{4}\right) \log{\left(- i c x + 1 \right)}}{420 c^{2}}"," ",0,"a*c**4*d**4*x**6/6 - 13*b*d**4*x/(6*c) + b*d**4*(-I*log(709*b*c*d**4*x - 709*I*b*d**4)/60 + 117*I*log(709*b*c*d**4*x + 709*I*b*d**4)/70)/c**2 + x**5*(-4*I*a*c**3*d**4/5 - b*c**3*d**4/30) + x**4*(-3*a*c**2*d**4/2 + I*b*c**2*d**4/5) + x**3*(4*I*a*c*d**4/3 + 5*b*c*d**4/9) + x**2*(a*d**4/2 - 16*I*b*d**4/15) + (-I*b*c**4*d**4*x**6/12 - 2*b*c**3*d**4*x**5/5 + 3*I*b*c**2*d**4*x**4/4 + 2*b*c*d**4*x**3/3 - I*b*d**4*x**2/4)*log(I*c*x + 1) - (-35*I*b*c**6*d**4*x**6 - 168*b*c**5*d**4*x**5 + 315*I*b*c**4*d**4*x**4 + 280*b*c**3*d**4*x**3 - 105*I*b*c**2*d**4*x**2 - 201*I*b*d**4)*log(-I*c*x + 1)/(420*c**2)","B",0
34,1,316,0,4.596361," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x)),x)","\frac{a c^{4} d^{4} x^{5}}{5} + \frac{b d^{4} \left(- \frac{\log{\left(41 b c d^{4} x - 41 i b d^{4} \right)}}{10} - \frac{43 \log{\left(41 b c d^{4} x + 41 i b d^{4} \right)}}{20}\right)}{c} + x^{4} \left(- i a c^{3} d^{4} - \frac{b c^{3} d^{4}}{20}\right) + x^{3} \left(- 2 a c^{2} d^{4} + \frac{i b c^{2} d^{4}}{3}\right) + x^{2} \left(2 i a c d^{4} + \frac{11 b c d^{4}}{10}\right) + x \left(a d^{4} - 3 i b d^{4}\right) + \left(- \frac{i b c^{4} d^{4} x^{5}}{10} - \frac{b c^{3} d^{4} x^{4}}{2} + i b c^{2} d^{4} x^{3} + b c d^{4} x^{2} - \frac{i b d^{4} x}{2}\right) \log{\left(i c x + 1 \right)} - \frac{\left(- 2 i b c^{5} d^{4} x^{5} - 10 b c^{4} d^{4} x^{4} + 20 i b c^{3} d^{4} x^{3} + 20 b c^{2} d^{4} x^{2} - 10 i b c d^{4} x + 19 b d^{4}\right) \log{\left(- i c x + 1 \right)}}{20 c}"," ",0,"a*c**4*d**4*x**5/5 + b*d**4*(-log(41*b*c*d**4*x - 41*I*b*d**4)/10 - 43*log(41*b*c*d**4*x + 41*I*b*d**4)/20)/c + x**4*(-I*a*c**3*d**4 - b*c**3*d**4/20) + x**3*(-2*a*c**2*d**4 + I*b*c**2*d**4/3) + x**2*(2*I*a*c*d**4 + 11*b*c*d**4/10) + x*(a*d**4 - 3*I*b*d**4) + (-I*b*c**4*d**4*x**5/10 - b*c**3*d**4*x**4/2 + I*b*c**2*d**4*x**3 + b*c*d**4*x**2 - I*b*d**4*x/2)*log(I*c*x + 1) - (-2*I*b*c**5*d**4*x**5 - 10*b*c**4*d**4*x**4 + 20*I*b*c**3*d**4*x**3 + 20*b*c**2*d**4*x**2 - 10*I*b*c*d**4*x + 19*b*d**4)*log(-I*c*x + 1)/(20*c)","B",0
35,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,1,366,0,71.851064," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x**6,x)","\frac{16 b c^{5} d^{4} \log{\left(10395 b^{2} c^{11} d^{8} x \right)}}{5} - \frac{b c^{5} d^{4} \log{\left(10395 b^{2} c^{11} d^{8} x - 10395 i b^{2} c^{10} d^{8} \right)}}{10} - \frac{31 b c^{5} d^{4} \log{\left(10395 b^{2} c^{11} d^{8} x + 10395 i b^{2} c^{10} d^{8} \right)}}{10} + \frac{- 12 a d^{4} + x^{4} \left(- 60 a c^{4} d^{4} + 180 i b c^{4} d^{4}\right) + x^{3} \left(120 i a c^{3} d^{4} + 66 b c^{3} d^{4}\right) + x^{2} \left(120 a c^{2} d^{4} - 20 i b c^{2} d^{4}\right) + x \left(- 60 i a c d^{4} - 3 b c d^{4}\right)}{60 x^{5}} + \frac{\left(- 5 i b c^{4} d^{4} x^{4} - 10 b c^{3} d^{4} x^{3} + 10 i b c^{2} d^{4} x^{2} + 5 b c d^{4} x - i b d^{4}\right) \log{\left(- i c x + 1 \right)}}{10 x^{5}} + \frac{\left(5 i b c^{4} d^{4} x^{4} + 10 b c^{3} d^{4} x^{3} - 10 i b c^{2} d^{4} x^{2} - 5 b c d^{4} x + i b d^{4}\right) \log{\left(i c x + 1 \right)}}{10 x^{5}}"," ",0,"16*b*c**5*d**4*log(10395*b**2*c**11*d**8*x)/5 - b*c**5*d**4*log(10395*b**2*c**11*d**8*x - 10395*I*b**2*c**10*d**8)/10 - 31*b*c**5*d**4*log(10395*b**2*c**11*d**8*x + 10395*I*b**2*c**10*d**8)/10 + (-12*a*d**4 + x**4*(-60*a*c**4*d**4 + 180*I*b*c**4*d**4) + x**3*(120*I*a*c**3*d**4 + 66*b*c**3*d**4) + x**2*(120*a*c**2*d**4 - 20*I*b*c**2*d**4) + x*(-60*I*a*c*d**4 - 3*b*c*d**4))/(60*x**5) + (-5*I*b*c**4*d**4*x**4 - 10*b*c**3*d**4*x**3 + 10*I*b*c**2*d**4*x**2 + 5*b*c*d**4*x - I*b*d**4)*log(-I*c*x + 1)/(10*x**5) + (5*I*b*c**4*d**4*x**4 + 10*b*c**3*d**4*x**3 - 10*I*b*c**2*d**4*x**2 - 5*b*c*d**4*x + I*b*d**4)*log(I*c*x + 1)/(10*x**5)","B",0
41,1,388,0,138.240681," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x**7,x)","\frac{32 i b c^{6} d^{4} \log{\left(2121535 b^{2} c^{13} d^{8} x \right)}}{15} + \frac{i b c^{6} d^{4} \log{\left(2121535 b^{2} c^{13} d^{8} x - 2121535 i b^{2} c^{12} d^{8} \right)}}{60} - \frac{43 i b c^{6} d^{4} \log{\left(2121535 b^{2} c^{13} d^{8} x + 2121535 i b^{2} c^{12} d^{8} \right)}}{20} + \frac{\left(- 15 i b c^{4} d^{4} x^{4} - 40 b c^{3} d^{4} x^{3} + 45 i b c^{2} d^{4} x^{2} + 24 b c d^{4} x - 5 i b d^{4}\right) \log{\left(- i c x + 1 \right)}}{60 x^{6}} + \frac{\left(15 i b c^{4} d^{4} x^{4} + 40 b c^{3} d^{4} x^{3} - 45 i b c^{2} d^{4} x^{2} - 24 b c d^{4} x + 5 i b d^{4}\right) \log{\left(i c x + 1 \right)}}{60 x^{6}} + \frac{- 15 a d^{4} - 195 b c^{5} d^{4} x^{5} + x^{4} \left(- 45 a c^{4} d^{4} + 96 i b c^{4} d^{4}\right) + x^{3} \left(120 i a c^{3} d^{4} + 50 b c^{3} d^{4}\right) + x^{2} \left(135 a c^{2} d^{4} - 18 i b c^{2} d^{4}\right) + x \left(- 72 i a c d^{4} - 3 b c d^{4}\right)}{90 x^{6}}"," ",0,"32*I*b*c**6*d**4*log(2121535*b**2*c**13*d**8*x)/15 + I*b*c**6*d**4*log(2121535*b**2*c**13*d**8*x - 2121535*I*b**2*c**12*d**8)/60 - 43*I*b*c**6*d**4*log(2121535*b**2*c**13*d**8*x + 2121535*I*b**2*c**12*d**8)/20 + (-15*I*b*c**4*d**4*x**4 - 40*b*c**3*d**4*x**3 + 45*I*b*c**2*d**4*x**2 + 24*b*c*d**4*x - 5*I*b*d**4)*log(-I*c*x + 1)/(60*x**6) + (15*I*b*c**4*d**4*x**4 + 40*b*c**3*d**4*x**3 - 45*I*b*c**2*d**4*x**2 - 24*b*c*d**4*x + 5*I*b*d**4)*log(I*c*x + 1)/(60*x**6) + (-15*a*d**4 - 195*b*c**5*d**4*x**5 + x**4*(-45*a*c**4*d**4 + 96*I*b*c**4*d**4) + x**3*(120*I*a*c**3*d**4 + 50*b*c**3*d**4) + x**2*(135*a*c**2*d**4 - 18*I*b*c**2*d**4) + x*(-72*I*a*c*d**4 - 3*b*c*d**4))/(90*x**6)","B",0
42,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**4*(a+b*atan(c*x))/x**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{6 i b \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{12 a c^{4} x^{4}}{c^{2} x^{2} + 1}\, dx + \int \frac{6 b c x}{c^{2} x^{2} + 1}\, dx + \int \frac{b c^{3} x^{3}}{c^{2} x^{2} + 1}\, dx + \int \frac{12 i a c^{3} x^{3}}{c^{2} x^{2} + 1}\, dx + \int \frac{3 i b c^{2} x^{2}}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{2 i b c^{4} x^{4}}{c^{2} x^{2} + 1}\right)\, dx + \int \left(- \frac{6 b c x \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\right)\, dx + \int \frac{6 b c^{3} x^{3} \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{6 i b c^{4} x^{4} \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\right)\, dx\right)}{12 c^{3} d} + \frac{\left(2 b c^{3} x^{3} + 3 i b c^{2} x^{2} - 6 b c x - 6 i b \log{\left(i c x + 1 \right)}\right) \log{\left(- i c x + 1 \right)}}{12 c^{4} d}"," ",0,"-I*(Integral(6*I*b*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(12*a*c**4*x**4/(c**2*x**2 + 1), x) + Integral(6*b*c*x/(c**2*x**2 + 1), x) + Integral(b*c**3*x**3/(c**2*x**2 + 1), x) + Integral(12*I*a*c**3*x**3/(c**2*x**2 + 1), x) + Integral(3*I*b*c**2*x**2/(c**2*x**2 + 1), x) + Integral(-2*I*b*c**4*x**4/(c**2*x**2 + 1), x) + Integral(-6*b*c*x*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(6*b*c**3*x**3*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(-6*I*b*c**4*x**4*log(I*c*x + 1)/(c**2*x**2 + 1), x))/(12*c**3*d) + (2*b*c**3*x**3 + 3*I*b*c**2*x**2 - 6*b*c*x - 6*I*b*log(I*c*x + 1))*log(-I*c*x + 1)/(12*c**4*d)","F",0
44,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{2 b \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{4 a c^{3} x^{3}}{c^{2} x^{2} + 1}\, dx + \int \frac{b c^{2} x^{2}}{c^{2} x^{2} + 1}\, dx + \int \frac{4 i a c^{2} x^{2}}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{2 i b c x}{c^{2} x^{2} + 1}\right)\, dx + \int \left(- \frac{i b c^{3} x^{3}}{c^{2} x^{2} + 1}\right)\, dx + \int \frac{2 b c^{2} x^{2} \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\, dx + \int \frac{2 i b c x \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{2 i b c^{3} x^{3} \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\right)\, dx\right)}{4 c^{2} d} + \frac{\left(b c^{2} x^{2} + 2 i b c x - 2 b \log{\left(i c x + 1 \right)}\right) \log{\left(- i c x + 1 \right)}}{4 c^{3} d}"," ",0,"-I*(Integral(2*b*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(4*a*c**3*x**3/(c**2*x**2 + 1), x) + Integral(b*c**2*x**2/(c**2*x**2 + 1), x) + Integral(4*I*a*c**2*x**2/(c**2*x**2 + 1), x) + Integral(-2*I*b*c*x/(c**2*x**2 + 1), x) + Integral(-I*b*c**3*x**3/(c**2*x**2 + 1), x) + Integral(2*b*c**2*x**2*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(2*I*b*c*x*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(-2*I*b*c**3*x**3*log(I*c*x + 1)/(c**2*x**2 + 1), x))/(4*c**2*d) + (b*c**2*x**2 + 2*I*b*c*x - 2*b*log(I*c*x + 1))*log(-I*c*x + 1)/(4*c**3*d)","F",0
45,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(d+I*c*d*x),x)","- \frac{i \left(\int \left(- \frac{i b \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\right)\, dx + \int \frac{2 a c^{2} x^{2}}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{b c x}{c^{2} x^{2} + 1}\right)\, dx + \int \frac{2 i a c x}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{i b c^{2} x^{2}}{c^{2} x^{2} + 1}\right)\, dx + \int \frac{2 b c x \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{i b c^{2} x^{2} \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\right)\, dx\right)}{2 c d} + \frac{\left(b c x + i b \log{\left(i c x + 1 \right)}\right) \log{\left(- i c x + 1 \right)}}{2 c^{2} d}"," ",0,"-I*(Integral(-I*b*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(2*a*c**2*x**2/(c**2*x**2 + 1), x) + Integral(-b*c*x/(c**2*x**2 + 1), x) + Integral(2*I*a*c*x/(c**2*x**2 + 1), x) + Integral(-I*b*c**2*x**2/(c**2*x**2 + 1), x) + Integral(2*b*c*x*log(I*c*x + 1)/(c**2*x**2 + 1), x) + Integral(-I*b*c**2*x**2*log(I*c*x + 1)/(c**2*x**2 + 1), x))/(2*c*d) + (b*c*x + I*b*log(I*c*x + 1))*log(-I*c*x + 1)/(2*c**2*d)","F",0
46,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/(d+I*c*d*x),x)","\frac{b \log{\left(- i c x + 1 \right)} \log{\left(i c x + 1 \right)}}{2 c d} - \frac{i \left(\int \frac{i a}{c^{2} x^{2} + 1}\, dx + \int \frac{a c x}{c^{2} x^{2} + 1}\, dx + \int \left(- \frac{i b c x \log{\left(i c x + 1 \right)}}{c^{2} x^{2} + 1}\right)\, dx\right)}{d}"," ",0,"b*log(-I*c*x + 1)*log(I*c*x + 1)/(2*c*d) - I*(Integral(I*a/(c**2*x**2 + 1), x) + Integral(a*c*x/(c**2*x**2 + 1), x) + Integral(-I*b*c*x*log(I*c*x + 1)/(c**2*x**2 + 1), x))/d","F",0
47,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a}{c x^{2} - i x}\, dx + \int \frac{b \operatorname{atan}{\left(c x \right)}}{c x^{2} - i x}\, dx\right)}{d}"," ",0,"-I*(Integral(a/(c*x**2 - I*x), x) + Integral(b*atan(c*x)/(c*x**2 - I*x), x))/d","F",0
48,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a}{c x^{3} - i x^{2}}\, dx + \int \frac{b \operatorname{atan}{\left(c x \right)}}{c x^{3} - i x^{2}}\, dx\right)}{d}"," ",0,"-I*(Integral(a/(c*x**3 - I*x**2), x) + Integral(b*atan(c*x)/(c*x**3 - I*x**2), x))/d","F",0
49,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a}{c x^{4} - i x^{3}}\, dx + \int \frac{b \operatorname{atan}{\left(c x \right)}}{c x^{4} - i x^{3}}\, dx\right)}{d}"," ",0,"-I*(Integral(a/(c*x**4 - I*x**3), x) + Integral(b*atan(c*x)/(c*x**4 - I*x**3), x))/d","F",0
50,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**4/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(d+I*c*d*x)**2,x)","\frac{\left(b c x \log{\left(i c x + 1 \right)} - i b \log{\left(i c x + 1 \right)} - i b\right) \log{\left(- i c x + 1 \right)}}{2 i c^{3} d^{2} x + 2 c^{2} d^{2}} - \frac{\int \frac{i b}{c^{3} x^{3} - i c^{2} x^{2} + c x - i}\, dx + \int \frac{i b \log{\left(i c x + 1 \right)}}{c^{3} x^{3} - i c^{2} x^{2} + c x - i}\, dx + \int \frac{2 a c^{2} x^{2}}{c^{3} x^{3} - i c^{2} x^{2} + c x - i}\, dx + \int \left(- \frac{b c x}{c^{3} x^{3} - i c^{2} x^{2} + c x - i}\right)\, dx + \int \frac{2 i a c x}{c^{3} x^{3} - i c^{2} x^{2} + c x - i}\, dx + \int \left(- \frac{b c x \log{\left(i c x + 1 \right)}}{c^{3} x^{3} - i c^{2} x^{2} + c x - i}\right)\, dx + \int \left(- \frac{2 i b c^{2} x^{2} \log{\left(i c x + 1 \right)}}{c^{3} x^{3} - i c^{2} x^{2} + c x - i}\right)\, dx}{2 c d^{2}}"," ",0,"(b*c*x*log(I*c*x + 1) - I*b*log(I*c*x + 1) - I*b)*log(-I*c*x + 1)/(2*I*c**3*d**2*x + 2*c**2*d**2) - (Integral(I*b/(c**3*x**3 - I*c**2*x**2 + c*x - I), x) + Integral(I*b*log(I*c*x + 1)/(c**3*x**3 - I*c**2*x**2 + c*x - I), x) + Integral(2*a*c**2*x**2/(c**3*x**3 - I*c**2*x**2 + c*x - I), x) + Integral(-b*c*x/(c**3*x**3 - I*c**2*x**2 + c*x - I), x) + Integral(2*I*a*c*x/(c**3*x**3 - I*c**2*x**2 + c*x - I), x) + Integral(-b*c*x*log(I*c*x + 1)/(c**3*x**3 - I*c**2*x**2 + c*x - I), x) + Integral(-2*I*b*c**2*x**2*log(I*c*x + 1)/(c**3*x**3 - I*c**2*x**2 + c*x - I), x))/(2*c*d**2)","F",0
54,1,116,0,1.944218," ","integrate((a+b*atan(c*x))/(d+I*c*d*x)**2,x)","\frac{i b \log{\left(- i c x + 1 \right)}}{2 c^{2} d^{2} x - 2 i c d^{2}} - \frac{i b \log{\left(i c x + 1 \right)}}{2 c^{2} d^{2} x - 2 i c d^{2}} - \frac{b \left(\frac{\log{\left(b x - \frac{i b}{c} \right)}}{4} - \frac{\log{\left(b x + \frac{i b}{c} \right)}}{4}\right)}{c d^{2}} - \frac{- 2 a + i b}{2 c^{2} d^{2} x - 2 i c d^{2}}"," ",0,"I*b*log(-I*c*x + 1)/(2*c**2*d**2*x - 2*I*c*d**2) - I*b*log(I*c*x + 1)/(2*c**2*d**2*x - 2*I*c*d**2) - b*(log(b*x - I*b/c)/4 - log(b*x + I*b/c)/4)/(c*d**2) - (-2*a + I*b)/(2*c**2*d**2*x - 2*I*c*d**2)","B",0
55,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(d+I*c*d*x)**2,x)","- \frac{\int \frac{a}{c^{2} x^{5} - 2 i c x^{4} - x^{3}}\, dx + \int \frac{b \operatorname{atan}{\left(c x \right)}}{c^{2} x^{5} - 2 i c x^{4} - x^{3}}\, dx}{d^{2}}"," ",0,"-(Integral(a/(c**2*x**5 - 2*I*c*x**4 - x**3), x) + Integral(b*atan(c*x)/(c**2*x**5 - 2*I*c*x**4 - x**3), x))/d**2","F",0
58,-1,0,0,0.000000," ","integrate(x**4*(a+b*atan(c*x))/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,1,194,0,10.221585," ","integrate(x*(a+b*atan(c*x))/(d+I*c*d*x)**3,x)","\frac{b \left(\frac{3 i \log{\left(x - \frac{i}{c} \right)}}{16} - \frac{3 i \log{\left(x + \frac{i}{c} \right)}}{16}\right)}{c^{2} d^{3}} + \frac{\left(- 2 i b c x - b\right) \log{\left(i c x + 1 \right)}}{4 i c^{4} d^{3} x^{2} + 8 c^{3} d^{3} x - 4 i c^{2} d^{3}} + \frac{\left(- 2 i b c x - b\right) \log{\left(- i c x + 1 \right)}}{- 4 i c^{4} d^{3} x^{2} - 8 c^{3} d^{3} x + 4 i c^{2} d^{3}} + \frac{4 a - 2 i b + x \left(8 i a c + 3 b c\right)}{- 8 c^{4} d^{3} x^{2} + 16 i c^{3} d^{3} x + 8 c^{2} d^{3}}"," ",0,"b*(3*I*log(x - I/c)/16 - 3*I*log(x + I/c)/16)/(c**2*d**3) + (-2*I*b*c*x - b)*log(I*c*x + 1)/(4*I*c**4*d**3*x**2 + 8*c**3*d**3*x - 4*I*c**2*d**3) + (-2*I*b*c*x - b)*log(-I*c*x + 1)/(-4*I*c**4*d**3*x**2 - 8*c**3*d**3*x + 4*I*c**2*d**3) + (4*a - 2*I*b + x*(8*I*a*c + 3*b*c))/(-8*c**4*d**3*x**2 + 16*I*c**3*d**3*x + 8*c**2*d**3)","B",0
62,1,158,0,3.691080," ","integrate((a+b*atan(c*x))/(d+I*c*d*x)**3,x)","\frac{b \log{\left(- i c x + 1 \right)}}{4 c^{3} d^{3} x^{2} - 8 i c^{2} d^{3} x - 4 c d^{3}} - \frac{b \log{\left(i c x + 1 \right)}}{4 c^{3} d^{3} x^{2} - 8 i c^{2} d^{3} x - 4 c d^{3}} - \frac{b \left(\frac{\log{\left(b x - \frac{i b}{c} \right)}}{16} - \frac{\log{\left(b x + \frac{i b}{c} \right)}}{16}\right)}{c d^{3}} - \frac{- 4 i a - i b c x - 2 b}{- 8 c^{3} d^{3} x^{2} + 16 i c^{2} d^{3} x + 8 c d^{3}}"," ",0,"b*log(-I*c*x + 1)/(4*c**3*d**3*x**2 - 8*I*c**2*d**3*x - 4*c*d**3) - b*log(I*c*x + 1)/(4*c**3*d**3*x**2 - 8*I*c**2*d**3*x - 4*c*d**3) - b*(log(b*x - I*b/c)/16 - log(b*x + I*b/c)/16)/(c*d**3) - (-4*I*a - I*b*c*x - 2*b)/(-8*c**3*d**3*x**2 + 16*I*c**2*d**3*x + 8*c*d**3)","B",0
63,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(d+I*c*d*x)**3,x)","\frac{i \left(\int \frac{a}{c^{3} x^{6} - 3 i c^{2} x^{5} - 3 c x^{4} + i x^{3}}\, dx + \int \frac{b \operatorname{atan}{\left(c x \right)}}{c^{3} x^{6} - 3 i c^{2} x^{5} - 3 c x^{4} + i x^{3}}\, dx\right)}{d^{3}}"," ",0,"I*(Integral(a/(c**3*x**6 - 3*I*c**2*x**5 - 3*c*x**4 + I*x**3), x) + Integral(b*atan(c*x)/(c**3*x**6 - 3*I*c**2*x**5 - 3*c*x**4 + I*x**3), x))/d**3","F",0
66,1,168,0,4.266583," ","integrate((a+b*atan(c*x))/(1+I*c*x)**4,x)","- \frac{i b \log{\left(- i c x + 1 \right)}}{6 c^{4} x^{3} - 18 i c^{3} x^{2} - 18 c^{2} x + 6 i c} + \frac{i b \log{\left(i c x + 1 \right)}}{6 c^{4} x^{3} - 18 i c^{3} x^{2} - 18 c^{2} x + 6 i c} + \frac{b \left(- \frac{\log{\left(b x - \frac{i b}{c} \right)}}{48} + \frac{\log{\left(b x + \frac{i b}{c} \right)}}{48}\right)}{c} + \frac{24 a + 3 i b c^{2} x^{2} + 9 b c x - 10 i b}{- 72 c^{4} x^{3} + 216 i c^{3} x^{2} + 216 c^{2} x - 72 i c}"," ",0,"-I*b*log(-I*c*x + 1)/(6*c**4*x**3 - 18*I*c**3*x**2 - 18*c**2*x + 6*I*c) + I*b*log(I*c*x + 1)/(6*c**4*x**3 - 18*I*c**3*x**2 - 18*c**2*x + 6*I*c) + b*(-log(b*x - I*b/c)/48 + log(b*x + I*b/c)/48)/c + (24*a + 3*I*b*c**2*x**2 + 9*b*c*x - 10*I*b)/(-72*c**4*x**3 + 216*I*c**3*x**2 + 216*c**2*x - 72*I*c)","B",0
67,0,0,0,0.000000," ","integrate(atan(a*x)/(c*x+I*a*c*x**2),x)","- \frac{i \int \frac{\operatorname{atan}{\left(a x \right)}}{a x^{2} - i x}\, dx}{c}"," ",0,"-I*Integral(atan(a*x)/(a*x**2 - I*x), x)/c","F",0
68,-1,0,0,0.000000," ","integrate(x**3*(d+I*c*d*x)*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate(x**2*(d+I*c*d*x)*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate(x*(d+I*c*d*x)*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))**2/x,x)","i d \left(\int a^{2} c\, dx + \int \left(- \frac{i a^{2}}{x}\right)\, dx + \int b^{2} c \operatorname{atan}^{2}{\left(c x \right)}\, dx + \int \left(- \frac{i b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{x}\right)\, dx + \int 2 a b c \operatorname{atan}{\left(c x \right)}\, dx + \int \left(- \frac{2 i a b \operatorname{atan}{\left(c x \right)}}{x}\right)\, dx\right)"," ",0,"I*d*(Integral(a**2*c, x) + Integral(-I*a**2/x, x) + Integral(b**2*c*atan(c*x)**2, x) + Integral(-I*b**2*atan(c*x)**2/x, x) + Integral(2*a*b*c*atan(c*x), x) + Integral(-2*I*a*b*atan(c*x)/x, x))","F",0
73,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))**2/x**2,x)","i d \left(\int \left(- \frac{i a^{2}}{x^{2}}\right)\, dx + \int \frac{a^{2} c}{x}\, dx + \int \left(- \frac{i b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{x^{2}}\right)\, dx + \int \frac{b^{2} c \operatorname{atan}^{2}{\left(c x \right)}}{x}\, dx + \int \left(- \frac{2 i a b \operatorname{atan}{\left(c x \right)}}{x^{2}}\right)\, dx + \int \frac{2 a b c \operatorname{atan}{\left(c x \right)}}{x}\, dx\right)"," ",0,"I*d*(Integral(-I*a**2/x**2, x) + Integral(a**2*c/x, x) + Integral(-I*b**2*atan(c*x)**2/x**2, x) + Integral(b**2*c*atan(c*x)**2/x, x) + Integral(-2*I*a*b*atan(c*x)/x**2, x) + Integral(2*a*b*c*atan(c*x)/x, x))","F",0
74,-1,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))**2/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(x**3*(d+I*c*d*x)**2*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(x**2*(d+I*c*d*x)**2*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(x*(d+I*c*d*x)**2*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,0,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))**2/x,x)","- d^{2} \left(\int \left(- \frac{a^{2}}{x}\right)\, dx + \int \left(- 2 i a^{2} c\right)\, dx + \int a^{2} c^{2} x\, dx + \int \left(- \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{x}\right)\, dx + \int \left(- 2 i b^{2} c \operatorname{atan}^{2}{\left(c x \right)}\right)\, dx + \int \left(- \frac{2 a b \operatorname{atan}{\left(c x \right)}}{x}\right)\, dx + \int b^{2} c^{2} x \operatorname{atan}^{2}{\left(c x \right)}\, dx + \int \left(- 4 i a b c \operatorname{atan}{\left(c x \right)}\right)\, dx + \int 2 a b c^{2} x \operatorname{atan}{\left(c x \right)}\, dx\right)"," ",0,"-d**2*(Integral(-a**2/x, x) + Integral(-2*I*a**2*c, x) + Integral(a**2*c**2*x, x) + Integral(-b**2*atan(c*x)**2/x, x) + Integral(-2*I*b**2*c*atan(c*x)**2, x) + Integral(-2*a*b*atan(c*x)/x, x) + Integral(b**2*c**2*x*atan(c*x)**2, x) + Integral(-4*I*a*b*c*atan(c*x), x) + Integral(2*a*b*c**2*x*atan(c*x), x))","F",0
81,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))**2/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))**2/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(x**3*(d+I*c*d*x)**3*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(x**2*(d+I*c*d*x)**3*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(x*(d+I*c*d*x)**3*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**2/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))**2/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**2/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))**2/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a^{2}}{c x^{2} - i x}\, dx + \int \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c x^{2} - i x}\, dx + \int \frac{2 a b \operatorname{atan}{\left(c x \right)}}{c x^{2} - i x}\, dx\right)}{d}"," ",0,"-I*(Integral(a**2/(c*x**2 - I*x), x) + Integral(b**2*atan(c*x)**2/(c*x**2 - I*x), x) + Integral(2*a*b*atan(c*x)/(c*x**2 - I*x), x))/d","F",0
100,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**2/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a^{2}}{c x^{3} - i x^{2}}\, dx + \int \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c x^{3} - i x^{2}}\, dx + \int \frac{2 a b \operatorname{atan}{\left(c x \right)}}{c x^{3} - i x^{2}}\, dx\right)}{d}"," ",0,"-I*(Integral(a**2/(c*x**3 - I*x**2), x) + Integral(b**2*atan(c*x)**2/(c*x**3 - I*x**2), x) + Integral(2*a*b*atan(c*x)/(c*x**3 - I*x**2), x))/d","F",0
101,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**3/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a^{2}}{c x^{4} - i x^{3}}\, dx + \int \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c x^{4} - i x^{3}}\, dx + \int \frac{2 a b \operatorname{atan}{\left(c x \right)}}{c x^{4} - i x^{3}}\, dx\right)}{d}"," ",0,"-I*(Integral(a**2/(c*x**4 - I*x**3), x) + Integral(b**2*atan(c*x)**2/(c*x**4 - I*x**3), x) + Integral(2*a*b*atan(c*x)/(c*x**4 - I*x**3), x))/d","F",0
102,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**4/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a^{2}}{c x^{5} - i x^{4}}\, dx + \int \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c x^{5} - i x^{4}}\, dx + \int \frac{2 a b \operatorname{atan}{\left(c x \right)}}{c x^{5} - i x^{4}}\, dx\right)}{d}"," ",0,"-I*(Integral(a**2/(c*x**5 - I*x**4), x) + Integral(b**2*atan(c*x)**2/(c*x**5 - I*x**4), x) + Integral(2*a*b*atan(c*x)/(c*x**5 - I*x**4), x))/d","F",0
103,-1,0,0,0.000000," ","integrate(x**4*(a+b*atan(c*x))**2/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))**2/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**2/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))**2/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,1,301,0,10.371192," ","integrate((a+b*atan(c*x))**2/(d+I*c*d*x)**2,x)","\frac{b \left(2 a - i b\right) \log{\left(- \frac{b \left(2 a - i b\right)}{c} + x \left(2 i a b + b^{2}\right) \right)}}{4 c d^{2}} - \frac{b \left(2 a - i b\right) \log{\left(\frac{b \left(2 a - i b\right)}{c} + x \left(2 i a b + b^{2}\right) \right)}}{4 c d^{2}} + \frac{\left(- 2 i a b - b^{2}\right) \log{\left(i c x + 1 \right)}}{2 c^{2} d^{2} x - 2 i c d^{2}} + \frac{\left(- b^{2} c x - i b^{2}\right) \log{\left(- i c x + 1 \right)}^{2}}{8 i c^{2} d^{2} x + 8 c d^{2}} + \frac{\left(- 4 a b + b^{2} c x \log{\left(i c x + 1 \right)} + i b^{2} \log{\left(i c x + 1 \right)} + 2 i b^{2}\right) \log{\left(- i c x + 1 \right)}}{4 i c^{2} d^{2} x + 4 c d^{2}} + \frac{\left(i b^{2} c x - b^{2}\right) \log{\left(i c x + 1 \right)}^{2}}{8 c^{2} d^{2} x - 8 i c d^{2}} - \frac{- 2 a^{2} + 2 i a b + b^{2}}{2 c^{2} d^{2} x - 2 i c d^{2}}"," ",0,"b*(2*a - I*b)*log(-b*(2*a - I*b)/c + x*(2*I*a*b + b**2))/(4*c*d**2) - b*(2*a - I*b)*log(b*(2*a - I*b)/c + x*(2*I*a*b + b**2))/(4*c*d**2) + (-2*I*a*b - b**2)*log(I*c*x + 1)/(2*c**2*d**2*x - 2*I*c*d**2) + (-b**2*c*x - I*b**2)*log(-I*c*x + 1)**2/(8*I*c**2*d**2*x + 8*c*d**2) + (-4*a*b + b**2*c*x*log(I*c*x + 1) + I*b**2*log(I*c*x + 1) + 2*I*b**2)*log(-I*c*x + 1)/(4*I*c**2*d**2*x + 4*c*d**2) + (I*b**2*c*x - b**2)*log(I*c*x + 1)**2/(8*c**2*d**2*x - 8*I*c*d**2) - (-2*a**2 + 2*I*a*b + b**2)/(2*c**2*d**2*x - 2*I*c*d**2)","B",0
108,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**2/(d+I*c*d*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**3/(d+I*c*d*x)**2,x)","- \frac{\int \frac{a^{2}}{c^{2} x^{5} - 2 i c x^{4} - x^{3}}\, dx + \int \frac{b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c^{2} x^{5} - 2 i c x^{4} - x^{3}}\, dx + \int \frac{2 a b \operatorname{atan}{\left(c x \right)}}{c^{2} x^{5} - 2 i c x^{4} - x^{3}}\, dx}{d^{2}}"," ",0,"-(Integral(a**2/(c**2*x**5 - 2*I*c*x**4 - x**3), x) + Integral(b**2*atan(c*x)**2/(c**2*x**5 - 2*I*c*x**4 - x**3), x) + Integral(2*a*b*atan(c*x)/(c**2*x**5 - 2*I*c*x**4 - x**3), x))/d**2","F",0
111,-1,0,0,0.000000," ","integrate(x**4*(a+b*atan(c*x))**2/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))**2/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**2/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,1,502,0,84.073308," ","integrate(x*(a+b*atan(c*x))**2/(d+I*c*d*x)**3,x)","- \frac{i b \left(12 a - 5 i b\right) \log{\left(- \frac{b \left(12 a - 5 i b\right)}{c} + x \left(12 i a b + 5 b^{2}\right) \right)}}{32 c^{2} d^{3}} + \frac{i b \left(12 a - 5 i b\right) \log{\left(\frac{b \left(12 a - 5 i b\right)}{c} + x \left(12 i a b + 5 b^{2}\right) \right)}}{32 c^{2} d^{3}} + \frac{\left(- 3 b^{2} c^{2} x^{2} - 2 i b^{2} c x - b^{2}\right) \log{\left(- i c x + 1 \right)}^{2}}{- 32 c^{4} d^{3} x^{2} + 64 i c^{3} d^{3} x + 32 c^{2} d^{3}} + \frac{\left(- 3 b^{2} c^{2} x^{2} - 2 i b^{2} c x - b^{2}\right) \log{\left(i c x + 1 \right)}^{2}}{- 32 c^{4} d^{3} x^{2} + 64 i c^{3} d^{3} x + 32 c^{2} d^{3}} + \frac{\left(- 8 a b c x + 4 i a b + 3 i b^{2} c x + 2 b^{2}\right) \log{\left(i c x + 1 \right)}}{8 c^{4} d^{3} x^{2} - 16 i c^{3} d^{3} x - 8 c^{2} d^{3}} - \frac{- 8 a^{2} + 8 i a b + 4 b^{2} + x \left(- 16 i a^{2} c - 12 a b c + 5 i b^{2} c\right)}{- 16 c^{4} d^{3} x^{2} + 32 i c^{3} d^{3} x + 16 c^{2} d^{3}} + \frac{\left(- 16 a b c x + 8 i a b + 3 b^{2} c^{2} x^{2} \log{\left(i c x + 1 \right)} + 2 i b^{2} c x \log{\left(i c x + 1 \right)} + 6 i b^{2} c x + b^{2} \log{\left(i c x + 1 \right)} + 4 b^{2}\right) \log{\left(- i c x + 1 \right)}}{- 16 c^{4} d^{3} x^{2} + 32 i c^{3} d^{3} x + 16 c^{2} d^{3}}"," ",0,"-I*b*(12*a - 5*I*b)*log(-b*(12*a - 5*I*b)/c + x*(12*I*a*b + 5*b**2))/(32*c**2*d**3) + I*b*(12*a - 5*I*b)*log(b*(12*a - 5*I*b)/c + x*(12*I*a*b + 5*b**2))/(32*c**2*d**3) + (-3*b**2*c**2*x**2 - 2*I*b**2*c*x - b**2)*log(-I*c*x + 1)**2/(-32*c**4*d**3*x**2 + 64*I*c**3*d**3*x + 32*c**2*d**3) + (-3*b**2*c**2*x**2 - 2*I*b**2*c*x - b**2)*log(I*c*x + 1)**2/(-32*c**4*d**3*x**2 + 64*I*c**3*d**3*x + 32*c**2*d**3) + (-8*a*b*c*x + 4*I*a*b + 3*I*b**2*c*x + 2*b**2)*log(I*c*x + 1)/(8*c**4*d**3*x**2 - 16*I*c**3*d**3*x - 8*c**2*d**3) - (-8*a**2 + 8*I*a*b + 4*b**2 + x*(-16*I*a**2*c - 12*a*b*c + 5*I*b**2*c))/(-16*c**4*d**3*x**2 + 32*I*c**3*d**3*x + 16*c**2*d**3) + (-16*a*b*c*x + 8*I*a*b + 3*b**2*c**2*x**2*log(I*c*x + 1) + 2*I*b**2*c*x*log(I*c*x + 1) + 6*I*b**2*c*x + b**2*log(I*c*x + 1) + 4*b**2)*log(-I*c*x + 1)/(-16*c**4*d**3*x**2 + 32*I*c**3*d**3*x + 16*c**2*d**3)","B",0
115,1,464,0,65.266900," ","integrate((a+b*atan(c*x))**2/(d+I*c*d*x)**3,x)","\frac{b \left(4 a - 3 i b\right) \log{\left(- \frac{b \left(4 a - 3 i b\right)}{c} + x \left(4 i a b + 3 b^{2}\right) \right)}}{32 c d^{3}} - \frac{b \left(4 a - 3 i b\right) \log{\left(\frac{b \left(4 a - 3 i b\right)}{c} + x \left(4 i a b + 3 b^{2}\right) \right)}}{32 c d^{3}} + \frac{\left(4 i a b + i b^{2} c x + 2 b^{2}\right) \log{\left(i c x + 1 \right)}}{- 8 i c^{3} d^{3} x^{2} - 16 c^{2} d^{3} x + 8 i c d^{3}} + \frac{\left(- b^{2} c^{2} x^{2} + 2 i b^{2} c x - 3 b^{2}\right) \log{\left(i c x + 1 \right)}^{2}}{32 i c^{3} d^{3} x^{2} + 64 c^{2} d^{3} x - 32 i c d^{3}} + \frac{8 i a^{2} + 8 a b - 4 i b^{2} + x \left(4 i a b c + 3 b^{2} c\right)}{- 16 c^{3} d^{3} x^{2} + 32 i c^{2} d^{3} x + 16 c d^{3}} + \frac{\left(- 8 a b + i b^{2} c^{2} x^{2} \log{\left(i c x + 1 \right)} + 2 b^{2} c x \log{\left(i c x + 1 \right)} - 2 b^{2} c x + 3 i b^{2} \log{\left(i c x + 1 \right)} + 4 i b^{2}\right) \log{\left(- i c x + 1 \right)}}{- 16 c^{3} d^{3} x^{2} + 32 i c^{2} d^{3} x + 16 c d^{3}} + \frac{\left(- i b^{2} c^{2} x^{2} - 2 b^{2} c x - 3 i b^{2}\right) \log{\left(- i c x + 1 \right)}^{2}}{- 32 c^{3} d^{3} x^{2} + 64 i c^{2} d^{3} x + 32 c d^{3}}"," ",0,"b*(4*a - 3*I*b)*log(-b*(4*a - 3*I*b)/c + x*(4*I*a*b + 3*b**2))/(32*c*d**3) - b*(4*a - 3*I*b)*log(b*(4*a - 3*I*b)/c + x*(4*I*a*b + 3*b**2))/(32*c*d**3) + (4*I*a*b + I*b**2*c*x + 2*b**2)*log(I*c*x + 1)/(-8*I*c**3*d**3*x**2 - 16*c**2*d**3*x + 8*I*c*d**3) + (-b**2*c**2*x**2 + 2*I*b**2*c*x - 3*b**2)*log(I*c*x + 1)**2/(32*I*c**3*d**3*x**2 + 64*c**2*d**3*x - 32*I*c*d**3) + (8*I*a**2 + 8*a*b - 4*I*b**2 + x*(4*I*a*b*c + 3*b**2*c))/(-16*c**3*d**3*x**2 + 32*I*c**2*d**3*x + 16*c*d**3) + (-8*a*b + I*b**2*c**2*x**2*log(I*c*x + 1) + 2*b**2*c*x*log(I*c*x + 1) - 2*b**2*c*x + 3*I*b**2*log(I*c*x + 1) + 4*I*b**2)*log(-I*c*x + 1)/(-16*c**3*d**3*x**2 + 32*I*c**2*d**3*x + 16*c*d**3) + (-I*b**2*c**2*x**2 - 2*b**2*c*x - 3*I*b**2)*log(-I*c*x + 1)**2/(-32*c**3*d**3*x**2 + 64*I*c**2*d**3*x + 32*c*d**3)","B",0
116,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**2/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,1,549,0,90.242359," ","integrate((a+b*atan(c*x))**2/(1+I*c*x)**4,x)","\frac{b \left(12 a - 11 i b\right) \log{\left(- \frac{b \left(12 a - 11 i b\right)}{c} + x \left(12 i a b + 11 b^{2}\right) \right)}}{288 c} - \frac{b \left(12 a - 11 i b\right) \log{\left(\frac{b \left(12 a - 11 i b\right)}{c} + x \left(12 i a b + 11 b^{2}\right) \right)}}{288 c} + \frac{\left(48 a b + 3 b^{2} c^{3} x^{3} \log{\left(i c x + 1 \right)} - 9 i b^{2} c^{2} x^{2} \log{\left(i c x + 1 \right)} + 6 i b^{2} c^{2} x^{2} - 9 b^{2} c x \log{\left(i c x + 1 \right)} + 18 b^{2} c x - 21 i b^{2} \log{\left(i c x + 1 \right)} - 20 i b^{2}\right) \log{\left(- i c x + 1 \right)}}{144 i c^{4} x^{3} + 432 c^{3} x^{2} - 432 i c^{2} x - 144 c} + \frac{\left(- b^{2} c^{3} x^{3} + 3 i b^{2} c^{2} x^{2} + 3 b^{2} c x + 7 i b^{2}\right) \log{\left(- i c x + 1 \right)}^{2}}{96 i c^{4} x^{3} + 288 c^{3} x^{2} - 288 i c^{2} x - 96 c} + \frac{\left(24 i a b - 3 b^{2} c^{2} x^{2} + 9 i b^{2} c x + 10 b^{2}\right) \log{\left(i c x + 1 \right)}}{72 c^{4} x^{3} - 216 i c^{3} x^{2} - 216 c^{2} x + 72 i c} + \frac{\left(- i b^{2} c^{3} x^{3} - 3 b^{2} c^{2} x^{2} + 3 i b^{2} c x - 7 b^{2}\right) \log{\left(i c x + 1 \right)}^{2}}{- 96 c^{4} x^{3} + 288 i c^{3} x^{2} + 288 c^{2} x - 96 i c} - \frac{- 144 a^{2} + 120 i a b + 56 b^{2} + x^{2} \left(- 36 i a b c^{2} - 33 b^{2} c^{2}\right) + x \left(- 108 a b c + 81 i b^{2} c\right)}{- 432 c^{4} x^{3} + 1296 i c^{3} x^{2} + 1296 c^{2} x - 432 i c}"," ",0,"b*(12*a - 11*I*b)*log(-b*(12*a - 11*I*b)/c + x*(12*I*a*b + 11*b**2))/(288*c) - b*(12*a - 11*I*b)*log(b*(12*a - 11*I*b)/c + x*(12*I*a*b + 11*b**2))/(288*c) + (48*a*b + 3*b**2*c**3*x**3*log(I*c*x + 1) - 9*I*b**2*c**2*x**2*log(I*c*x + 1) + 6*I*b**2*c**2*x**2 - 9*b**2*c*x*log(I*c*x + 1) + 18*b**2*c*x - 21*I*b**2*log(I*c*x + 1) - 20*I*b**2)*log(-I*c*x + 1)/(144*I*c**4*x**3 + 432*c**3*x**2 - 432*I*c**2*x - 144*c) + (-b**2*c**3*x**3 + 3*I*b**2*c**2*x**2 + 3*b**2*c*x + 7*I*b**2)*log(-I*c*x + 1)**2/(96*I*c**4*x**3 + 288*c**3*x**2 - 288*I*c**2*x - 96*c) + (24*I*a*b - 3*b**2*c**2*x**2 + 9*I*b**2*c*x + 10*b**2)*log(I*c*x + 1)/(72*c**4*x**3 - 216*I*c**3*x**2 - 216*c**2*x + 72*I*c) + (-I*b**2*c**3*x**3 - 3*b**2*c**2*x**2 + 3*I*b**2*c*x - 7*b**2)*log(I*c*x + 1)**2/(-96*c**4*x**3 + 288*I*c**3*x**2 + 288*c**2*x - 96*I*c) - (-144*a**2 + 120*I*a*b + 56*b**2 + x**2*(-36*I*a*b*c**2 - 33*b**2*c**2) + x*(-108*a*b*c + 81*I*b**2*c))/(-432*c**4*x**3 + 1296*I*c**3*x**2 + 1296*c**2*x - 432*I*c)","B",0
119,0,0,0,0.000000," ","integrate(atan(a*x)**2/(c*x-I*a*c*x**2),x)","\frac{i \int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a x^{2} + i x}\, dx}{c}"," ",0,"I*Integral(atan(a*x)**2/(a*x**2 + I*x), x)/c","F",0
120,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**3*(a+b*atan(c*x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((d+I*c*d*x)**2*(a+b*atan(c*x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*atan(c*x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,1,627,0,37.132372," ","integrate((a+b*atan(c*x))**3/(d+I*c*d*x)**2,x)","- \frac{3 i b \left(a \left(1 - i\right) - b\right) \left(a \left(1 - i\right) - i b\right) \log{\left(- \frac{3 b \left(a \left(1 - i\right) - b\right) \left(a \left(1 - i\right) - i b\right)}{c} + x \left(- 6 a^{2} b + 6 i a b^{2} + 3 b^{3}\right) \right)}}{8 c d^{2}} + \frac{3 i b \left(a \left(1 - i\right) - b\right) \left(a \left(1 - i\right) - i b\right) \log{\left(\frac{3 b \left(a \left(1 - i\right) - b\right) \left(a \left(1 - i\right) - i b\right)}{c} + x \left(- 6 a^{2} b + 6 i a b^{2} + 3 b^{3}\right) \right)}}{8 c d^{2}} + \frac{\left(- i b^{3} c x + b^{3}\right) \log{\left(- i c x + 1 \right)}^{3}}{16 i c^{2} d^{2} x + 16 c d^{2}} + \frac{\left(i b^{3} c x - b^{3}\right) \log{\left(i c x + 1 \right)}^{3}}{16 i c^{2} d^{2} x + 16 c d^{2}} + \frac{\left(- 6 a b^{2} c x - 6 i a b^{2} + 3 i b^{3} c x \log{\left(i c x + 1 \right)} + 3 i b^{3} c x - 3 b^{3} \log{\left(i c x + 1 \right)} - 3 b^{3}\right) \log{\left(- i c x + 1 \right)}^{2}}{16 i c^{2} d^{2} x + 16 c d^{2}} + \frac{\left(- 24 a^{2} b + 12 a b^{2} c x \log{\left(i c x + 1 \right)} + 12 i a b^{2} \log{\left(i c x + 1 \right)} + 24 i a b^{2} - 3 i b^{3} c x \log{\left(i c x + 1 \right)}^{2} - 6 i b^{3} c x \log{\left(i c x + 1 \right)} + 3 b^{3} \log{\left(i c x + 1 \right)}^{2} + 6 b^{3} \log{\left(i c x + 1 \right)} + 12 b^{3}\right) \log{\left(- i c x + 1 \right)}}{16 i c^{2} d^{2} x + 16 c d^{2}} + \frac{\left(6 a^{2} b - 6 i a b^{2} - 3 b^{3}\right) \log{\left(i c x + 1 \right)}}{4 i c^{2} d^{2} x + 4 c d^{2}} + \frac{\left(6 a b^{2} c x + 6 i a b^{2} - 3 i b^{3} c x + 3 b^{3}\right) \log{\left(i c x + 1 \right)}^{2}}{- 16 i c^{2} d^{2} x - 16 c d^{2}} - \frac{- 4 a^{3} + 6 i a^{2} b + 6 a b^{2} - 3 i b^{3}}{4 c^{2} d^{2} x - 4 i c d^{2}}"," ",0,"-3*I*b*(a*(1 - I) - b)*(a*(1 - I) - I*b)*log(-3*b*(a*(1 - I) - b)*(a*(1 - I) - I*b)/c + x*(-6*a**2*b + 6*I*a*b**2 + 3*b**3))/(8*c*d**2) + 3*I*b*(a*(1 - I) - b)*(a*(1 - I) - I*b)*log(3*b*(a*(1 - I) - b)*(a*(1 - I) - I*b)/c + x*(-6*a**2*b + 6*I*a*b**2 + 3*b**3))/(8*c*d**2) + (-I*b**3*c*x + b**3)*log(-I*c*x + 1)**3/(16*I*c**2*d**2*x + 16*c*d**2) + (I*b**3*c*x - b**3)*log(I*c*x + 1)**3/(16*I*c**2*d**2*x + 16*c*d**2) + (-6*a*b**2*c*x - 6*I*a*b**2 + 3*I*b**3*c*x*log(I*c*x + 1) + 3*I*b**3*c*x - 3*b**3*log(I*c*x + 1) - 3*b**3)*log(-I*c*x + 1)**2/(16*I*c**2*d**2*x + 16*c*d**2) + (-24*a**2*b + 12*a*b**2*c*x*log(I*c*x + 1) + 12*I*a*b**2*log(I*c*x + 1) + 24*I*a*b**2 - 3*I*b**3*c*x*log(I*c*x + 1)**2 - 6*I*b**3*c*x*log(I*c*x + 1) + 3*b**3*log(I*c*x + 1)**2 + 6*b**3*log(I*c*x + 1) + 12*b**3)*log(-I*c*x + 1)/(16*I*c**2*d**2*x + 16*c*d**2) + (6*a**2*b - 6*I*a*b**2 - 3*b**3)*log(I*c*x + 1)/(4*I*c**2*d**2*x + 4*c*d**2) + (6*a*b**2*c*x + 6*I*a*b**2 - 3*I*b**3*c*x + 3*b**3)*log(I*c*x + 1)**2/(-16*I*c**2*d**2*x - 16*c*d**2) - (-4*a**3 + 6*I*a**2*b + 6*a*b**2 - 3*I*b**3)/(4*c**2*d**2*x - 4*I*c*d**2)","B",0
125,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/(d+I*c*d*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/(d+I*c*d*x)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**3/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))**3/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/(d+I*c*d*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a^{3}}{c x^{2} - i x}\, dx + \int \frac{b^{3} \operatorname{atan}^{3}{\left(c x \right)}}{c x^{2} - i x}\, dx + \int \frac{3 a b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c x^{2} - i x}\, dx + \int \frac{3 a^{2} b \operatorname{atan}{\left(c x \right)}}{c x^{2} - i x}\, dx\right)}{d}"," ",0,"-I*(Integral(a**3/(c*x**2 - I*x), x) + Integral(b**3*atan(c*x)**3/(c*x**2 - I*x), x) + Integral(3*a*b**2*atan(c*x)**2/(c*x**2 - I*x), x) + Integral(3*a**2*b*atan(c*x)/(c*x**2 - I*x), x))/d","F",0
131,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x**2/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a^{3}}{c x^{3} - i x^{2}}\, dx + \int \frac{b^{3} \operatorname{atan}^{3}{\left(c x \right)}}{c x^{3} - i x^{2}}\, dx + \int \frac{3 a b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c x^{3} - i x^{2}}\, dx + \int \frac{3 a^{2} b \operatorname{atan}{\left(c x \right)}}{c x^{3} - i x^{2}}\, dx\right)}{d}"," ",0,"-I*(Integral(a**3/(c*x**3 - I*x**2), x) + Integral(b**3*atan(c*x)**3/(c*x**3 - I*x**2), x) + Integral(3*a*b**2*atan(c*x)**2/(c*x**3 - I*x**2), x) + Integral(3*a**2*b*atan(c*x)/(c*x**3 - I*x**2), x))/d","F",0
132,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**3/x**3/(d+I*c*d*x),x)","- \frac{i \left(\int \frac{a^{3}}{c x^{4} - i x^{3}}\, dx + \int \frac{b^{3} \operatorname{atan}^{3}{\left(c x \right)}}{c x^{4} - i x^{3}}\, dx + \int \frac{3 a b^{2} \operatorname{atan}^{2}{\left(c x \right)}}{c x^{4} - i x^{3}}\, dx + \int \frac{3 a^{2} b \operatorname{atan}{\left(c x \right)}}{c x^{4} - i x^{3}}\, dx\right)}{d}"," ",0,"-I*(Integral(a**3/(c*x**4 - I*x**3), x) + Integral(b**3*atan(c*x)**3/(c*x**4 - I*x**3), x) + Integral(3*a*b**2*atan(c*x)**2/(c*x**4 - I*x**3), x) + Integral(3*a**2*b*atan(c*x)/(c*x**4 - I*x**3), x))/d","F",0
133,0,0,0,0.000000," ","integrate(1/(d+I*c*d*x)/(a+b*atan(c*x)),x)","- \frac{i \int \frac{1}{a c x - i a + b c x \operatorname{atan}{\left(c x \right)} - i b \operatorname{atan}{\left(c x \right)}}\, dx}{d}"," ",0,"-I*Integral(1/(a*c*x - I*a + b*c*x*atan(c*x) - I*b*atan(c*x)), x)/d","F",0
134,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(e*x+d),x)","\int \frac{x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{d + e x}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))/(d + e*x), x)","F",0
135,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(e*x+d),x)","\int \frac{x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{d + e x}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))/(d + e*x), x)","F",0
136,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(e*x+d),x)","\int \frac{x \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{d + e x}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))/(d + e*x), x)","F",0
137,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*atan(c*x))/(d + e*x), x)","F",0
138,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(e*x+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x*(d + e*x)), x)","F",0
139,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(e*x+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**3*(d + e*x)), x)","F",0
141,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))**2/(e*x+d),x)","\int \frac{x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))**2/(d + e*x), x)","F",0
142,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**2/(e*x+d),x)","\int \frac{x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))**2/(d + e*x), x)","F",0
143,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))**2/(e*x+d),x)","\int \frac{x \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))**2/(d + e*x), x)","F",0
144,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(d + e*x), x)","F",0
145,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(x*(d + e*x)), x)","F",0
146,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**2/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**3/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(x**3*(d + e*x)), x)","F",0
148,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*atan(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*atan(c*x))*(d + e*x)), x)","F",0
149,1,65,0,1.455916," ","integrate(x**3*(a**2*c*x**2+c)*atan(a*x),x)","\begin{cases} \frac{a^{2} c x^{6} \operatorname{atan}{\left(a x \right)}}{6} - \frac{a c x^{5}}{30} + \frac{c x^{4} \operatorname{atan}{\left(a x \right)}}{4} - \frac{c x^{3}}{36 a} + \frac{c x}{12 a^{3}} - \frac{c \operatorname{atan}{\left(a x \right)}}{12 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x**6*atan(a*x)/6 - a*c*x**5/30 + c*x**4*atan(a*x)/4 - c*x**3/(36*a) + c*x/(12*a**3) - c*atan(a*x)/(12*a**4), Ne(a, 0)), (0, True))","A",0
150,1,61,0,1.004286," ","integrate(x**2*(a**2*c*x**2+c)*atan(a*x),x)","\begin{cases} \frac{a^{2} c x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{a c x^{4}}{20} + \frac{c x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{c x^{2}}{15 a} + \frac{c \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{15 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x**5*atan(a*x)/5 - a*c*x**4/20 + c*x**3*atan(a*x)/3 - c*x**2/(15*a) + c*log(x**2 + a**(-2))/(15*a**3), Ne(a, 0)), (0, True))","A",0
151,1,54,0,0.798767," ","integrate(x*(a**2*c*x**2+c)*atan(a*x),x)","\begin{cases} \frac{a^{2} c x^{4} \operatorname{atan}{\left(a x \right)}}{4} - \frac{a c x^{3}}{12} + \frac{c x^{2} \operatorname{atan}{\left(a x \right)}}{2} - \frac{c x}{4 a} + \frac{c \operatorname{atan}{\left(a x \right)}}{4 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x**4*atan(a*x)/4 - a*c*x**3/12 + c*x**2*atan(a*x)/2 - c*x/(4*a) + c*atan(a*x)/(4*a**2), Ne(a, 0)), (0, True))","A",0
152,1,48,0,0.572362," ","integrate((a**2*c*x**2+c)*atan(a*x),x)","\begin{cases} \frac{a^{2} c x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{a c x^{2}}{6} + c x \operatorname{atan}{\left(a x \right)} - \frac{c \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x**3*atan(a*x)/3 - a*c*x**2/6 + c*x*atan(a*x) - c*log(x**2 + a**(-2))/(3*a), Ne(a, 0)), (0, True))","A",0
153,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)/x,x)","c \left(\int \frac{\operatorname{atan}{\left(a x \right)}}{x}\, dx + \int a^{2} x \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(atan(a*x)/x, x) + Integral(a**2*x*atan(a*x), x))","F",0
154,1,41,0,0.751984," ","integrate((a**2*c*x**2+c)*atan(a*x)/x**2,x)","\begin{cases} a^{2} c x \operatorname{atan}{\left(a x \right)} + a c \log{\left(x \right)} - a c \log{\left(x^{2} + \frac{1}{a^{2}} \right)} - \frac{c \operatorname{atan}{\left(a x \right)}}{x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x*atan(a*x) + a*c*log(x) - a*c*log(x**2 + a**(-2)) - c*atan(a*x)/x, Ne(a, 0)), (0, True))","A",0
155,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)/x**3,x)","c \left(\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{a^{2} \operatorname{atan}{\left(a x \right)}}{x}\, dx\right)"," ",0,"c*(Integral(atan(a*x)/x**3, x) + Integral(a**2*atan(a*x)/x, x))","F",0
156,1,61,0,1.105943," ","integrate((a**2*c*x**2+c)*atan(a*x)/x**4,x)","\begin{cases} \frac{2 a^{3} c \log{\left(x \right)}}{3} - \frac{a^{3} c \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3} - \frac{a^{2} c \operatorname{atan}{\left(a x \right)}}{x} - \frac{a c}{6 x^{2}} - \frac{c \operatorname{atan}{\left(a x \right)}}{3 x^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*c*log(x)/3 - a**3*c*log(x**2 + a**(-2))/3 - a**2*c*atan(a*x)/x - a*c/(6*x**2) - c*atan(a*x)/(3*x**3), Ne(a, 0)), (0, True))","A",0
157,1,104,0,2.500420," ","integrate(x**3*(a**2*c*x**2+c)**2*atan(a*x),x)","\begin{cases} \frac{a^{4} c^{2} x^{8} \operatorname{atan}{\left(a x \right)}}{8} - \frac{a^{3} c^{2} x^{7}}{56} + \frac{a^{2} c^{2} x^{6} \operatorname{atan}{\left(a x \right)}}{3} - \frac{a c^{2} x^{5}}{24} + \frac{c^{2} x^{4} \operatorname{atan}{\left(a x \right)}}{4} - \frac{c^{2} x^{3}}{72 a} + \frac{c^{2} x}{24 a^{3}} - \frac{c^{2} \operatorname{atan}{\left(a x \right)}}{24 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**8*atan(a*x)/8 - a**3*c**2*x**7/56 + a**2*c**2*x**6*atan(a*x)/3 - a*c**2*x**5/24 + c**2*x**4*atan(a*x)/4 - c**2*x**3/(72*a) + c**2*x/(24*a**3) - c**2*atan(a*x)/(24*a**4), Ne(a, 0)), (0, True))","A",0
158,1,105,0,1.826789," ","integrate(x**2*(a**2*c*x**2+c)**2*atan(a*x),x)","\begin{cases} \frac{a^{4} c^{2} x^{7} \operatorname{atan}{\left(a x \right)}}{7} - \frac{a^{3} c^{2} x^{6}}{42} + \frac{2 a^{2} c^{2} x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{9 a c^{2} x^{4}}{140} + \frac{c^{2} x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{4 c^{2} x^{2}}{105 a} + \frac{4 c^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{105 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**7*atan(a*x)/7 - a**3*c**2*x**6/42 + 2*a**2*c**2*x**5*atan(a*x)/5 - 9*a*c**2*x**4/140 + c**2*x**3*atan(a*x)/3 - 4*c**2*x**2/(105*a) + 4*c**2*log(x**2 + a**(-2))/(105*a**3), Ne(a, 0)), (0, True))","A",0
159,1,92,0,1.506064," ","integrate(x*(a**2*c*x**2+c)**2*atan(a*x),x)","\begin{cases} \frac{a^{4} c^{2} x^{6} \operatorname{atan}{\left(a x \right)}}{6} - \frac{a^{3} c^{2} x^{5}}{30} + \frac{a^{2} c^{2} x^{4} \operatorname{atan}{\left(a x \right)}}{2} - \frac{a c^{2} x^{3}}{9} + \frac{c^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{2} - \frac{c^{2} x}{6 a} + \frac{c^{2} \operatorname{atan}{\left(a x \right)}}{6 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**6*atan(a*x)/6 - a**3*c**2*x**5/30 + a**2*c**2*x**4*atan(a*x)/2 - a*c**2*x**3/9 + c**2*x**2*atan(a*x)/2 - c**2*x/(6*a) + c**2*atan(a*x)/(6*a**2), Ne(a, 0)), (0, True))","A",0
160,1,88,0,1.135875," ","integrate((a**2*c*x**2+c)**2*atan(a*x),x)","\begin{cases} \frac{a^{4} c^{2} x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{a^{3} c^{2} x^{4}}{20} + \frac{2 a^{2} c^{2} x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{7 a c^{2} x^{2}}{30} + c^{2} x \operatorname{atan}{\left(a x \right)} - \frac{4 c^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{15 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**5*atan(a*x)/5 - a**3*c**2*x**4/20 + 2*a**2*c**2*x**3*atan(a*x)/3 - 7*a*c**2*x**2/30 + c**2*x*atan(a*x) - 4*c**2*log(x**2 + a**(-2))/(15*a), Ne(a, 0)), (0, True))","A",0
161,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)/x,x)","c^{2} \left(\int \frac{\operatorname{atan}{\left(a x \right)}}{x}\, dx + \int 2 a^{2} x \operatorname{atan}{\left(a x \right)}\, dx + \int a^{4} x^{3} \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)/x, x) + Integral(2*a**2*x*atan(a*x), x) + Integral(a**4*x**3*atan(a*x), x))","F",0
162,1,82,0,1.394587," ","integrate((a**2*c*x**2+c)**2*atan(a*x)/x**2,x)","\begin{cases} \frac{a^{4} c^{2} x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{a^{3} c^{2} x^{2}}{6} + 2 a^{2} c^{2} x \operatorname{atan}{\left(a x \right)} + a c^{2} \log{\left(x \right)} - \frac{4 a c^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3} - \frac{c^{2} \operatorname{atan}{\left(a x \right)}}{x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**3*atan(a*x)/3 - a**3*c**2*x**2/6 + 2*a**2*c**2*x*atan(a*x) + a*c**2*log(x) - 4*a*c**2*log(x**2 + a**(-2))/3 - c**2*atan(a*x)/x, Ne(a, 0)), (0, True))","A",0
163,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)/x**3,x)","c^{2} \left(\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{2 a^{2} \operatorname{atan}{\left(a x \right)}}{x}\, dx + \int a^{4} x \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)/x**3, x) + Integral(2*a**2*atan(a*x)/x, x) + Integral(a**4*x*atan(a*x), x))","F",0
164,1,87,0,1.396207," ","integrate((a**2*c*x**2+c)**2*atan(a*x)/x**4,x)","\begin{cases} a^{4} c^{2} x \operatorname{atan}{\left(a x \right)} + \frac{5 a^{3} c^{2} \log{\left(x \right)}}{3} - \frac{4 a^{3} c^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3} - \frac{2 a^{2} c^{2} \operatorname{atan}{\left(a x \right)}}{x} - \frac{a c^{2}}{6 x^{2}} - \frac{c^{2} \operatorname{atan}{\left(a x \right)}}{3 x^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x*atan(a*x) + 5*a**3*c**2*log(x)/3 - 4*a**3*c**2*log(x**2 + a**(-2))/3 - 2*a**2*c**2*atan(a*x)/x - a*c**2/(6*x**2) - c**2*atan(a*x)/(3*x**3), Ne(a, 0)), (0, True))","A",0
165,1,138,0,3.826333," ","integrate(x**3*(a**2*c*x**2+c)**3*atan(a*x),x)","\begin{cases} \frac{a^{6} c^{3} x^{10} \operatorname{atan}{\left(a x \right)}}{10} - \frac{a^{5} c^{3} x^{9}}{90} + \frac{3 a^{4} c^{3} x^{8} \operatorname{atan}{\left(a x \right)}}{8} - \frac{11 a^{3} c^{3} x^{7}}{280} + \frac{a^{2} c^{3} x^{6} \operatorname{atan}{\left(a x \right)}}{2} - \frac{9 a c^{3} x^{5}}{200} + \frac{c^{3} x^{4} \operatorname{atan}{\left(a x \right)}}{4} - \frac{c^{3} x^{3}}{120 a} + \frac{c^{3} x}{40 a^{3}} - \frac{c^{3} \operatorname{atan}{\left(a x \right)}}{40 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**10*atan(a*x)/10 - a**5*c**3*x**9/90 + 3*a**4*c**3*x**8*atan(a*x)/8 - 11*a**3*c**3*x**7/280 + a**2*c**3*x**6*atan(a*x)/2 - 9*a*c**3*x**5/200 + c**3*x**4*atan(a*x)/4 - c**3*x**3/(120*a) + c**3*x/(40*a**3) - c**3*atan(a*x)/(40*a**4), Ne(a, 0)), (0, True))","A",0
166,1,138,0,2.974390," ","integrate(x**2*(a**2*c*x**2+c)**3*atan(a*x),x)","\begin{cases} \frac{a^{6} c^{3} x^{9} \operatorname{atan}{\left(a x \right)}}{9} - \frac{a^{5} c^{3} x^{8}}{72} + \frac{3 a^{4} c^{3} x^{7} \operatorname{atan}{\left(a x \right)}}{7} - \frac{10 a^{3} c^{3} x^{6}}{189} + \frac{3 a^{2} c^{3} x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{89 a c^{3} x^{4}}{1260} + \frac{c^{3} x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{8 c^{3} x^{2}}{315 a} + \frac{8 c^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{315 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**9*atan(a*x)/9 - a**5*c**3*x**8/72 + 3*a**4*c**3*x**7*atan(a*x)/7 - 10*a**3*c**3*x**6/189 + 3*a**2*c**3*x**5*atan(a*x)/5 - 89*a*c**3*x**4/1260 + c**3*x**3*atan(a*x)/3 - 8*c**3*x**2/(315*a) + 8*c**3*log(x**2 + a**(-2))/(315*a**3), Ne(a, 0)), (0, True))","A",0
167,1,124,0,2.432404," ","integrate(x*(a**2*c*x**2+c)**3*atan(a*x),x)","\begin{cases} \frac{a^{6} c^{3} x^{8} \operatorname{atan}{\left(a x \right)}}{8} - \frac{a^{5} c^{3} x^{7}}{56} + \frac{a^{4} c^{3} x^{6} \operatorname{atan}{\left(a x \right)}}{2} - \frac{3 a^{3} c^{3} x^{5}}{40} + \frac{3 a^{2} c^{3} x^{4} \operatorname{atan}{\left(a x \right)}}{4} - \frac{a c^{3} x^{3}}{8} + \frac{c^{3} x^{2} \operatorname{atan}{\left(a x \right)}}{2} - \frac{c^{3} x}{8 a} + \frac{c^{3} \operatorname{atan}{\left(a x \right)}}{8 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**8*atan(a*x)/8 - a**5*c**3*x**7/56 + a**4*c**3*x**6*atan(a*x)/2 - 3*a**3*c**3*x**5/40 + 3*a**2*c**3*x**4*atan(a*x)/4 - a*c**3*x**3/8 + c**3*x**2*atan(a*x)/2 - c**3*x/(8*a) + c**3*atan(a*x)/(8*a**2), Ne(a, 0)), (0, True))","A",0
168,1,117,0,1.906039," ","integrate((a**2*c*x**2+c)**3*atan(a*x),x)","\begin{cases} \frac{a^{6} c^{3} x^{7} \operatorname{atan}{\left(a x \right)}}{7} - \frac{a^{5} c^{3} x^{6}}{42} + \frac{3 a^{4} c^{3} x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{4 a^{3} c^{3} x^{4}}{35} + a^{2} c^{3} x^{3} \operatorname{atan}{\left(a x \right)} - \frac{19 a c^{3} x^{2}}{70} + c^{3} x \operatorname{atan}{\left(a x \right)} - \frac{8 c^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{35 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**7*atan(a*x)/7 - a**5*c**3*x**6/42 + 3*a**4*c**3*x**5*atan(a*x)/5 - 4*a**3*c**3*x**4/35 + a**2*c**3*x**3*atan(a*x) - 19*a*c**3*x**2/70 + c**3*x*atan(a*x) - 8*c**3*log(x**2 + a**(-2))/(35*a), Ne(a, 0)), (0, True))","A",0
169,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)/x,x)","c^{3} \left(\int \frac{\operatorname{atan}{\left(a x \right)}}{x}\, dx + \int 3 a^{2} x \operatorname{atan}{\left(a x \right)}\, dx + \int 3 a^{4} x^{3} \operatorname{atan}{\left(a x \right)}\, dx + \int a^{6} x^{5} \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)/x, x) + Integral(3*a**2*x*atan(a*x), x) + Integral(3*a**4*x**3*atan(a*x), x) + Integral(a**6*x**5*atan(a*x), x))","F",0
170,1,110,0,2.237000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)/x**2,x)","\begin{cases} \frac{a^{6} c^{3} x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{a^{5} c^{3} x^{4}}{20} + a^{4} c^{3} x^{3} \operatorname{atan}{\left(a x \right)} - \frac{2 a^{3} c^{3} x^{2}}{5} + 3 a^{2} c^{3} x \operatorname{atan}{\left(a x \right)} + a c^{3} \log{\left(x \right)} - \frac{8 a c^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{5} - \frac{c^{3} \operatorname{atan}{\left(a x \right)}}{x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**5*atan(a*x)/5 - a**5*c**3*x**4/20 + a**4*c**3*x**3*atan(a*x) - 2*a**3*c**3*x**2/5 + 3*a**2*c**3*x*atan(a*x) + a*c**3*log(x) - 8*a*c**3*log(x**2 + a**(-2))/5 - c**3*atan(a*x)/x, Ne(a, 0)), (0, True))","A",0
171,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)/x**3,x)","c^{3} \left(\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{3 a^{2} \operatorname{atan}{\left(a x \right)}}{x}\, dx + \int 3 a^{4} x \operatorname{atan}{\left(a x \right)}\, dx + \int a^{6} x^{3} \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)/x**3, x) + Integral(3*a**2*atan(a*x)/x, x) + Integral(3*a**4*x*atan(a*x), x) + Integral(a**6*x**3*atan(a*x), x))","F",0
172,1,117,0,2.173239," ","integrate((a**2*c*x**2+c)**3*atan(a*x)/x**4,x)","\begin{cases} \frac{a^{6} c^{3} x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{a^{5} c^{3} x^{2}}{6} + 3 a^{4} c^{3} x \operatorname{atan}{\left(a x \right)} + \frac{8 a^{3} c^{3} \log{\left(x \right)}}{3} - \frac{8 a^{3} c^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3} - \frac{3 a^{2} c^{3} \operatorname{atan}{\left(a x \right)}}{x} - \frac{a c^{3}}{6 x^{2}} - \frac{c^{3} \operatorname{atan}{\left(a x \right)}}{3 x^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**3*atan(a*x)/3 - a**5*c**3*x**2/6 + 3*a**4*c**3*x*atan(a*x) + 8*a**3*c**3*log(x)/3 - 8*a**3*c**3*log(x**2 + a**(-2))/3 - 3*a**2*c**3*atan(a*x)/x - a*c**3/(6*x**2) - c**3*atan(a*x)/(3*x**3), Ne(a, 0)), (0, True))","A",0
173,1,110,0,1.833501," ","integrate(x**4*atan(a*x)/(a**2*c*x**2+c),x)","\begin{cases} \frac{x^{3} \operatorname{atan}{\left(a x \right)}}{3 a^{2} c} - \frac{x^{2}}{6 a^{3} c} - \frac{x \operatorname{atan}{\left(a x \right)}}{a^{4} c} + \frac{2 \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3 a^{5} c} + \frac{\operatorname{atan}^{2}{\left(a x \right)}}{2 a^{5} c} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(\frac{x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{x^{4}}{20 a} + \frac{x^{2}}{10 a^{3}} - \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{10 a^{5}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3*atan(a*x)/(3*a**2*c) - x**2/(6*a**3*c) - x*atan(a*x)/(a**4*c) + 2*log(x**2 + a**(-2))/(3*a**5*c) + atan(a*x)**2/(2*a**5*c), Ne(c, 0)), (zoo*(x**5*atan(a*x)/5 - x**4/(20*a) + x**2/(10*a**3) - log(a**2*x**2 + 1)/(10*a**5)), True))","A",0
174,0,0,0,0.000000," ","integrate(x**3*atan(a*x)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{3} \operatorname{atan}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**3*atan(a*x)/(a**2*x**2 + 1), x)/c","F",0
175,1,75,0,1.047080," ","integrate(x**2*atan(a*x)/(a**2*c*x**2+c),x)","\begin{cases} \frac{x \operatorname{atan}{\left(a x \right)}}{a^{2} c} - \frac{\log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 a^{3} c} - \frac{\operatorname{atan}^{2}{\left(a x \right)}}{2 a^{3} c} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(\frac{x^{3} \operatorname{atan}{\left(a x \right)}}{3} - \frac{x^{2}}{6 a} + \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{6 a^{3}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*atan(a*x)/(a**2*c) - log(x**2 + a**(-2))/(2*a**3*c) - atan(a*x)**2/(2*a**3*c), Ne(c, 0)), (zoo*(x**3*atan(a*x)/3 - x**2/(6*a) + log(a**2*x**2 + 1)/(6*a**3)), True))","A",0
176,0,0,0,0.000000," ","integrate(x*atan(a*x)/(a**2*c*x**2+c),x)","\frac{\int \frac{x \operatorname{atan}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*atan(a*x)/(a**2*x**2 + 1), x)/c","F",0
177,1,36,0,2.368823," ","integrate(atan(a*x)/(a**2*c*x**2+c),x)","\begin{cases} 0 & \text{for}\: a = 0 \\\tilde{\infty} \left(\begin{cases} 0 & \text{for}\: a = 0 \\\frac{a x \operatorname{atan}{\left(a x \right)} - \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{2}}{a} & \text{otherwise} \end{cases}\right) & \text{for}\: c = 0 \\\frac{\operatorname{atan}^{2}{\left(a x \right)}}{2 a c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, Eq(a, 0)), (zoo*Piecewise((0, Eq(a, 0)), ((a*x*atan(a*x) - log(a**2*x**2 + 1)/2)/a, True)), Eq(c, 0)), (atan(a*x)**2/(2*a*c), True))","A",0
178,0,0,0,0.000000," ","integrate(atan(a*x)/x/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}{\left(a x \right)}}{a^{2} x^{3} + x}\, dx}{c}"," ",0,"Integral(atan(a*x)/(a**2*x**3 + x), x)/c","F",0
179,1,68,0,1.469054," ","integrate(atan(a*x)/x**2/(a**2*c*x**2+c),x)","\begin{cases} \frac{a \log{\left(x \right)}}{c} - \frac{a \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 c} - \frac{a \operatorname{atan}^{2}{\left(a x \right)}}{2 c} - \frac{\operatorname{atan}{\left(a x \right)}}{c x} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(a \log{\left(x \right)} - \frac{a \log{\left(a^{2} x^{2} + 1 \right)}}{2} - \frac{\operatorname{atan}{\left(a x \right)}}{x}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(x)/c - a*log(x**2 + a**(-2))/(2*c) - a*atan(a*x)**2/(2*c) - atan(a*x)/(c*x), Ne(c, 0)), (zoo*(a*log(x) - a*log(a**2*x**2 + 1)/2 - atan(a*x)/x), True))","A",0
180,0,0,0,0.000000," ","integrate(atan(a*x)/x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}{\left(a x \right)}}{a^{2} x^{5} + x^{3}}\, dx}{c}"," ",0,"Integral(atan(a*x)/(a**2*x**5 + x**3), x)/c","F",0
181,1,117,0,2.526197," ","integrate(atan(a*x)/x**4/(a**2*c*x**2+c),x)","\begin{cases} - \frac{4 a^{3} \log{\left(x \right)}}{3 c} + \frac{2 a^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3 c} + \frac{a^{3} \operatorname{atan}^{2}{\left(a x \right)}}{2 c} + \frac{a^{2} \operatorname{atan}{\left(a x \right)}}{c x} - \frac{a}{6 c x^{2}} - \frac{\operatorname{atan}{\left(a x \right)}}{3 c x^{3}} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(- \frac{a^{3} \log{\left(x \right)}}{3} + \frac{a^{3} \log{\left(a^{2} x^{2} + 1 \right)}}{6} - \frac{a}{6 x^{2}} - \frac{\operatorname{atan}{\left(a x \right)}}{3 x^{3}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**3*log(x)/(3*c) + 2*a**3*log(x**2 + a**(-2))/(3*c) + a**3*atan(a*x)**2/(2*c) + a**2*atan(a*x)/(c*x) - a/(6*c*x**2) - atan(a*x)/(3*c*x**3), Ne(c, 0)), (zoo*(-a**3*log(x)/3 + a**3*log(a**2*x**2 + 1)/6 - a/(6*x**2) - atan(a*x)/(3*x**3)), True))","A",0
182,0,0,0,0.000000," ","integrate(x**5*atan(a*x)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{5} \operatorname{atan}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**5*atan(a*x)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
183,1,264,0,2.086937," ","integrate(x**4*atan(a*x)/(a**2*c*x**2+c)**2,x)","\begin{cases} \frac{4 a^{3} x^{3} \operatorname{atan}{\left(a x \right)}}{4 a^{7} c^{2} x^{2} + 4 a^{5} c^{2}} - \frac{2 a^{2} x^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{4 a^{7} c^{2} x^{2} + 4 a^{5} c^{2}} - \frac{3 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{4 a^{7} c^{2} x^{2} + 4 a^{5} c^{2}} + \frac{6 a x \operatorname{atan}{\left(a x \right)}}{4 a^{7} c^{2} x^{2} + 4 a^{5} c^{2}} - \frac{2 \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{4 a^{7} c^{2} x^{2} + 4 a^{5} c^{2}} - \frac{3 \operatorname{atan}^{2}{\left(a x \right)}}{4 a^{7} c^{2} x^{2} + 4 a^{5} c^{2}} + \frac{1}{4 a^{7} c^{2} x^{2} + 4 a^{5} c^{2}} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(\frac{x^{5} \operatorname{atan}{\left(a x \right)}}{5} - \frac{x^{4}}{20 a} + \frac{x^{2}}{10 a^{3}} - \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{10 a^{5}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a**3*x**3*atan(a*x)/(4*a**7*c**2*x**2 + 4*a**5*c**2) - 2*a**2*x**2*log(x**2 + a**(-2))/(4*a**7*c**2*x**2 + 4*a**5*c**2) - 3*a**2*x**2*atan(a*x)**2/(4*a**7*c**2*x**2 + 4*a**5*c**2) + 6*a*x*atan(a*x)/(4*a**7*c**2*x**2 + 4*a**5*c**2) - 2*log(x**2 + a**(-2))/(4*a**7*c**2*x**2 + 4*a**5*c**2) - 3*atan(a*x)**2/(4*a**7*c**2*x**2 + 4*a**5*c**2) + 1/(4*a**7*c**2*x**2 + 4*a**5*c**2), Ne(c, 0)), (zoo*(x**5*atan(a*x)/5 - x**4/(20*a) + x**2/(10*a**3) - log(a**2*x**2 + 1)/(10*a**5)), True))","A",0
184,0,0,0,0.000000," ","integrate(x**3*atan(a*x)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{3} \operatorname{atan}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**3*atan(a*x)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
185,0,0,0,0.000000," ","integrate(x**2*atan(a*x)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{2} \operatorname{atan}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**2*atan(a*x)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
186,1,107,0,1.423811," ","integrate(x*atan(a*x)/(a**2*c*x**2+c)**2,x)","\begin{cases} \frac{a^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{4 a^{4} c^{2} x^{2} + 4 a^{2} c^{2}} + \frac{a x}{4 a^{4} c^{2} x^{2} + 4 a^{2} c^{2}} - \frac{\operatorname{atan}{\left(a x \right)}}{4 a^{4} c^{2} x^{2} + 4 a^{2} c^{2}} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(\frac{x^{2} \operatorname{atan}{\left(a x \right)}}{2} - \frac{x}{2 a} + \frac{\operatorname{atan}{\left(a x \right)}}{2 a^{2}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**2*atan(a*x)/(4*a**4*c**2*x**2 + 4*a**2*c**2) + a*x/(4*a**4*c**2*x**2 + 4*a**2*c**2) - atan(a*x)/(4*a**4*c**2*x**2 + 4*a**2*c**2), Ne(c, 0)), (zoo*(x**2*atan(a*x)/2 - x/(2*a) + atan(a*x)/(2*a**2)), True))","A",0
187,-2,0,0,0.000000," ","integrate(atan(a*x)/(a**2*c*x**2+c)**2,x)","\text{Exception raised: RecursionError}"," ",0,"Exception raised: RecursionError","F(-2)",0
188,-1,0,0,0.000000," ","integrate(atan(a*x)/x/(a**2*c*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,1,272,0,1.424091," ","integrate(atan(a*x)/x**2/(a**2*c*x**2+c)**2,x)","\frac{4 a^{3} x^{3} \log{\left(x \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} - \frac{2 a^{3} x^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} - \frac{3 a^{3} x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} - \frac{6 a^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} + \frac{4 a x \log{\left(x \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} - \frac{2 a x \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} - \frac{3 a x \operatorname{atan}^{2}{\left(a x \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} - \frac{a x}{4 a^{2} c^{2} x^{3} + 4 c^{2} x} - \frac{4 \operatorname{atan}{\left(a x \right)}}{4 a^{2} c^{2} x^{3} + 4 c^{2} x}"," ",0,"4*a**3*x**3*log(x)/(4*a**2*c**2*x**3 + 4*c**2*x) - 2*a**3*x**3*log(x**2 + a**(-2))/(4*a**2*c**2*x**3 + 4*c**2*x) - 3*a**3*x**3*atan(a*x)**2/(4*a**2*c**2*x**3 + 4*c**2*x) - 6*a**2*x**2*atan(a*x)/(4*a**2*c**2*x**3 + 4*c**2*x) + 4*a*x*log(x)/(4*a**2*c**2*x**3 + 4*c**2*x) - 2*a*x*log(x**2 + a**(-2))/(4*a**2*c**2*x**3 + 4*c**2*x) - 3*a*x*atan(a*x)**2/(4*a**2*c**2*x**3 + 4*c**2*x) - a*x/(4*a**2*c**2*x**3 + 4*c**2*x) - 4*atan(a*x)/(4*a**2*c**2*x**3 + 4*c**2*x)","B",0
190,0,0,0,0.000000," ","integrate(atan(a*x)/x**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}{\left(a x \right)}}{a^{4} x^{7} + 2 a^{2} x^{5} + x^{3}}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)/(a**4*x**7 + 2*a**2*x**5 + x**3), x)/c**2","F",0
191,1,360,0,2.160470," ","integrate(atan(a*x)/x**4/(a**2*c*x**2+c)**2,x)","- \frac{28 a^{5} x^{5} \log{\left(x \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} + \frac{14 a^{5} x^{5} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} + \frac{15 a^{5} x^{5} \operatorname{atan}^{2}{\left(a x \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} + \frac{30 a^{4} x^{4} \operatorname{atan}{\left(a x \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} - \frac{28 a^{3} x^{3} \log{\left(x \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} + \frac{14 a^{3} x^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} + \frac{15 a^{3} x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} + \frac{a^{3} x^{3}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} + \frac{20 a^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} - \frac{2 a x}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}} - \frac{4 \operatorname{atan}{\left(a x \right)}}{12 a^{2} c^{2} x^{5} + 12 c^{2} x^{3}}"," ",0,"-28*a**5*x**5*log(x)/(12*a**2*c**2*x**5 + 12*c**2*x**3) + 14*a**5*x**5*log(x**2 + a**(-2))/(12*a**2*c**2*x**5 + 12*c**2*x**3) + 15*a**5*x**5*atan(a*x)**2/(12*a**2*c**2*x**5 + 12*c**2*x**3) + 30*a**4*x**4*atan(a*x)/(12*a**2*c**2*x**5 + 12*c**2*x**3) - 28*a**3*x**3*log(x)/(12*a**2*c**2*x**5 + 12*c**2*x**3) + 14*a**3*x**3*log(x**2 + a**(-2))/(12*a**2*c**2*x**5 + 12*c**2*x**3) + 15*a**3*x**3*atan(a*x)**2/(12*a**2*c**2*x**5 + 12*c**2*x**3) + a**3*x**3/(12*a**2*c**2*x**5 + 12*c**2*x**3) + 20*a**2*x**2*atan(a*x)/(12*a**2*c**2*x**5 + 12*c**2*x**3) - 2*a*x/(12*a**2*c**2*x**5 + 12*c**2*x**3) - 4*atan(a*x)/(12*a**2*c**2*x**5 + 12*c**2*x**3)","B",0
192,1,243,0,2.687388," ","integrate(x**3*atan(a*x)/(a**2*c*x**2+c)**3,x)","\begin{cases} \frac{5 a^{4} x^{4} \operatorname{atan}{\left(a x \right)}}{32 a^{8} c^{3} x^{4} + 64 a^{6} c^{3} x^{2} + 32 a^{4} c^{3}} + \frac{5 a^{3} x^{3}}{32 a^{8} c^{3} x^{4} + 64 a^{6} c^{3} x^{2} + 32 a^{4} c^{3}} - \frac{6 a^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{32 a^{8} c^{3} x^{4} + 64 a^{6} c^{3} x^{2} + 32 a^{4} c^{3}} + \frac{3 a x}{32 a^{8} c^{3} x^{4} + 64 a^{6} c^{3} x^{2} + 32 a^{4} c^{3}} - \frac{3 \operatorname{atan}{\left(a x \right)}}{32 a^{8} c^{3} x^{4} + 64 a^{6} c^{3} x^{2} + 32 a^{4} c^{3}} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(\frac{x^{4} \operatorname{atan}{\left(a x \right)}}{4} - \frac{x^{3}}{12 a} + \frac{x}{4 a^{3}} - \frac{\operatorname{atan}{\left(a x \right)}}{4 a^{4}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**4*x**4*atan(a*x)/(32*a**8*c**3*x**4 + 64*a**6*c**3*x**2 + 32*a**4*c**3) + 5*a**3*x**3/(32*a**8*c**3*x**4 + 64*a**6*c**3*x**2 + 32*a**4*c**3) - 6*a**2*x**2*atan(a*x)/(32*a**8*c**3*x**4 + 64*a**6*c**3*x**2 + 32*a**4*c**3) + 3*a*x/(32*a**8*c**3*x**4 + 64*a**6*c**3*x**2 + 32*a**4*c**3) - 3*atan(a*x)/(32*a**8*c**3*x**4 + 64*a**6*c**3*x**2 + 32*a**4*c**3), Ne(c, 0)), (zoo*(x**4*atan(a*x)/4 - x**3/(12*a) + x/(4*a**3) - atan(a*x)/(4*a**4)), True))","A",0
193,0,0,0,0.000000," ","integrate(x**2*atan(a*x)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{2} \operatorname{atan}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**2*atan(a*x)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
194,1,235,0,2.488818," ","integrate(x*atan(a*x)/(a**2*c*x**2+c)**3,x)","\begin{cases} \frac{3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)}}{32 a^{6} c^{3} x^{4} + 64 a^{4} c^{3} x^{2} + 32 a^{2} c^{3}} + \frac{3 a^{3} x^{3}}{32 a^{6} c^{3} x^{4} + 64 a^{4} c^{3} x^{2} + 32 a^{2} c^{3}} + \frac{6 a^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{32 a^{6} c^{3} x^{4} + 64 a^{4} c^{3} x^{2} + 32 a^{2} c^{3}} + \frac{5 a x}{32 a^{6} c^{3} x^{4} + 64 a^{4} c^{3} x^{2} + 32 a^{2} c^{3}} - \frac{5 \operatorname{atan}{\left(a x \right)}}{32 a^{6} c^{3} x^{4} + 64 a^{4} c^{3} x^{2} + 32 a^{2} c^{3}} & \text{for}\: c \neq 0 \\\tilde{\infty} \left(\frac{x^{2} \operatorname{atan}{\left(a x \right)}}{2} - \frac{x}{2 a} + \frac{\operatorname{atan}{\left(a x \right)}}{2 a^{2}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*x**4*atan(a*x)/(32*a**6*c**3*x**4 + 64*a**4*c**3*x**2 + 32*a**2*c**3) + 3*a**3*x**3/(32*a**6*c**3*x**4 + 64*a**4*c**3*x**2 + 32*a**2*c**3) + 6*a**2*x**2*atan(a*x)/(32*a**6*c**3*x**4 + 64*a**4*c**3*x**2 + 32*a**2*c**3) + 5*a*x/(32*a**6*c**3*x**4 + 64*a**4*c**3*x**2 + 32*a**2*c**3) - 5*atan(a*x)/(32*a**6*c**3*x**4 + 64*a**4*c**3*x**2 + 32*a**2*c**3), Ne(c, 0)), (zoo*(x**2*atan(a*x)/2 - x/(2*a) + atan(a*x)/(2*a**2)), True))","A",0
195,-2,0,0,0.000000," ","integrate(atan(a*x)/(a**2*c*x**2+c)**3,x)","\text{Exception raised: RecursionError}"," ",0,"Exception raised: RecursionError","F(-2)",0
196,-2,0,0,0.000000," ","integrate(atan(a*x)/x/(a**2*c*x**2+c)**3,x)","\text{Exception raised: RecursionError}"," ",0,"Exception raised: RecursionError","F(-2)",0
197,1,602,0,2.513916," ","integrate(atan(a*x)/x**2/(a**2*c*x**2+c)**3,x)","\frac{16 a^{5} x^{5} \log{\left(x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{8 a^{5} x^{5} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{15 a^{5} x^{5} \operatorname{atan}^{2}{\left(a x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{30 a^{4} x^{4} \operatorname{atan}{\left(a x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} + \frac{32 a^{3} x^{3} \log{\left(x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{16 a^{3} x^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{30 a^{3} x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{7 a^{3} x^{3}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{50 a^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} + \frac{16 a x \log{\left(x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{8 a x \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{15 a x \operatorname{atan}^{2}{\left(a x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{8 a x}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x} - \frac{16 \operatorname{atan}{\left(a x \right)}}{16 a^{4} c^{3} x^{5} + 32 a^{2} c^{3} x^{3} + 16 c^{3} x}"," ",0,"16*a**5*x**5*log(x)/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 8*a**5*x**5*log(x**2 + a**(-2))/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 15*a**5*x**5*atan(a*x)**2/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 30*a**4*x**4*atan(a*x)/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) + 32*a**3*x**3*log(x)/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 16*a**3*x**3*log(x**2 + a**(-2))/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 30*a**3*x**3*atan(a*x)**2/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 7*a**3*x**3/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 50*a**2*x**2*atan(a*x)/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) + 16*a*x*log(x)/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 8*a*x*log(x**2 + a**(-2))/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 15*a*x*atan(a*x)**2/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 8*a*x/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x) - 16*atan(a*x)/(16*a**4*c**3*x**5 + 32*a**2*c**3*x**3 + 16*c**3*x)","B",0
198,0,0,0,0.000000," ","integrate(atan(a*x)/x**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}{\left(a x \right)}}{a^{6} x^{9} + 3 a^{4} x^{7} + 3 a^{2} x^{5} + x^{3}}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)/(a**6*x**9 + 3*a**4*x**7 + 3*a**2*x**5 + x**3), x)/c**3","F",0
199,1,722,0,3.654591," ","integrate(atan(a*x)/x**4/(a**2*c*x**2+c)**3,x)","- \frac{160 a^{7} x^{7} \log{\left(x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{80 a^{7} x^{7} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{105 a^{7} x^{7} \operatorname{atan}^{2}{\left(a x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{210 a^{6} x^{6} \operatorname{atan}{\left(a x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} - \frac{320 a^{5} x^{5} \log{\left(x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{160 a^{5} x^{5} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{210 a^{5} x^{5} \operatorname{atan}^{2}{\left(a x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{25 a^{5} x^{5}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{350 a^{4} x^{4} \operatorname{atan}{\left(a x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} - \frac{160 a^{3} x^{3} \log{\left(x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{80 a^{3} x^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{105 a^{3} x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{20 a^{3} x^{3}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} + \frac{112 a^{2} x^{2} \operatorname{atan}{\left(a x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} - \frac{8 a x}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}} - \frac{16 \operatorname{atan}{\left(a x \right)}}{48 a^{4} c^{3} x^{7} + 96 a^{2} c^{3} x^{5} + 48 c^{3} x^{3}}"," ",0,"-160*a**7*x**7*log(x)/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 80*a**7*x**7*log(x**2 + a**(-2))/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 105*a**7*x**7*atan(a*x)**2/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 210*a**6*x**6*atan(a*x)/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) - 320*a**5*x**5*log(x)/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 160*a**5*x**5*log(x**2 + a**(-2))/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 210*a**5*x**5*atan(a*x)**2/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 25*a**5*x**5/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 350*a**4*x**4*atan(a*x)/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) - 160*a**3*x**3*log(x)/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 80*a**3*x**3*log(x**2 + a**(-2))/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 105*a**3*x**3*atan(a*x)**2/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 20*a**3*x**3/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) + 112*a**2*x**2*atan(a*x)/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) - 8*a*x/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3) - 16*atan(a*x)/(48*a**4*c**3*x**7 + 96*a**2*c**3*x**5 + 48*c**3*x**3)","B",0
200,0,0,0,0.000000," ","integrate(x**3*atan(a*x)*(a**2*c*x**2+c)**(1/2),x)","\int x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*sqrt(c*(a**2*x**2 + 1))*atan(a*x), x)","F",0
201,0,0,0,0.000000," ","integrate(x**2*atan(a*x)*(a**2*c*x**2+c)**(1/2),x)","\int x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*sqrt(c*(a**2*x**2 + 1))*atan(a*x), x)","F",0
202,0,0,0,0.000000," ","integrate(x*atan(a*x)*(a**2*c*x**2+c)**(1/2),x)","\int x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x), x)","F",0
203,0,0,0,0.000000," ","integrate(atan(a*x)*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x), x)","F",0
204,0,0,0,0.000000," ","integrate(atan(a*x)*(a**2*c*x**2+c)**(1/2)/x,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)/x, x)","F",0
205,0,0,0,0.000000," ","integrate(atan(a*x)*(a**2*c*x**2+c)**(1/2)/x**2,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)/x**2, x)","F",0
206,0,0,0,0.000000," ","integrate(atan(a*x)*(a**2*c*x**2+c)**(1/2)/x**3,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)/x**3, x)","F",0
207,0,0,0,0.000000," ","integrate(atan(a*x)*(a**2*c*x**2+c)**(1/2)/x**4,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)/x**4, x)","F",0
208,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**(3/2)*atan(a*x),x)","\int x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x), x)","F",0
209,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(3/2)*atan(a*x),x)","\int x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x), x)","F",0
210,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)*atan(a*x),x)","\int x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x), x)","F",0
211,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x), x)","F",0
212,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)/x,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)/x, x)","F",0
213,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)/x**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)/x**2, x)","F",0
214,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)/x**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)/x**3, x)","F",0
215,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)/x**4,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)/x**4, x)","F",0
216,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**(5/2)*atan(a*x),x)","\int x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x), x)","F",0
217,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(5/2)*atan(a*x),x)","\int x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x), x)","F",0
218,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)*atan(a*x),x)","\int x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x), x)","F",0
219,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x), x)","F",0
220,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)/x,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)/x, x)","F",0
221,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)/x**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)/x**2, x)","F",0
222,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)/x**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)/x**3, x)","F",0
223,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)/x**4,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)/x**4, x)","F",0
224,0,0,0,0.000000," ","integrate(x**3*atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{3} \operatorname{atan}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*atan(a*x)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
225,0,0,0,0.000000," ","integrate(x**2*atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \operatorname{atan}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*atan(a*x)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
226,-2,0,0,0.000000," ","integrate(x*atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
227,0,0,0,0.000000," ","integrate(atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
228,0,0,0,0.000000," ","integrate(atan(a*x)/x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)/(x*sqrt(c*(a**2*x**2 + 1))), x)","F",0
229,0,0,0,0.000000," ","integrate(atan(a*x)/x**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)/(x**2*sqrt(c*(a**2*x**2 + 1))), x)","F",0
230,0,0,0,0.000000," ","integrate(atan(a*x)/x**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)/(x**3*sqrt(c*(a**2*x**2 + 1))), x)","F",0
231,0,0,0,0.000000," ","integrate(atan(a*x)/x**4/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{4} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)/(x**4*sqrt(c*(a**2*x**2 + 1))), x)","F",0
232,-2,0,0,0.000000," ","integrate(x**3*atan(a*x)/(a**2*c*x**2+c)**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
233,0,0,0,0.000000," ","integrate(x**2*atan(a*x)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{2} \operatorname{atan}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
234,-2,0,0,0.000000," ","integrate(x*atan(a*x)/(a**2*c*x**2+c)**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
235,0,0,0,0.000000," ","integrate(atan(a*x)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
236,0,0,0,0.000000," ","integrate(atan(a*x)/x/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(x*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
237,0,0,0,0.000000," ","integrate(atan(a*x)/x**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(x**2*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
238,0,0,0,0.000000," ","integrate(atan(a*x)/x**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(x**3*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
239,0,0,0,0.000000," ","integrate(atan(a*x)/x**4/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{4} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(x**4*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
240,0,0,0,0.000000," ","integrate(x**5*atan(a*x)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{5} \operatorname{atan}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5*atan(a*x)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
241,0,0,0,0.000000," ","integrate(x**4*atan(a*x)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{4} \operatorname{atan}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*atan(a*x)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
242,-2,0,0,0.000000," ","integrate(x**3*atan(a*x)/(a**2*c*x**2+c)**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
243,0,0,0,0.000000," ","integrate(x**2*atan(a*x)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{2} \operatorname{atan}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
244,-2,0,0,0.000000," ","integrate(x*atan(a*x)/(a**2*c*x**2+c)**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
245,0,0,0,0.000000," ","integrate(atan(a*x)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
246,-2,0,0,0.000000," ","integrate(atan(a*x)/x/(a**2*c*x**2+c)**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
247,0,0,0,0.000000," ","integrate(atan(a*x)/x**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(x**2*(c*(a**2*x**2 + 1))**(5/2)), x)","F",0
248,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3*atan(a*x),x)","c^{3} \left(\int x^{m} \operatorname{atan}{\left(a x \right)}\, dx + \int 3 a^{2} x^{2} x^{m} \operatorname{atan}{\left(a x \right)}\, dx + \int 3 a^{4} x^{4} x^{m} \operatorname{atan}{\left(a x \right)}\, dx + \int a^{6} x^{6} x^{m} \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(x**m*atan(a*x), x) + Integral(3*a**2*x**2*x**m*atan(a*x), x) + Integral(3*a**4*x**4*x**m*atan(a*x), x) + Integral(a**6*x**6*x**m*atan(a*x), x))","F",0
249,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2*atan(a*x),x)","c^{2} \left(\int x^{m} \operatorname{atan}{\left(a x \right)}\, dx + \int 2 a^{2} x^{2} x^{m} \operatorname{atan}{\left(a x \right)}\, dx + \int a^{4} x^{4} x^{m} \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**m*atan(a*x), x) + Integral(2*a**2*x**2*x**m*atan(a*x), x) + Integral(a**4*x**4*x**m*atan(a*x), x))","F",0
250,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)*atan(a*x),x)","c \left(\int x^{m} \operatorname{atan}{\left(a x \right)}\, dx + \int a^{2} x^{2} x^{m} \operatorname{atan}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**m*atan(a*x), x) + Integral(a**2*x**2*x**m*atan(a*x), x))","F",0
251,0,0,0,0.000000," ","integrate(x**m*atan(a*x)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{m} \operatorname{atan}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**m*atan(a*x)/(a**2*x**2 + 1), x)/c","F",0
252,0,0,0,0.000000," ","integrate(x**m*atan(a*x)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{m} \operatorname{atan}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**m*atan(a*x)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
253,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)*atan(a*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)*atan(a*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)*atan(a*x),x)","\int x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))*atan(a*x), x)","F",0
256,0,0,0,0.000000," ","integrate(x**m*atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m} \operatorname{atan}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**m*atan(a*x)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
257,0,0,0,0.000000," ","integrate(x**m*atan(a*x)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{m} \operatorname{atan}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*atan(a*x)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
258,1,121,0,1.949311," ","integrate(x**3*(a**2*c*x**2+c)*atan(a*x)**2,x)","\begin{cases} \frac{a^{2} c x^{6} \operatorname{atan}^{2}{\left(a x \right)}}{6} - \frac{a c x^{5} \operatorname{atan}{\left(a x \right)}}{15} + \frac{c x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{4} + \frac{c x^{4}}{60} - \frac{c x^{3} \operatorname{atan}{\left(a x \right)}}{18 a} - \frac{c x^{2}}{180 a^{2}} + \frac{c x \operatorname{atan}{\left(a x \right)}}{6 a^{3}} - \frac{7 c \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{90 a^{4}} - \frac{c \operatorname{atan}^{2}{\left(a x \right)}}{12 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x**6*atan(a*x)**2/6 - a*c*x**5*atan(a*x)/15 + c*x**4*atan(a*x)**2/4 + c*x**4/60 - c*x**3*atan(a*x)/(18*a) - c*x**2/(180*a**2) + c*x*atan(a*x)/(6*a**3) - 7*c*log(x**2 + a**(-2))/(90*a**4) - c*atan(a*x)**2/(12*a**4), Ne(a, 0)), (0, True))","A",0
259,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)*atan(a*x)**2,x)","c \left(\int x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**2*atan(a*x)**2, x) + Integral(a**2*x**4*atan(a*x)**2, x))","F",0
260,1,94,0,1.133591," ","integrate(x*(a**2*c*x**2+c)*atan(a*x)**2,x)","\begin{cases} \frac{a^{2} c x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{4} - \frac{a c x^{3} \operatorname{atan}{\left(a x \right)}}{6} + \frac{c x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{2} + \frac{c x^{2}}{12} - \frac{c x \operatorname{atan}{\left(a x \right)}}{2 a} + \frac{c \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{6 a^{2}} + \frac{c \operatorname{atan}^{2}{\left(a x \right)}}{4 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x**4*atan(a*x)**2/4 - a*c*x**3*atan(a*x)/6 + c*x**2*atan(a*x)**2/2 + c*x**2/12 - c*x*atan(a*x)/(2*a) + c*log(x**2 + a**(-2))/(6*a**2) + c*atan(a*x)**2/(4*a**2), Ne(a, 0)), (0, True))","A",0
261,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**2,x)","c \left(\int a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*atan(a*x)**2, x) + Integral(atan(a*x)**2, x))","F",0
262,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**2/x,x)","c \left(\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx + \int a^{2} x \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**2/x, x) + Integral(a**2*x*atan(a*x)**2, x))","F",0
263,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**2/x**2,x)","c \left(\int a^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c*(Integral(a**2*atan(a*x)**2, x) + Integral(atan(a*x)**2/x**2, x))","F",0
264,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**2/x**3,x)","c \left(\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{a^{2} \operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**2/x**3, x) + Integral(a**2*atan(a*x)**2/x, x))","F",0
265,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**2/x**4,x)","c \left(\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{4}}\, dx + \int \frac{a^{2} \operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**2/x**4, x) + Integral(a**2*atan(a*x)**2/x**2, x))","F",0
266,1,185,0,3.285079," ","integrate(x**3*(a**2*c*x**2+c)**2*atan(a*x)**2,x)","\begin{cases} \frac{a^{4} c^{2} x^{8} \operatorname{atan}^{2}{\left(a x \right)}}{8} - \frac{a^{3} c^{2} x^{7} \operatorname{atan}{\left(a x \right)}}{28} + \frac{a^{2} c^{2} x^{6} \operatorname{atan}^{2}{\left(a x \right)}}{3} + \frac{a^{2} c^{2} x^{6}}{168} - \frac{a c^{2} x^{5} \operatorname{atan}{\left(a x \right)}}{12} + \frac{c^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{4} + \frac{c^{2} x^{4}}{84} - \frac{c^{2} x^{3} \operatorname{atan}{\left(a x \right)}}{36 a} - \frac{5 c^{2} x^{2}}{504 a^{2}} + \frac{c^{2} x \operatorname{atan}{\left(a x \right)}}{12 a^{3}} - \frac{2 c^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{63 a^{4}} - \frac{c^{2} \operatorname{atan}^{2}{\left(a x \right)}}{24 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**8*atan(a*x)**2/8 - a**3*c**2*x**7*atan(a*x)/28 + a**2*c**2*x**6*atan(a*x)**2/3 + a**2*c**2*x**6/168 - a*c**2*x**5*atan(a*x)/12 + c**2*x**4*atan(a*x)**2/4 + c**2*x**4/84 - c**2*x**3*atan(a*x)/(36*a) - 5*c**2*x**2/(504*a**2) + c**2*x*atan(a*x)/(12*a**3) - 2*c**2*log(x**2 + a**(-2))/(63*a**4) - c**2*atan(a*x)**2/(24*a**4), Ne(a, 0)), (0, True))","A",0
267,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**2*atan(a*x)**2,x)","c^{2} \left(\int x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int 2 a^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{4} x^{6} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**2*atan(a*x)**2, x) + Integral(2*a**2*x**4*atan(a*x)**2, x) + Integral(a**4*x**6*atan(a*x)**2, x))","F",0
268,1,158,0,2.024992," ","integrate(x*(a**2*c*x**2+c)**2*atan(a*x)**2,x)","\begin{cases} \frac{a^{4} c^{2} x^{6} \operatorname{atan}^{2}{\left(a x \right)}}{6} - \frac{a^{3} c^{2} x^{5} \operatorname{atan}{\left(a x \right)}}{15} + \frac{a^{2} c^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{2} + \frac{a^{2} c^{2} x^{4}}{60} - \frac{2 a c^{2} x^{3} \operatorname{atan}{\left(a x \right)}}{9} + \frac{c^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{2} + \frac{7 c^{2} x^{2}}{90} - \frac{c^{2} x \operatorname{atan}{\left(a x \right)}}{3 a} + \frac{4 c^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{45 a^{2}} + \frac{c^{2} \operatorname{atan}^{2}{\left(a x \right)}}{6 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*x**6*atan(a*x)**2/6 - a**3*c**2*x**5*atan(a*x)/15 + a**2*c**2*x**4*atan(a*x)**2/2 + a**2*c**2*x**4/60 - 2*a*c**2*x**3*atan(a*x)/9 + c**2*x**2*atan(a*x)**2/2 + 7*c**2*x**2/90 - c**2*x*atan(a*x)/(3*a) + 4*c**2*log(x**2 + a**(-2))/(45*a**2) + c**2*atan(a*x)**2/(6*a**2), Ne(a, 0)), (0, True))","A",0
269,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**2,x)","c^{2} \left(\int 2 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*atan(a*x)**2, x) + Integral(a**4*x**4*atan(a*x)**2, x) + Integral(atan(a*x)**2, x))","F",0
270,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**2/x,x)","c^{2} \left(\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx + \int 2 a^{2} x \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{4} x^{3} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)**2/x, x) + Integral(2*a**2*x*atan(a*x)**2, x) + Integral(a**4*x**3*atan(a*x)**2, x))","F",0
271,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**2/x**2,x)","c^{2} \left(\int 2 a^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx + \int a^{4} x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*atan(a*x)**2, x) + Integral(atan(a*x)**2/x**2, x) + Integral(a**4*x**2*atan(a*x)**2, x))","F",0
272,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**2/x**3,x)","c^{2} \left(\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{2 a^{2} \operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx + \int a^{4} x \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)**2/x**3, x) + Integral(2*a**2*atan(a*x)**2/x, x) + Integral(a**4*x*atan(a*x)**2, x))","F",0
273,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**2/x**4,x)","c^{2} \left(\int a^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{4}}\, dx + \int \frac{2 a^{2} \operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c**2*(Integral(a**4*atan(a*x)**2, x) + Integral(atan(a*x)**2/x**4, x) + Integral(2*a**2*atan(a*x)**2/x**2, x))","F",0
274,1,241,0,4.969954," ","integrate(x**3*(a**2*c*x**2+c)**3*atan(a*x)**2,x)","\begin{cases} \frac{a^{6} c^{3} x^{10} \operatorname{atan}^{2}{\left(a x \right)}}{10} - \frac{a^{5} c^{3} x^{9} \operatorname{atan}{\left(a x \right)}}{45} + \frac{3 a^{4} c^{3} x^{8} \operatorname{atan}^{2}{\left(a x \right)}}{8} + \frac{a^{4} c^{3} x^{8}}{360} - \frac{11 a^{3} c^{3} x^{7} \operatorname{atan}{\left(a x \right)}}{140} + \frac{a^{2} c^{3} x^{6} \operatorname{atan}^{2}{\left(a x \right)}}{2} + \frac{71 a^{2} c^{3} x^{6}}{7560} - \frac{9 a c^{3} x^{5} \operatorname{atan}{\left(a x \right)}}{100} + \frac{c^{3} x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{4} + \frac{53 c^{3} x^{4}}{6300} - \frac{c^{3} x^{3} \operatorname{atan}{\left(a x \right)}}{60 a} - \frac{107 c^{3} x^{2}}{12600 a^{2}} + \frac{c^{3} x \operatorname{atan}{\left(a x \right)}}{20 a^{3}} - \frac{26 c^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{1575 a^{4}} - \frac{c^{3} \operatorname{atan}^{2}{\left(a x \right)}}{40 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**10*atan(a*x)**2/10 - a**5*c**3*x**9*atan(a*x)/45 + 3*a**4*c**3*x**8*atan(a*x)**2/8 + a**4*c**3*x**8/360 - 11*a**3*c**3*x**7*atan(a*x)/140 + a**2*c**3*x**6*atan(a*x)**2/2 + 71*a**2*c**3*x**6/7560 - 9*a*c**3*x**5*atan(a*x)/100 + c**3*x**4*atan(a*x)**2/4 + 53*c**3*x**4/6300 - c**3*x**3*atan(a*x)/(60*a) - 107*c**3*x**2/(12600*a**2) + c**3*x*atan(a*x)/(20*a**3) - 26*c**3*log(x**2 + a**(-2))/(1575*a**4) - c**3*atan(a*x)**2/(40*a**4), Ne(a, 0)), (0, True))","A",0
275,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**3*atan(a*x)**2,x)","c^{3} \left(\int x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int 3 a^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int 3 a^{4} x^{6} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{6} x^{8} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(x**2*atan(a*x)**2, x) + Integral(3*a**2*x**4*atan(a*x)**2, x) + Integral(3*a**4*x**6*atan(a*x)**2, x) + Integral(a**6*x**8*atan(a*x)**2, x))","F",0
276,1,207,0,3.285383," ","integrate(x*(a**2*c*x**2+c)**3*atan(a*x)**2,x)","\begin{cases} \frac{a^{6} c^{3} x^{8} \operatorname{atan}^{2}{\left(a x \right)}}{8} - \frac{a^{5} c^{3} x^{7} \operatorname{atan}{\left(a x \right)}}{28} + \frac{a^{4} c^{3} x^{6} \operatorname{atan}^{2}{\left(a x \right)}}{2} + \frac{a^{4} c^{3} x^{6}}{168} - \frac{3 a^{3} c^{3} x^{5} \operatorname{atan}{\left(a x \right)}}{20} + \frac{3 a^{2} c^{3} x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{4} + \frac{a^{2} c^{3} x^{4}}{35} - \frac{a c^{3} x^{3} \operatorname{atan}{\left(a x \right)}}{4} + \frac{c^{3} x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{2} + \frac{19 c^{3} x^{2}}{280} - \frac{c^{3} x \operatorname{atan}{\left(a x \right)}}{4 a} + \frac{2 c^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{35 a^{2}} + \frac{c^{3} \operatorname{atan}^{2}{\left(a x \right)}}{8 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**6*c**3*x**8*atan(a*x)**2/8 - a**5*c**3*x**7*atan(a*x)/28 + a**4*c**3*x**6*atan(a*x)**2/2 + a**4*c**3*x**6/168 - 3*a**3*c**3*x**5*atan(a*x)/20 + 3*a**2*c**3*x**4*atan(a*x)**2/4 + a**2*c**3*x**4/35 - a*c**3*x**3*atan(a*x)/4 + c**3*x**2*atan(a*x)**2/2 + 19*c**3*x**2/280 - c**3*x*atan(a*x)/(4*a) + 2*c**3*log(x**2 + a**(-2))/(35*a**2) + c**3*atan(a*x)**2/(8*a**2), Ne(a, 0)), (0, True))","A",0
277,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**2,x)","c^{3} \left(\int 3 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int 3 a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{6} x^{6} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2*atan(a*x)**2, x) + Integral(3*a**4*x**4*atan(a*x)**2, x) + Integral(a**6*x**6*atan(a*x)**2, x) + Integral(atan(a*x)**2, x))","F",0
278,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**2/x,x)","c^{3} \left(\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx + \int 3 a^{2} x \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int 3 a^{4} x^{3} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{6} x^{5} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)**2/x, x) + Integral(3*a**2*x*atan(a*x)**2, x) + Integral(3*a**4*x**3*atan(a*x)**2, x) + Integral(a**6*x**5*atan(a*x)**2, x))","F",0
279,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**2/x**2,x)","c^{3} \left(\int 3 a^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx + \int 3 a^{4} x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{6} x^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*atan(a*x)**2, x) + Integral(atan(a*x)**2/x**2, x) + Integral(3*a**4*x**2*atan(a*x)**2, x) + Integral(a**6*x**4*atan(a*x)**2, x))","F",0
280,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**2/x**3,x)","c^{3} \left(\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{3 a^{2} \operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx + \int 3 a^{4} x \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{6} x^{3} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)**2/x**3, x) + Integral(3*a**2*atan(a*x)**2/x, x) + Integral(3*a**4*x*atan(a*x)**2, x) + Integral(a**6*x**3*atan(a*x)**2, x))","F",0
281,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**2/x**4,x)","c^{3} \left(\int 3 a^{4} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{4}}\, dx + \int \frac{3 a^{2} \operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx + \int a^{6} x^{2} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**4*atan(a*x)**2, x) + Integral(atan(a*x)**2/x**4, x) + Integral(3*a**2*atan(a*x)**2/x**2, x) + Integral(a**6*x**2*atan(a*x)**2, x))","F",0
282,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**2/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**4*atan(a*x)**2/(a**2*x**2 + 1), x)/c","F",0
283,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**2/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**3*atan(a*x)**2/(a**2*x**2 + 1), x)/c","F",0
284,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**2/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**2*atan(a*x)**2/(a**2*x**2 + 1), x)/c","F",0
285,0,0,0,0.000000," ","integrate(x*atan(a*x)**2/(a**2*c*x**2+c),x)","\frac{\int \frac{x \operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*atan(a*x)**2/(a**2*x**2 + 1), x)/c","F",0
286,0,0,0,0.000000," ","integrate(atan(a*x)**2/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(atan(a*x)**2/(a**2*x**2 + 1), x)/c","F",0
287,0,0,0,0.000000," ","integrate(atan(a*x)**2/x/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{3} + x}\, dx}{c}"," ",0,"Integral(atan(a*x)**2/(a**2*x**3 + x), x)/c","F",0
288,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**2/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{4} + x^{2}}\, dx}{c}"," ",0,"Integral(atan(a*x)**2/(a**2*x**4 + x**2), x)/c","F",0
289,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{5} + x^{3}}\, dx}{c}"," ",0,"Integral(atan(a*x)**2/(a**2*x**5 + x**3), x)/c","F",0
290,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**4/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{6} + x^{4}}\, dx}{c}"," ",0,"Integral(atan(a*x)**2/(a**2*x**6 + x**4), x)/c","F",0
291,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**2/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**3*atan(a*x)**2/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
292,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**2/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**2*atan(a*x)**2/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
293,0,0,0,0.000000," ","integrate(x*atan(a*x)**2/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x \operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x*atan(a*x)**2/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
294,0,0,0,0.000000," ","integrate(atan(a*x)**2/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**2/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
295,0,0,0,0.000000," ","integrate(atan(a*x)**2/x/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{5} + 2 a^{2} x^{3} + x}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**2/(a**4*x**5 + 2*a**2*x**3 + x), x)/c**2","F",0
296,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**2/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{6} + 2 a^{2} x^{4} + x^{2}}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**2/(a**4*x**6 + 2*a**2*x**4 + x**2), x)/c**2","F",0
297,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{7} + 2 a^{2} x^{5} + x^{3}}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**2/(a**4*x**7 + 2*a**2*x**5 + x**3), x)/c**2","F",0
298,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**4/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{8} + 2 a^{2} x^{6} + x^{4}}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**2/(a**4*x**8 + 2*a**2*x**6 + x**4), x)/c**2","F",0
299,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**2/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**3*atan(a*x)**2/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
300,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**2/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**2*atan(a*x)**2/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
301,0,0,0,0.000000," ","integrate(x*atan(a*x)**2/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x \operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x*atan(a*x)**2/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
302,0,0,0,0.000000," ","integrate(atan(a*x)**2/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**2/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
303,0,0,0,0.000000," ","integrate(atan(a*x)**2/x/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{7} + 3 a^{4} x^{5} + 3 a^{2} x^{3} + x}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**2/(a**6*x**7 + 3*a**4*x**5 + 3*a**2*x**3 + x), x)/c**3","F",0
304,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**2/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{8} + 3 a^{4} x^{6} + 3 a^{2} x^{4} + x^{2}}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**2/(a**6*x**8 + 3*a**4*x**6 + 3*a**2*x**4 + x**2), x)/c**3","F",0
305,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{9} + 3 a^{4} x^{7} + 3 a^{2} x^{5} + x^{3}}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**2/(a**6*x**9 + 3*a**4*x**7 + 3*a**2*x**5 + x**3), x)/c**3","F",0
306,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**4/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{a^{6} x^{10} + 3 a^{4} x^{8} + 3 a^{2} x^{6} + x^{4}}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**2/(a**6*x**10 + 3*a**4*x**8 + 3*a**2*x**6 + x**4), x)/c**3","F",0
307,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**2*(a**2*c*x**2+c)**(1/2),x)","\int x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2, x)","F",0
308,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**2*(a**2*c*x**2+c)**(1/2),x)","\int x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2, x)","F",0
309,0,0,0,0.000000," ","integrate(x*atan(a*x)**2*(a**2*c*x**2+c)**(1/2),x)","\int x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2, x)","F",0
310,0,0,0,0.000000," ","integrate(atan(a*x)**2*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2, x)","F",0
311,0,0,0,0.000000," ","integrate(atan(a*x)**2*(a**2*c*x**2+c)**(1/2)/x,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2/x, x)","F",0
312,0,0,0,0.000000," ","integrate(atan(a*x)**2*(a**2*c*x**2+c)**(1/2)/x**2,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2/x**2, x)","F",0
313,0,0,0,0.000000," ","integrate(atan(a*x)**2*(a**2*c*x**2+c)**(1/2)/x**3,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2/x**3, x)","F",0
314,0,0,0,0.000000," ","integrate(atan(a*x)**2*(a**2*c*x**2+c)**(1/2)/x**4,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2/x**4, x)","F",0
315,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**(3/2)*atan(a*x)**2,x)","\int x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2, x)","F",0
316,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(3/2)*atan(a*x)**2,x)","\int x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2, x)","F",0
317,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)*atan(a*x)**2,x)","\int x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2, x)","F",0
318,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**2,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2, x)","F",0
319,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**2/x,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2/x, x)","F",0
320,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**2/x**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2/x**2, x)","F",0
321,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**2/x**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2/x**3, x)","F",0
322,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**2/x**4,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2/x**4, x)","F",0
323,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**(5/2)*atan(a*x)**2,x)","\int x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2, x)","F",0
324,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(5/2)*atan(a*x)**2,x)","\int x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2, x)","F",0
325,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)*atan(a*x)**2,x)","\int x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2, x)","F",0
326,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**2,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2, x)","F",0
327,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**2/x,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2/x, x)","F",0
328,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**2/x**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2/x**2, x)","F",0
329,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**2/x**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2/x**3, x)","F",0
330,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**2/x**4,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2/x**4, x)","F",0
331,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*atan(a*x)**2/sqrt(c*(a**2*x**2 + 1)), x)","F",0
332,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*atan(a*x)**2/sqrt(c*(a**2*x**2 + 1)), x)","F",0
333,0,0,0,0.000000," ","integrate(x*atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x \operatorname{atan}^{2}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x*atan(a*x)**2/sqrt(c*(a**2*x**2 + 1)), x)","F",0
334,0,0,0,0.000000," ","integrate(atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**2/sqrt(c*(a**2*x**2 + 1)), x)","F",0
335,0,0,0,0.000000," ","integrate(atan(a*x)**2/x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**2/(x*sqrt(c*(a**2*x**2 + 1))), x)","F",0
336,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**2/(x**2*sqrt(c*(a**2*x**2 + 1))), x)","F",0
337,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**2/(x**3*sqrt(c*(a**2*x**2 + 1))), x)","F",0
338,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**4/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{4} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**2/(x**4*sqrt(c*(a**2*x**2 + 1))), x)","F",0
339,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*atan(a*x)**2/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
340,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)**2/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate(x*atan(a*x)**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*atan(a*x)**2/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
342,0,0,0,0.000000," ","integrate(atan(a*x)**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate(atan(a*x)**2/x/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(x*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
344,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(x**2*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
345,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(x**3*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
346,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**4/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{4} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(x**4*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
347,0,0,0,0.000000," ","integrate(x**5*atan(a*x)**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{5} \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5*atan(a*x)**2/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
348,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{4} \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*atan(a*x)**2/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
349,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{3} \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*atan(a*x)**2/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
350,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{2} \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)**2/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
351,0,0,0,0.000000," ","integrate(x*atan(a*x)**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*atan(a*x)**2/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
352,0,0,0,0.000000," ","integrate(atan(a*x)**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
353,0,0,0,0.000000," ","integrate(atan(a*x)**2/x/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(x*(c*(a**2*x**2 + 1))**(5/2)), x)","F",0
354,0,0,0,0.000000," ","integrate(atan(a*x)**2/x**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{2}{\left(a x \right)}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**2/(x**2*(c*(a**2*x**2 + 1))**(5/2)), x)","F",0
355,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2*atan(a*x)**2,x)","c^{2} \left(\int x^{m} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int 2 a^{2} x^{2} x^{m} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{4} x^{4} x^{m} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**m*atan(a*x)**2, x) + Integral(2*a**2*x**2*x**m*atan(a*x)**2, x) + Integral(a**4*x**4*x**m*atan(a*x)**2, x))","F",0
356,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)*atan(a*x)**2,x)","c \left(\int x^{m} \operatorname{atan}^{2}{\left(a x \right)}\, dx + \int a^{2} x^{2} x^{m} \operatorname{atan}^{2}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**m*atan(a*x)**2, x) + Integral(a**2*x**2*x**m*atan(a*x)**2, x))","F",0
357,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**2/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{m} \operatorname{atan}^{2}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**m*atan(a*x)**2/(a**2*x**2 + 1), x)/c","F",0
358,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**2/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{m} \operatorname{atan}^{2}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**m*atan(a*x)**2/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
359,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)*atan(a*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)*atan(a*x)**2,x)","\int x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2, x)","F",0
361,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m} \operatorname{atan}^{2}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**m*atan(a*x)**2/sqrt(c*(a**2*x**2 + 1)), x)","F",0
362,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{m} \operatorname{atan}^{2}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*atan(a*x)**2/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)*atan(a*x)**3,x)","c \left(\int x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{2} x^{5} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**3*atan(a*x)**3, x) + Integral(a**2*x**5*atan(a*x)**3, x))","F",0
364,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)*atan(a*x)**3,x)","c \left(\int x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{2} x^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**2*atan(a*x)**3, x) + Integral(a**2*x**4*atan(a*x)**3, x))","F",0
365,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)*atan(a*x)**3,x)","c \left(\int x \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{2} x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x*atan(a*x)**3, x) + Integral(a**2*x**3*atan(a*x)**3, x))","F",0
366,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**3,x)","c \left(\int a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*atan(a*x)**3, x) + Integral(atan(a*x)**3, x))","F",0
367,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**3/x,x)","c \left(\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx + \int a^{2} x \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**3/x, x) + Integral(a**2*x*atan(a*x)**3, x))","F",0
368,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**3/x**2,x)","c \left(\int a^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c*(Integral(a**2*atan(a*x)**3, x) + Integral(atan(a*x)**3/x**2, x))","F",0
369,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**3/x**3,x)","c \left(\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{a^{2} \operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**3/x**3, x) + Integral(a**2*atan(a*x)**3/x, x))","F",0
370,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**3/x**4,x)","c \left(\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{4}}\, dx + \int \frac{a^{2} \operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**3/x**4, x) + Integral(a**2*atan(a*x)**3/x**2, x))","F",0
371,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**2*atan(a*x)**3,x)","c^{2} \left(\int x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 2 a^{2} x^{5} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{4} x^{7} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**3*atan(a*x)**3, x) + Integral(2*a**2*x**5*atan(a*x)**3, x) + Integral(a**4*x**7*atan(a*x)**3, x))","F",0
372,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**2*atan(a*x)**3,x)","c^{2} \left(\int x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 2 a^{2} x^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{4} x^{6} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**2*atan(a*x)**3, x) + Integral(2*a**2*x**4*atan(a*x)**3, x) + Integral(a**4*x**6*atan(a*x)**3, x))","F",0
373,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2*atan(a*x)**3,x)","c^{2} \left(\int x \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 2 a^{2} x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{4} x^{5} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x*atan(a*x)**3, x) + Integral(2*a**2*x**3*atan(a*x)**3, x) + Integral(a**4*x**5*atan(a*x)**3, x))","F",0
374,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**3,x)","c^{2} \left(\int 2 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*atan(a*x)**3, x) + Integral(a**4*x**4*atan(a*x)**3, x) + Integral(atan(a*x)**3, x))","F",0
375,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**3/x,x)","c^{2} \left(\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx + \int 2 a^{2} x \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{4} x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)**3/x, x) + Integral(2*a**2*x*atan(a*x)**3, x) + Integral(a**4*x**3*atan(a*x)**3, x))","F",0
376,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**3/x**2,x)","c^{2} \left(\int 2 a^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx + \int a^{4} x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*atan(a*x)**3, x) + Integral(atan(a*x)**3/x**2, x) + Integral(a**4*x**2*atan(a*x)**3, x))","F",0
377,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**3/x**3,x)","c^{2} \left(\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{2 a^{2} \operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx + \int a^{4} x \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)**3/x**3, x) + Integral(2*a**2*atan(a*x)**3/x, x) + Integral(a**4*x*atan(a*x)**3, x))","F",0
378,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**3/x**4,x)","c^{2} \left(\int a^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{4}}\, dx + \int \frac{2 a^{2} \operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c**2*(Integral(a**4*atan(a*x)**3, x) + Integral(atan(a*x)**3/x**4, x) + Integral(2*a**2*atan(a*x)**3/x**2, x))","F",0
379,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**3*atan(a*x)**3,x)","c^{3} \left(\int x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{2} x^{5} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{4} x^{7} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{6} x^{9} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(x**3*atan(a*x)**3, x) + Integral(3*a**2*x**5*atan(a*x)**3, x) + Integral(3*a**4*x**7*atan(a*x)**3, x) + Integral(a**6*x**9*atan(a*x)**3, x))","F",0
380,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**3*atan(a*x)**3,x)","c^{3} \left(\int x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{2} x^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{4} x^{6} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{6} x^{8} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(x**2*atan(a*x)**3, x) + Integral(3*a**2*x**4*atan(a*x)**3, x) + Integral(3*a**4*x**6*atan(a*x)**3, x) + Integral(a**6*x**8*atan(a*x)**3, x))","F",0
381,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3*atan(a*x)**3,x)","c^{3} \left(\int x \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{2} x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{4} x^{5} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{6} x^{7} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(x*atan(a*x)**3, x) + Integral(3*a**2*x**3*atan(a*x)**3, x) + Integral(3*a**4*x**5*atan(a*x)**3, x) + Integral(a**6*x**7*atan(a*x)**3, x))","F",0
382,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**3,x)","c^{3} \left(\int 3 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{6} x^{6} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2*atan(a*x)**3, x) + Integral(3*a**4*x**4*atan(a*x)**3, x) + Integral(a**6*x**6*atan(a*x)**3, x) + Integral(atan(a*x)**3, x))","F",0
383,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**3/x,x)","c^{3} \left(\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx + \int 3 a^{2} x \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 3 a^{4} x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{6} x^{5} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)**3/x, x) + Integral(3*a**2*x*atan(a*x)**3, x) + Integral(3*a**4*x**3*atan(a*x)**3, x) + Integral(a**6*x**5*atan(a*x)**3, x))","F",0
384,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**3/x**2,x)","c^{3} \left(\int 3 a^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx + \int 3 a^{4} x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{6} x^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*atan(a*x)**3, x) + Integral(atan(a*x)**3/x**2, x) + Integral(3*a**4*x**2*atan(a*x)**3, x) + Integral(a**6*x**4*atan(a*x)**3, x))","F",0
385,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**3/x**3,x)","c^{3} \left(\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{3}}\, dx + \int \frac{3 a^{2} \operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx + \int 3 a^{4} x \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{6} x^{3} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)**3/x**3, x) + Integral(3*a**2*atan(a*x)**3/x, x) + Integral(3*a**4*x*atan(a*x)**3, x) + Integral(a**6*x**3*atan(a*x)**3, x))","F",0
386,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**3/x**4,x)","c^{3} \left(\int 3 a^{4} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{4}}\, dx + \int \frac{3 a^{2} \operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx + \int a^{6} x^{2} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**4*atan(a*x)**3, x) + Integral(atan(a*x)**3/x**4, x) + Integral(3*a**2*atan(a*x)**3/x**2, x) + Integral(a**6*x**2*atan(a*x)**3, x))","F",0
387,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**3/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{4} \operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**4*atan(a*x)**3/(a**2*x**2 + 1), x)/c","F",0
388,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**3/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{3} \operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**3*atan(a*x)**3/(a**2*x**2 + 1), x)/c","F",0
389,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**3/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{2} \operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**2*atan(a*x)**3/(a**2*x**2 + 1), x)/c","F",0
390,0,0,0,0.000000," ","integrate(x*atan(a*x)**3/(a**2*c*x**2+c),x)","\frac{\int \frac{x \operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*atan(a*x)**3/(a**2*x**2 + 1), x)/c","F",0
391,0,0,0,0.000000," ","integrate(atan(a*x)**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(atan(a*x)**3/(a**2*x**2 + 1), x)/c","F",0
392,0,0,0,0.000000," ","integrate(atan(a*x)**3/x/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{3} + x}\, dx}{c}"," ",0,"Integral(atan(a*x)**3/(a**2*x**3 + x), x)/c","F",0
393,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**2/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{4} + x^{2}}\, dx}{c}"," ",0,"Integral(atan(a*x)**3/(a**2*x**4 + x**2), x)/c","F",0
394,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{5} + x^{3}}\, dx}{c}"," ",0,"Integral(atan(a*x)**3/(a**2*x**5 + x**3), x)/c","F",0
395,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**4/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{6} + x^{4}}\, dx}{c}"," ",0,"Integral(atan(a*x)**3/(a**2*x**6 + x**4), x)/c","F",0
396,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**3*atan(a*x)**3/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
397,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**2*atan(a*x)**3/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
398,0,0,0,0.000000," ","integrate(x*atan(a*x)**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x \operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x*atan(a*x)**3/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
399,0,0,0,0.000000," ","integrate(atan(a*x)**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**3/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
400,0,0,0,0.000000," ","integrate(atan(a*x)**3/x/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{5} + 2 a^{2} x^{3} + x}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**3/(a**4*x**5 + 2*a**2*x**3 + x), x)/c**2","F",0
401,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**2/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{6} + 2 a^{2} x^{4} + x^{2}}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**3/(a**4*x**6 + 2*a**2*x**4 + x**2), x)/c**2","F",0
402,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{7} + 2 a^{2} x^{5} + x^{3}}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**3/(a**4*x**7 + 2*a**2*x**5 + x**3), x)/c**2","F",0
403,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**4/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{8} + 2 a^{2} x^{6} + x^{4}}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**3/(a**4*x**8 + 2*a**2*x**6 + x**4), x)/c**2","F",0
404,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**3*atan(a*x)**3/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
405,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**2*atan(a*x)**3/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
406,0,0,0,0.000000," ","integrate(x*atan(a*x)**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x \operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x*atan(a*x)**3/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
407,0,0,0,0.000000," ","integrate(atan(a*x)**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**3/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
408,0,0,0,0.000000," ","integrate(atan(a*x)**3/x/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{7} + 3 a^{4} x^{5} + 3 a^{2} x^{3} + x}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**3/(a**6*x**7 + 3*a**4*x**5 + 3*a**2*x**3 + x), x)/c**3","F",0
409,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**2/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{8} + 3 a^{4} x^{6} + 3 a^{2} x^{4} + x^{2}}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**3/(a**6*x**8 + 3*a**4*x**6 + 3*a**2*x**4 + x**2), x)/c**3","F",0
410,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**3/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{9} + 3 a^{4} x^{7} + 3 a^{2} x^{5} + x^{3}}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**3/(a**6*x**9 + 3*a**4*x**7 + 3*a**2*x**5 + x**3), x)/c**3","F",0
411,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**4/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{a^{6} x^{10} + 3 a^{4} x^{8} + 3 a^{2} x^{6} + x^{4}}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**3/(a**6*x**10 + 3*a**4*x**8 + 3*a**2*x**6 + x**4), x)/c**3","F",0
412,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**3*(a**2*c*x**2+c)**(1/2),x)","\int x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3, x)","F",0
413,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**3*(a**2*c*x**2+c)**(1/2),x)","\int x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3, x)","F",0
414,0,0,0,0.000000," ","integrate(x*atan(a*x)**3*(a**2*c*x**2+c)**(1/2),x)","\int x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3, x)","F",0
415,0,0,0,0.000000," ","integrate(atan(a*x)**3*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3, x)","F",0
416,0,0,0,0.000000," ","integrate(atan(a*x)**3*(a**2*c*x**2+c)**(1/2)/x,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3/x, x)","F",0
417,0,0,0,0.000000," ","integrate(atan(a*x)**3*(a**2*c*x**2+c)**(1/2)/x**2,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3/x**2, x)","F",0
418,0,0,0,0.000000," ","integrate(atan(a*x)**3*(a**2*c*x**2+c)**(1/2)/x**3,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3/x**3, x)","F",0
419,0,0,0,0.000000," ","integrate(atan(a*x)**3*(a**2*c*x**2+c)**(1/2)/x**4,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3/x**4, x)","F",0
420,0,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**(3/2)*atan(a*x)**3,x)","\int x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3, x)","F",0
421,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(3/2)*atan(a*x)**3,x)","\int x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3, x)","F",0
422,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)*atan(a*x)**3,x)","\int x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3, x)","F",0
423,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**3,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3, x)","F",0
424,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**3/x,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3/x, x)","F",0
425,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**3/x**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3/x**2, x)","F",0
426,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**3/x**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3/x**3, x)","F",0
427,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**3/x**4,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3/x**4, x)","F",0
428,-1,0,0,0.000000," ","integrate(x**3*(a**2*c*x**2+c)**(5/2)*atan(a*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(5/2)*atan(a*x)**3,x)","\int x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3, x)","F",0
430,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)*atan(a*x)**3,x)","\int x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3, x)","F",0
431,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**3,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3, x)","F",0
432,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**3/x,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3/x, x)","F",0
433,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**3/x**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3/x**2, x)","F",0
434,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**3/x**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3/x**3, x)","F",0
435,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**3/x**4,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3/x**4, x)","F",0
436,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{3} \operatorname{atan}^{3}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*atan(a*x)**3/sqrt(c*(a**2*x**2 + 1)), x)","F",0
437,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \operatorname{atan}^{3}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*atan(a*x)**3/sqrt(c*(a**2*x**2 + 1)), x)","F",0
438,0,0,0,0.000000," ","integrate(x*atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x \operatorname{atan}^{3}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x*atan(a*x)**3/sqrt(c*(a**2*x**2 + 1)), x)","F",0
439,0,0,0,0.000000," ","integrate(atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**3/sqrt(c*(a**2*x**2 + 1)), x)","F",0
440,0,0,0,0.000000," ","integrate(atan(a*x)**3/x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**3/(x*sqrt(c*(a**2*x**2 + 1))), x)","F",0
441,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**3/(x**2*sqrt(c*(a**2*x**2 + 1))), x)","F",0
442,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**3/(x**3*sqrt(c*(a**2*x**2 + 1))), x)","F",0
443,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**4/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{4} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**3/(x**4*sqrt(c*(a**2*x**2 + 1))), x)","F",0
444,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{3} \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*atan(a*x)**3/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
445,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{2} \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)**3/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
446,0,0,0,0.000000," ","integrate(x*atan(a*x)**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*atan(a*x)**3/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
447,0,0,0,0.000000," ","integrate(atan(a*x)**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**3/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
448,0,0,0,0.000000," ","integrate(atan(a*x)**3/x/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**3/(x*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
449,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**3/(x**2*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
450,0,0,0,0.000000," ","integrate(x**5*atan(a*x)**3/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{5} \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**5*atan(a*x)**3/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
451,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**3/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{4} \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*atan(a*x)**3/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
452,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**3/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{3} \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*atan(a*x)**3/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
453,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**3/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{2} \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)**3/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
454,0,0,0,0.000000," ","integrate(x*atan(a*x)**3/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*atan(a*x)**3/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
455,0,0,0,0.000000," ","integrate(atan(a*x)**3/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**3/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
456,0,0,0,0.000000," ","integrate(atan(a*x)**3/x/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**3/(x*(c*(a**2*x**2 + 1))**(5/2)), x)","F",0
457,0,0,0,0.000000," ","integrate(atan(a*x)**3/x**2/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{3}{\left(a x \right)}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**3/(x**2*(c*(a**2*x**2 + 1))**(5/2)), x)","F",0
458,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2*atan(a*x)**3,x)","c^{2} \left(\int x^{m} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int 2 a^{2} x^{2} x^{m} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{4} x^{4} x^{m} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**m*atan(a*x)**3, x) + Integral(2*a**2*x**2*x**m*atan(a*x)**3, x) + Integral(a**4*x**4*x**m*atan(a*x)**3, x))","F",0
459,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)*atan(a*x)**3,x)","c \left(\int x^{m} \operatorname{atan}^{3}{\left(a x \right)}\, dx + \int a^{2} x^{2} x^{m} \operatorname{atan}^{3}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**m*atan(a*x)**3, x) + Integral(a**2*x**2*x**m*atan(a*x)**3, x))","F",0
460,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**3/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{m} \operatorname{atan}^{3}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**m*atan(a*x)**3/(a**2*x**2 + 1), x)/c","F",0
461,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**3/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{m} \operatorname{atan}^{3}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**m*atan(a*x)**3/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
462,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)*atan(a*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**3*(a**2*c*x**2+c)**(1/2),x)","\int x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3, x)","F",0
464,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m} \operatorname{atan}^{3}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**m*atan(a*x)**3/sqrt(c*(a**2*x**2 + 1)), x)","F",0
465,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**3/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{m} \operatorname{atan}^{3}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*atan(a*x)**3/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
466,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)/atan(a*x),x)","c \left(\int \frac{x}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{3}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x/atan(a*x), x) + Integral(a**2*x**3/atan(a*x), x))","F",0
467,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/atan(a*x),x)","c \left(\int \frac{a^{2} x^{2}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/atan(a*x), x) + Integral(1/atan(a*x), x))","F",0
468,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/x/atan(a*x),x)","c \left(\int \frac{1}{x \operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{2} x}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(1/(x*atan(a*x)), x) + Integral(a**2*x/atan(a*x), x))","F",0
469,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2/atan(a*x),x)","c^{2} \left(\int \frac{x}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{3}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{5}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x/atan(a*x), x) + Integral(2*a**2*x**3/atan(a*x), x) + Integral(a**4*x**5/atan(a*x), x))","F",0
470,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/atan(a*x),x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/atan(a*x), x) + Integral(a**4*x**4/atan(a*x), x) + Integral(1/atan(a*x), x))","F",0
471,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/x/atan(a*x),x)","c^{2} \left(\int \frac{1}{x \operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{3}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(1/(x*atan(a*x)), x) + Integral(2*a**2*x/atan(a*x), x) + Integral(a**4*x**3/atan(a*x), x))","F",0
472,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3/atan(a*x),x)","c^{3} \left(\int \frac{x}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{3}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{5}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{7}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x/atan(a*x), x) + Integral(3*a**2*x**3/atan(a*x), x) + Integral(3*a**4*x**5/atan(a*x), x) + Integral(a**6*x**7/atan(a*x), x))","F",0
473,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/atan(a*x),x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/atan(a*x), x) + Integral(3*a**4*x**4/atan(a*x), x) + Integral(a**6*x**6/atan(a*x), x) + Integral(1/atan(a*x), x))","F",0
474,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/x/atan(a*x),x)","c^{3} \left(\int \frac{1}{x \operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{3}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{5}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(1/(x*atan(a*x)), x) + Integral(3*a**2*x/atan(a*x), x) + Integral(3*a**4*x**3/atan(a*x), x) + Integral(a**6*x**5/atan(a*x), x))","F",0
475,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)/atan(a*x),x)","\frac{\int \frac{x^{2}}{a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**2/(a**2*x**2*atan(a*x) + atan(a*x)), x)/c","F",0
476,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)/atan(a*x),x)","\frac{\int \frac{x}{a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x/(a**2*x**2*atan(a*x) + atan(a*x)), x)/c","F",0
477,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/atan(a*x),x)","\begin{cases} \frac{\log{\left(\operatorname{atan}{\left(a x \right)} \right)}}{a c} & \text{for}\: c \neq 0 \\\tilde{\infty} \int \frac{1}{\operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(atan(a*x))/(a*c), Ne(c, 0)), (zoo*Integral(1/atan(a*x), x), True))","F",0
478,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)/atan(a*x),x)","\frac{\int \frac{1}{a^{2} x^{3} \operatorname{atan}{\left(a x \right)} + x \operatorname{atan}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**3*atan(a*x) + x*atan(a*x)), x)/c","F",0
479,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)/atan(a*x),x)","\frac{\int \frac{1}{a^{2} x^{4} \operatorname{atan}{\left(a x \right)} + x^{2} \operatorname{atan}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**4*atan(a*x) + x**2*atan(a*x)), x)/c","F",0
480,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{x^{4}}{a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**4/(a**4*x**4*atan(a*x) + 2*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**2","F",0
481,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{x^{3}}{a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**3/(a**4*x**4*atan(a*x) + 2*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**2","F",0
482,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{x^{2}}{a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**2/(a**4*x**4*atan(a*x) + 2*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**2","F",0
483,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{x}{a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x/(a**4*x**4*atan(a*x) + 2*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**2","F",0
484,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{1}{a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*atan(a*x) + 2*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**2","F",0
485,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{1}{a^{4} x^{5} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{3} \operatorname{atan}{\left(a x \right)} + x \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**5*atan(a*x) + 2*a**2*x**3*atan(a*x) + x*atan(a*x)), x)/c**2","F",0
486,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{1}{a^{4} x^{6} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{4} \operatorname{atan}{\left(a x \right)} + x^{2} \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**6*atan(a*x) + 2*a**2*x**4*atan(a*x) + x**2*atan(a*x)), x)/c**2","F",0
487,0,0,0,0.000000," ","integrate(x**6/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{x^{6}}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**6/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
488,0,0,0,0.000000," ","integrate(x**5/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{x^{5}}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**5/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
489,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{x^{4}}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**4/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
490,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{x^{3}}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**3/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
491,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{x^{2}}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**2/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
492,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{x}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
493,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{1}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
494,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{1}{a^{6} x^{7} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{5} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atan}{\left(a x \right)} + x \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**7*atan(a*x) + 3*a**4*x**5*atan(a*x) + 3*a**2*x**3*atan(a*x) + x*atan(a*x)), x)/c**3","F",0
495,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{1}{a^{6} x^{8} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{4} \operatorname{atan}{\left(a x \right)} + x^{2} \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**8*atan(a*x) + 3*a**4*x**6*atan(a*x) + 3*a**2*x**4*atan(a*x) + x**2*atan(a*x)), x)/c**3","F",0
496,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(1/2)/atan(a*x),x)","\int \frac{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))/atan(a*x), x)","F",0
497,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/atan(a*x),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/atan(a*x), x)","F",0
498,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/x/atan(a*x),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{x \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/(x*atan(a*x)), x)","F",0
499,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)/atan(a*x), x)","F",0
500,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/atan(a*x), x)","F",0
501,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/x/atan(a*x),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{x \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/(x*atan(a*x)), x)","F",0
502,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(5/2)/atan(a*x), x)","F",0
503,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)/atan(a*x), x)","F",0
504,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/x/atan(a*x),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{x \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)/(x*atan(a*x)), x)","F",0
505,0,0,0,0.000000," ","integrate(x/atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)), x)","F",0
506,0,0,0,0.000000," ","integrate(1/atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)), x)","F",0
507,0,0,0,0.000000," ","integrate(1/x/atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)), x)","F",0
508,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)), x)","F",0
509,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)), x)","F",0
510,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)), x)","F",0
511,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)), x)","F",0
512,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)), x)","F",0
513,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{1}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)), x)","F",0
514,0,0,0,0.000000," ","integrate(x**5/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{x^{5}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**5/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
515,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{x^{4}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
516,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
517,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
518,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
519,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
520,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
521,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\int \frac{1}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)), x)","F",0
522,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3/atan(a*x),x)","c^{3} \left(\int \frac{x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{2} x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4} x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6} x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x**m/atan(a*x), x) + Integral(3*a**2*x**2*x**m/atan(a*x), x) + Integral(3*a**4*x**4*x**m/atan(a*x), x) + Integral(a**6*x**6*x**m/atan(a*x), x))","F",0
523,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2/atan(a*x),x)","c^{2} \left(\int \frac{x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{2} x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4} x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x**m/atan(a*x), x) + Integral(2*a**2*x**2*x**m/atan(a*x), x) + Integral(a**4*x**4*x**m/atan(a*x), x))","F",0
524,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)/atan(a*x),x)","c \left(\int \frac{x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{2} x^{m}}{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x**m/atan(a*x), x) + Integral(a**2*x**2*x**m/atan(a*x), x))","F",0
525,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)/atan(a*x),x)","\frac{\int \frac{x^{m}}{a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**m/(a**2*x**2*atan(a*x) + atan(a*x)), x)/c","F",0
526,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**2/atan(a*x),x)","\frac{\int \frac{x^{m}}{a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**m/(a**4*x**4*atan(a*x) + 2*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**2","F",0
527,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**3/atan(a*x),x)","\frac{\int \frac{x^{m}}{a^{6} x^{6} \operatorname{atan}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}{\left(a x \right)} + \operatorname{atan}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**m/(a**6*x**6*atan(a*x) + 3*a**4*x**4*atan(a*x) + 3*a**2*x**2*atan(a*x) + atan(a*x)), x)/c**3","F",0
528,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{x^{m} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*(c*(a**2*x**2 + 1))**(3/2)/atan(a*x), x)","F",0
530,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)/atan(a*x),x)","\int \frac{x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))/atan(a*x), x)","F",0
531,0,0,0,0.000000," ","integrate(x**m/atan(a*x)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m}}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)), x)","F",0
532,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(3/2)/atan(a*x),x)","\int \frac{x^{m}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)), x)","F",0
533,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(5/2)/atan(a*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)/atan(a*x)**2,x)","c \left(\int \frac{x}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{3}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x/atan(a*x)**2, x) + Integral(a**2*x**3/atan(a*x)**2, x))","F",0
535,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/atan(a*x)**2,x)","c \left(\int \frac{a^{2} x^{2}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/atan(a*x)**2, x) + Integral(atan(a*x)**(-2), x))","F",0
536,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/x/atan(a*x)**2,x)","c \left(\int \frac{1}{x \operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{2} x}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(1/(x*atan(a*x)**2), x) + Integral(a**2*x/atan(a*x)**2, x))","F",0
537,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2/atan(a*x)**2,x)","c^{2} \left(\int \frac{x}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{3}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{5}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x/atan(a*x)**2, x) + Integral(2*a**2*x**3/atan(a*x)**2, x) + Integral(a**4*x**5/atan(a*x)**2, x))","F",0
538,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/atan(a*x)**2,x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/atan(a*x)**2, x) + Integral(a**4*x**4/atan(a*x)**2, x) + Integral(atan(a*x)**(-2), x))","F",0
539,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/x/atan(a*x)**2,x)","c^{2} \left(\int \frac{1}{x \operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{3}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(1/(x*atan(a*x)**2), x) + Integral(2*a**2*x/atan(a*x)**2, x) + Integral(a**4*x**3/atan(a*x)**2, x))","F",0
540,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3/atan(a*x)**2,x)","c^{3} \left(\int \frac{x}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{3}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{5}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{7}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x/atan(a*x)**2, x) + Integral(3*a**2*x**3/atan(a*x)**2, x) + Integral(3*a**4*x**5/atan(a*x)**2, x) + Integral(a**6*x**7/atan(a*x)**2, x))","F",0
541,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/atan(a*x)**2,x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/atan(a*x)**2, x) + Integral(3*a**4*x**4/atan(a*x)**2, x) + Integral(a**6*x**6/atan(a*x)**2, x) + Integral(atan(a*x)**(-2), x))","F",0
542,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/x/atan(a*x)**2,x)","c^{3} \left(\int \frac{1}{x \operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{3}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{5}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(1/(x*atan(a*x)**2), x) + Integral(3*a**2*x/atan(a*x)**2, x) + Integral(3*a**4*x**3/atan(a*x)**2, x) + Integral(a**6*x**5/atan(a*x)**2, x))","F",0
543,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{x^{3}}{a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**3/(a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c","F",0
544,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{x^{2}}{a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**2/(a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c","F",0
545,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{x}{a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x/(a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c","F",0
546,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/atan(a*x)**2,x)","\begin{cases} - \frac{1}{a c \operatorname{atan}{\left(a x \right)}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int \frac{1}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(a*c*atan(a*x)), Ne(c, 0)), (zoo*Integral(atan(a*x)**(-2), x), True))","F",0
547,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{2} x^{3} \operatorname{atan}^{2}{\left(a x \right)} + x \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**3*atan(a*x)**2 + x*atan(a*x)**2), x)/c","F",0
548,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + x^{2} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**4*atan(a*x)**2 + x**2*atan(a*x)**2), x)/c","F",0
549,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{2} x^{5} \operatorname{atan}^{2}{\left(a x \right)} + x^{3} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**5*atan(a*x)**2 + x**3*atan(a*x)**2), x)/c","F",0
550,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{2} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + x^{4} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**6*atan(a*x)**2 + x**4*atan(a*x)**2), x)/c","F",0
551,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{x^{3}}{a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**3/(a**4*x**4*atan(a*x)**2 + 2*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**2","F",0
552,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{x^{2}}{a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**2/(a**4*x**4*atan(a*x)**2 + 2*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**2","F",0
553,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{x}{a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x/(a**4*x**4*atan(a*x)**2 + 2*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**2","F",0
554,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*atan(a*x)**2 + 2*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**2","F",0
555,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{4} x^{5} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{3} \operatorname{atan}^{2}{\left(a x \right)} + x \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**5*atan(a*x)**2 + 2*a**2*x**3*atan(a*x)**2 + x*atan(a*x)**2), x)/c**2","F",0
556,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{4} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + x^{2} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**6*atan(a*x)**2 + 2*a**2*x**4*atan(a*x)**2 + x**2*atan(a*x)**2), x)/c**2","F",0
557,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{4} x^{7} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{5} \operatorname{atan}^{2}{\left(a x \right)} + x^{3} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**7*atan(a*x)**2 + 2*a**2*x**5*atan(a*x)**2 + x**3*atan(a*x)**2), x)/c**2","F",0
558,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{4} x^{8} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + x^{4} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**8*atan(a*x)**2 + 2*a**2*x**6*atan(a*x)**2 + x**4*atan(a*x)**2), x)/c**2","F",0
559,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{x^{3}}{a^{6} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**3/(a**6*x**6*atan(a*x)**2 + 3*a**4*x**4*atan(a*x)**2 + 3*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**3","F",0
560,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{x^{2}}{a^{6} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**2/(a**6*x**6*atan(a*x)**2 + 3*a**4*x**4*atan(a*x)**2 + 3*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**3","F",0
561,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{x}{a^{6} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x/(a**6*x**6*atan(a*x)**2 + 3*a**4*x**4*atan(a*x)**2 + 3*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**3","F",0
562,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{6} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**6*atan(a*x)**2 + 3*a**4*x**4*atan(a*x)**2 + 3*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**3","F",0
563,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{6} x^{7} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{5} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atan}^{2}{\left(a x \right)} + x \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**7*atan(a*x)**2 + 3*a**4*x**5*atan(a*x)**2 + 3*a**2*x**3*atan(a*x)**2 + x*atan(a*x)**2), x)/c**3","F",0
564,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{6} x^{8} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + x^{2} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**8*atan(a*x)**2 + 3*a**4*x**6*atan(a*x)**2 + 3*a**2*x**4*atan(a*x)**2 + x**2*atan(a*x)**2), x)/c**3","F",0
565,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{6} x^{9} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{7} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{5} \operatorname{atan}^{2}{\left(a x \right)} + x^{3} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**9*atan(a*x)**2 + 3*a**4*x**7*atan(a*x)**2 + 3*a**2*x**5*atan(a*x)**2 + x**3*atan(a*x)**2), x)/c**3","F",0
566,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{1}{a^{6} x^{10} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{8} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + x^{4} \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**10*atan(a*x)**2 + 3*a**4*x**8*atan(a*x)**2 + 3*a**2*x**6*atan(a*x)**2 + x**4*atan(a*x)**2), x)/c**3","F",0
567,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(1/2)/atan(a*x)**2,x)","\int \frac{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))/atan(a*x)**2, x)","F",0
568,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/atan(a*x)**2,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/atan(a*x)**2, x)","F",0
569,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/x/atan(a*x)**2,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{x \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/(x*atan(a*x)**2), x)","F",0
570,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)/atan(a*x)**2, x)","F",0
571,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/atan(a*x)**2, x)","F",0
572,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/x/atan(a*x)**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{x \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/(x*atan(a*x)**2), x)","F",0
573,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(5/2)/atan(a*x)**2, x)","F",0
574,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)/atan(a*x)**2, x)","F",0
575,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/x/atan(a*x)**2,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{x \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)/(x*atan(a*x)**2), x)","F",0
576,0,0,0,0.000000," ","integrate(x/atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2), x)","F",0
577,0,0,0,0.000000," ","integrate(1/atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2), x)","F",0
578,0,0,0,0.000000," ","integrate(1/x/atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2), x)","F",0
579,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
580,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
581,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
582,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
583,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
584,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{1}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
585,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{1}{x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**3*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
586,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{1}{x^{4} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**4*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
587,0,0,0,0.000000," ","integrate(x**5/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{x^{5}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**5/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
588,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{x^{4}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
589,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
590,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
591,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
593,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
594,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{1}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
595,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{1}{x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**3*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
596,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\int \frac{1}{x^{4} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**4*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**2), x)","F",0
597,-1,0,0,0.000000," ","integrate((f*x)**(1/2)/(c**2*d*x**2+d)**2/(a+b*atan(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3/atan(a*x)**2,x)","c^{3} \left(\int \frac{x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{2} x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4} x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6} x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x**m/atan(a*x)**2, x) + Integral(3*a**2*x**2*x**m/atan(a*x)**2, x) + Integral(3*a**4*x**4*x**m/atan(a*x)**2, x) + Integral(a**6*x**6*x**m/atan(a*x)**2, x))","F",0
599,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2/atan(a*x)**2,x)","c^{2} \left(\int \frac{x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{2} x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4} x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x**m/atan(a*x)**2, x) + Integral(2*a**2*x**2*x**m/atan(a*x)**2, x) + Integral(a**4*x**4*x**m/atan(a*x)**2, x))","F",0
600,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)/atan(a*x)**2,x)","c \left(\int \frac{x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{2} x^{m}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x**m/atan(a*x)**2, x) + Integral(a**2*x**2*x**m/atan(a*x)**2, x))","F",0
601,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)/atan(a*x)**2,x)","\frac{\int \frac{x^{m}}{a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**m/(a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c","F",0
602,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**2/atan(a*x)**2,x)","\frac{\int \frac{x^{m}}{a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**m/(a**4*x**4*atan(a*x)**2 + 2*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**2","F",0
603,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**3/atan(a*x)**2,x)","\frac{\int \frac{x^{m}}{a^{6} x^{6} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{2}{\left(a x \right)} + \operatorname{atan}^{2}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**m/(a**6*x**6*atan(a*x)**2 + 3*a**4*x**4*atan(a*x)**2 + 3*a**2*x**2*atan(a*x)**2 + atan(a*x)**2), x)/c**3","F",0
604,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)/atan(a*x)**2,x)","\int \frac{x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))/atan(a*x)**2, x)","F",0
607,0,0,0,0.000000," ","integrate(x**m/atan(a*x)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m}}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**2), x)","F",0
608,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(3/2)/atan(a*x)**2,x)","\int \frac{x^{m}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**2), x)","F",0
609,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(5/2)/atan(a*x)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)/atan(a*x)**3,x)","c \left(\int \frac{x}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{3}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x/atan(a*x)**3, x) + Integral(a**2*x**3/atan(a*x)**3, x))","F",0
611,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/atan(a*x)**3,x)","c \left(\int \frac{a^{2} x^{2}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/atan(a*x)**3, x) + Integral(atan(a*x)**(-3), x))","F",0
612,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/x/atan(a*x)**3,x)","c \left(\int \frac{1}{x \operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{2} x}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(1/(x*atan(a*x)**3), x) + Integral(a**2*x/atan(a*x)**3, x))","F",0
613,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2/atan(a*x)**3,x)","c^{2} \left(\int \frac{x}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{3}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{5}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x/atan(a*x)**3, x) + Integral(2*a**2*x**3/atan(a*x)**3, x) + Integral(a**4*x**5/atan(a*x)**3, x))","F",0
614,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/atan(a*x)**3,x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/atan(a*x)**3, x) + Integral(a**4*x**4/atan(a*x)**3, x) + Integral(atan(a*x)**(-3), x))","F",0
615,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/x/atan(a*x)**3,x)","c^{2} \left(\int \frac{1}{x \operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{3}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(1/(x*atan(a*x)**3), x) + Integral(2*a**2*x/atan(a*x)**3, x) + Integral(a**4*x**3/atan(a*x)**3, x))","F",0
616,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3/atan(a*x)**3,x)","c^{3} \left(\int \frac{x}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{3}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{5}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{7}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x/atan(a*x)**3, x) + Integral(3*a**2*x**3/atan(a*x)**3, x) + Integral(3*a**4*x**5/atan(a*x)**3, x) + Integral(a**6*x**7/atan(a*x)**3, x))","F",0
617,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/atan(a*x)**3,x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/atan(a*x)**3, x) + Integral(3*a**4*x**4/atan(a*x)**3, x) + Integral(a**6*x**6/atan(a*x)**3, x) + Integral(atan(a*x)**(-3), x))","F",0
618,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/x/atan(a*x)**3,x)","c^{3} \left(\int \frac{1}{x \operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{3}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{5}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(1/(x*atan(a*x)**3), x) + Integral(3*a**2*x/atan(a*x)**3, x) + Integral(3*a**4*x**3/atan(a*x)**3, x) + Integral(a**6*x**5/atan(a*x)**3, x))","F",0
619,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{x^{3}}{a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**3/(a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c","F",0
620,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{x^{2}}{a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**2/(a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c","F",0
621,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{x}{a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x/(a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c","F",0
622,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/atan(a*x)**3,x)","\begin{cases} - \frac{1}{2 a c \operatorname{atan}^{2}{\left(a x \right)}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int \frac{1}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*a*c*atan(a*x)**2), Ne(c, 0)), (zoo*Integral(atan(a*x)**(-3), x), True))","F",0
623,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{2} x^{3} \operatorname{atan}^{3}{\left(a x \right)} + x \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**3*atan(a*x)**3 + x*atan(a*x)**3), x)/c","F",0
624,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{2} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + x^{2} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**4*atan(a*x)**3 + x**2*atan(a*x)**3), x)/c","F",0
625,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{2} x^{5} \operatorname{atan}^{3}{\left(a x \right)} + x^{3} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**5*atan(a*x)**3 + x**3*atan(a*x)**3), x)/c","F",0
626,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{2} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + x^{4} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**6*atan(a*x)**3 + x**4*atan(a*x)**3), x)/c","F",0
627,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{x^{3}}{a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**3/(a**4*x**4*atan(a*x)**3 + 2*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**2","F",0
628,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{x^{2}}{a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**2/(a**4*x**4*atan(a*x)**3 + 2*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**2","F",0
629,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{x}{a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x/(a**4*x**4*atan(a*x)**3 + 2*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**2","F",0
630,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*atan(a*x)**3 + 2*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**2","F",0
631,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{4} x^{5} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{3} \operatorname{atan}^{3}{\left(a x \right)} + x \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**5*atan(a*x)**3 + 2*a**2*x**3*atan(a*x)**3 + x*atan(a*x)**3), x)/c**2","F",0
632,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{4} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + x^{2} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**6*atan(a*x)**3 + 2*a**2*x**4*atan(a*x)**3 + x**2*atan(a*x)**3), x)/c**2","F",0
633,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{4} x^{7} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{5} \operatorname{atan}^{3}{\left(a x \right)} + x^{3} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**7*atan(a*x)**3 + 2*a**2*x**5*atan(a*x)**3 + x**3*atan(a*x)**3), x)/c**2","F",0
634,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{4} x^{8} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + x^{4} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**8*atan(a*x)**3 + 2*a**2*x**6*atan(a*x)**3 + x**4*atan(a*x)**3), x)/c**2","F",0
635,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{x^{3}}{a^{6} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**3/(a**6*x**6*atan(a*x)**3 + 3*a**4*x**4*atan(a*x)**3 + 3*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**3","F",0
636,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{x^{2}}{a^{6} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**2/(a**6*x**6*atan(a*x)**3 + 3*a**4*x**4*atan(a*x)**3 + 3*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**3","F",0
637,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{x}{a^{6} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x/(a**6*x**6*atan(a*x)**3 + 3*a**4*x**4*atan(a*x)**3 + 3*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**3","F",0
638,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{6} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**6*atan(a*x)**3 + 3*a**4*x**4*atan(a*x)**3 + 3*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**3","F",0
639,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{6} x^{7} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{5} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atan}^{3}{\left(a x \right)} + x \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**7*atan(a*x)**3 + 3*a**4*x**5*atan(a*x)**3 + 3*a**2*x**3*atan(a*x)**3 + x*atan(a*x)**3), x)/c**3","F",0
640,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{6} x^{8} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + x^{2} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**8*atan(a*x)**3 + 3*a**4*x**6*atan(a*x)**3 + 3*a**2*x**4*atan(a*x)**3 + x**2*atan(a*x)**3), x)/c**3","F",0
641,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{6} x^{9} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{7} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{5} \operatorname{atan}^{3}{\left(a x \right)} + x^{3} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**9*atan(a*x)**3 + 3*a**4*x**7*atan(a*x)**3 + 3*a**2*x**5*atan(a*x)**3 + x**3*atan(a*x)**3), x)/c**3","F",0
642,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{1}{a^{6} x^{10} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{8} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + x^{4} \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**10*atan(a*x)**3 + 3*a**4*x**8*atan(a*x)**3 + 3*a**2*x**6*atan(a*x)**3 + x**4*atan(a*x)**3), x)/c**3","F",0
643,0,0,0,0.000000," ","integrate(x**3/(a**2*x**2+1)/atan(a*x)**3-3/2*x**2/a/atan(a*x)**2,x)","- \frac{\int \left(- \frac{2 a x^{3}}{a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\right)\, dx + \int \frac{3 x^{2} \operatorname{atan}{\left(a x \right)}}{a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{4} \operatorname{atan}{\left(a x \right)}}{a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{2 a}"," ",0,"-(Integral(-2*a*x**3/(a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x) + Integral(3*x**2*atan(a*x)/(a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x) + Integral(3*a**2*x**4*atan(a*x)/(a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x))/(2*a)","F",0
644,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(1/2)/atan(a*x)**3,x)","\int \frac{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))/atan(a*x)**3, x)","F",0
645,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/atan(a*x)**3,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/atan(a*x)**3, x)","F",0
646,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/x/atan(a*x)**3,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{x \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/(x*atan(a*x)**3), x)","F",0
647,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)/atan(a*x)**3, x)","F",0
648,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/atan(a*x)**3, x)","F",0
649,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/x/atan(a*x)**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{x \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/(x*atan(a*x)**3), x)","F",0
650,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(5/2)/atan(a*x)**3, x)","F",0
651,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)/atan(a*x)**3, x)","F",0
652,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/x/atan(a*x)**3,x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{x \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)/(x*atan(a*x)**3), x)","F",0
653,0,0,0,0.000000," ","integrate(x/atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3), x)","F",0
654,0,0,0,0.000000," ","integrate(1/atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3), x)","F",0
655,0,0,0,0.000000," ","integrate(1/x/atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3), x)","F",0
656,0,0,0,0.000000," ","integrate(1/x**2/atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3), x)","F",0
657,0,0,0,0.000000," ","integrate(1/x**3/atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**3*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3), x)","F",0
658,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
659,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
660,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
661,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
662,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
663,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{1}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
664,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{1}{x^{3} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**3*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
665,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{1}{x^{4} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**4*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
666,0,0,0,0.000000," ","integrate(x**5/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{x^{5}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**5/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
667,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{x^{4}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
668,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
669,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
670,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
671,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
672,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
673,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\int \frac{1}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(c*(a**2*x**2 + 1))**(5/2)*atan(a*x)**3), x)","F",0
674,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3/atan(a*x)**3,x)","c^{3} \left(\int \frac{x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{2} x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4} x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6} x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x**m/atan(a*x)**3, x) + Integral(3*a**2*x**2*x**m/atan(a*x)**3, x) + Integral(3*a**4*x**4*x**m/atan(a*x)**3, x) + Integral(a**6*x**6*x**m/atan(a*x)**3, x))","F",0
675,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2/atan(a*x)**3,x)","c^{2} \left(\int \frac{x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{2} x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4} x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x**m/atan(a*x)**3, x) + Integral(2*a**2*x**2*x**m/atan(a*x)**3, x) + Integral(a**4*x**4*x**m/atan(a*x)**3, x))","F",0
676,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)/atan(a*x)**3,x)","c \left(\int \frac{x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{2} x^{m}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x**m/atan(a*x)**3, x) + Integral(a**2*x**2*x**m/atan(a*x)**3, x))","F",0
677,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)/atan(a*x)**3,x)","\frac{\int \frac{x^{m}}{a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**m/(a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c","F",0
678,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**2/atan(a*x)**3,x)","\frac{\int \frac{x^{m}}{a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**m/(a**4*x**4*atan(a*x)**3 + 2*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**2","F",0
679,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**3/atan(a*x)**3,x)","\frac{\int \frac{x^{m}}{a^{6} x^{6} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{3}{\left(a x \right)} + \operatorname{atan}^{3}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**m/(a**6*x**6*atan(a*x)**3 + 3*a**4*x**4*atan(a*x)**3 + 3*a**2*x**2*atan(a*x)**3 + atan(a*x)**3), x)/c**3","F",0
680,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
681,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
682,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)/atan(a*x)**3,x)","\int \frac{x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))/atan(a*x)**3, x)","F",0
683,0,0,0,0.000000," ","integrate(x**m/atan(a*x)**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m}}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**3), x)","F",0
684,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(3/2)/atan(a*x)**3,x)","\int \frac{x^{m}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**3), x)","F",0
685,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(5/2)/atan(a*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
686,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)*atan(a*x)**(1/2),x)","c \left(\int x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{2} x^{2} x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x**m*sqrt(atan(a*x)), x) + Integral(a**2*x**2*x**m*sqrt(atan(a*x)), x))","F",0
687,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)*atan(a*x)**(1/2),x)","c \left(\int x \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{2} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x*sqrt(atan(a*x)), x) + Integral(a**2*x**3*sqrt(atan(a*x)), x))","F",0
688,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(1/2),x)","c \left(\int a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*sqrt(atan(a*x)), x) + Integral(sqrt(atan(a*x)), x))","F",0
689,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(1/2)/x,x)","c \left(\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x}\, dx + \int a^{2} x \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(sqrt(atan(a*x))/x, x) + Integral(a**2*x*sqrt(atan(a*x)), x))","F",0
690,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2*atan(a*x)**(1/2),x)","c^{2} \left(\int x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int 2 a^{2} x^{2} x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{4} x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x**m*sqrt(atan(a*x)), x) + Integral(2*a**2*x**2*x**m*sqrt(atan(a*x)), x) + Integral(a**4*x**4*x**m*sqrt(atan(a*x)), x))","F",0
691,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2*atan(a*x)**(1/2),x)","c^{2} \left(\int x \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int 2 a^{2} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{5} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x*sqrt(atan(a*x)), x) + Integral(2*a**2*x**3*sqrt(atan(a*x)), x) + Integral(a**4*x**5*sqrt(atan(a*x)), x))","F",0
692,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(1/2),x)","c^{2} \left(\int 2 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*sqrt(atan(a*x)), x) + Integral(a**4*x**4*sqrt(atan(a*x)), x) + Integral(sqrt(atan(a*x)), x))","F",0
693,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(1/2)/x,x)","c^{2} \left(\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x}\, dx + \int 2 a^{2} x \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(sqrt(atan(a*x))/x, x) + Integral(2*a**2*x*sqrt(atan(a*x)), x) + Integral(a**4*x**3*sqrt(atan(a*x)), x))","F",0
694,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3*atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3*atan(a*x)**(1/2),x)","c^{3} \left(\int x \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int 3 a^{2} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int 3 a^{4} x^{5} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{6} x^{7} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x*sqrt(atan(a*x)), x) + Integral(3*a**2*x**3*sqrt(atan(a*x)), x) + Integral(3*a**4*x**5*sqrt(atan(a*x)), x) + Integral(a**6*x**7*sqrt(atan(a*x)), x))","F",0
696,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(1/2),x)","c^{3} \left(\int 3 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int 3 a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{6} x^{6} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2*sqrt(atan(a*x)), x) + Integral(3*a**4*x**4*sqrt(atan(a*x)), x) + Integral(a**6*x**6*sqrt(atan(a*x)), x) + Integral(sqrt(atan(a*x)), x))","F",0
697,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(1/2)/x,x)","c^{3} \left(\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x}\, dx + \int 3 a^{2} x \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int 3 a^{4} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{6} x^{5} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(sqrt(atan(a*x))/x, x) + Integral(3*a**2*x*sqrt(atan(a*x)), x) + Integral(3*a**4*x**3*sqrt(atan(a*x)), x) + Integral(a**6*x**5*sqrt(atan(a*x)), x))","F",0
698,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**(1/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**m*sqrt(atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
699,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(1/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**3*sqrt(atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
700,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(1/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**2*sqrt(atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
701,0,0,0,0.000000," ","integrate(x*atan(a*x)**(1/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*sqrt(atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
702,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(sqrt(atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
703,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x/(a**2*c*x**2+c),x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{3} + x}\, dx}{c}"," ",0,"Integral(sqrt(atan(a*x))/(a**2*x**3 + x), x)/c","F",0
704,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x**2/(a**2*c*x**2+c),x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{4} + x^{2}}\, dx}{c}"," ",0,"Integral(sqrt(atan(a*x))/(a**2*x**4 + x**2), x)/c","F",0
705,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{5} + x^{3}}\, dx}{c}"," ",0,"Integral(sqrt(atan(a*x))/(a**2*x**5 + x**3), x)/c","F",0
706,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x**4/(a**2*c*x**2+c),x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{2} x^{6} + x^{4}}\, dx}{c}"," ",0,"Integral(sqrt(atan(a*x))/(a**2*x**6 + x**4), x)/c","F",0
707,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**(1/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**m*sqrt(atan(a*x))/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
708,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(1/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**3*sqrt(atan(a*x))/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
709,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(1/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**2*sqrt(atan(a*x))/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
710,0,0,0,0.000000," ","integrate(x*atan(a*x)**(1/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x*sqrt(atan(a*x))/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
711,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(sqrt(atan(a*x))/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
712,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{4} x^{5} + 2 a^{2} x^{3} + x}\, dx}{c^{2}}"," ",0,"Integral(sqrt(atan(a*x))/(a**4*x**5 + 2*a**2*x**3 + x), x)/c**2","F",0
713,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(1/2)/(a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,0,0,0,0.000000," ","integrate(x**5*atan(a*x)**(1/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{5} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**5*sqrt(atan(a*x))/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
715,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**(1/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**4*sqrt(atan(a*x))/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
716,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(1/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**3*sqrt(atan(a*x))/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
717,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(1/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**2*sqrt(atan(a*x))/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
718,0,0,0,0.000000," ","integrate(x*atan(a*x)**(1/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x \sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x*sqrt(atan(a*x))/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
719,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(sqrt(atan(a*x))/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
720,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{a^{6} x^{7} + 3 a^{4} x^{5} + 3 a^{2} x^{3} + x}\, dx}{c^{3}}"," ",0,"Integral(sqrt(atan(a*x))/(a**6*x**7 + 3*a**4*x**5 + 3*a**2*x**3 + x), x)/c**3","F",0
721,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)*atan(a*x)**(1/2),x)","\int x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x)), x)","F",0
722,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(1/2)*atan(a*x)**(1/2),x)","\int x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2*sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x)), x)","F",0
723,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(1/2)*atan(a*x)**(1/2),x)","\int x \sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x)), x)","F",0
724,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)*atan(a*x)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x)), x)","F",0
725,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(1/2),x)","\int x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)*sqrt(atan(a*x)), x)","F",0
728,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**(1/2),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*sqrt(atan(a*x)), x)","F",0
729,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,-1,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**m*sqrt(atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
734,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*sqrt(atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
735,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*sqrt(atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
736,0,0,0,0.000000," ","integrate(x*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x \sqrt{\operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x*sqrt(atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
737,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
738,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(x*sqrt(c*(a**2*x**2 + 1))), x)","F",0
739,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(x**2*sqrt(c*(a**2*x**2 + 1))), x)","F",0
740,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(x**3*sqrt(c*(a**2*x**2 + 1))), x)","F",0
741,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x**4/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x^{4} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(x**4*sqrt(c*(a**2*x**2 + 1))), x)","F",0
742,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{m} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
743,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
744,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
745,0,0,0,0.000000," ","integrate(x*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
746,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
747,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(x*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
748,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(x**2*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
749,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
751,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
752,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
753,0,0,0,0.000000," ","integrate(x*atan(a*x)**(1/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x \sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
754,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
755,0,0,0,0.000000," ","integrate(atan(a*x)**(1/2)/x/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\sqrt{\operatorname{atan}{\left(a x \right)}}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(atan(a*x))/(x*(c*(a**2*x**2 + 1))**(5/2)), x)","F",0
756,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)*atan(a*x)**(3/2),x)","c \left(\int x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{2} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**2*atan(a*x)**(3/2), x) + Integral(a**2*x**4*atan(a*x)**(3/2), x))","F",0
758,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)*atan(a*x)**(3/2),x)","c \left(\int x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{2} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x*atan(a*x)**(3/2), x) + Integral(a**2*x**3*atan(a*x)**(3/2), x))","F",0
759,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(3/2),x)","c \left(\int a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*atan(a*x)**(3/2), x) + Integral(atan(a*x)**(3/2), x))","F",0
760,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(3/2)/x,x)","c \left(\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x}\, dx + \int a^{2} x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**(3/2)/x, x) + Integral(a**2*x*atan(a*x)**(3/2), x))","F",0
761,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(3/2)/x**2,x)","c \left(\int a^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c*(Integral(a**2*atan(a*x)**(3/2), x) + Integral(atan(a*x)**(3/2)/x**2, x))","F",0
762,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**2*atan(a*x)**(3/2),x)","c^{2} \left(\int x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 2 a^{2} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**2*atan(a*x)**(3/2), x) + Integral(2*a**2*x**4*atan(a*x)**(3/2), x) + Integral(a**4*x**6*atan(a*x)**(3/2), x))","F",0
764,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2*atan(a*x)**(3/2),x)","c^{2} \left(\int x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 2 a^{2} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x*atan(a*x)**(3/2), x) + Integral(2*a**2*x**3*atan(a*x)**(3/2), x) + Integral(a**4*x**5*atan(a*x)**(3/2), x))","F",0
765,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(3/2),x)","c^{2} \left(\int 2 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*atan(a*x)**(3/2), x) + Integral(a**4*x**4*atan(a*x)**(3/2), x) + Integral(atan(a*x)**(3/2), x))","F",0
766,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(3/2)/x,x)","c^{2} \left(\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x}\, dx + \int 2 a^{2} x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)**(3/2)/x, x) + Integral(2*a**2*x*atan(a*x)**(3/2), x) + Integral(a**4*x**3*atan(a*x)**(3/2), x))","F",0
767,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(3/2)/x**2,x)","c^{2} \left(\int 2 a^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x^{2}}\, dx + \int a^{4} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*atan(a*x)**(3/2), x) + Integral(atan(a*x)**(3/2)/x**2, x) + Integral(a**4*x**2*atan(a*x)**(3/2), x))","F",0
768,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**3*atan(a*x)**(3/2),x)","c^{3} \left(\int x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 3 a^{2} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 3 a^{4} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{8} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(x**2*atan(a*x)**(3/2), x) + Integral(3*a**2*x**4*atan(a*x)**(3/2), x) + Integral(3*a**4*x**6*atan(a*x)**(3/2), x) + Integral(a**6*x**8*atan(a*x)**(3/2), x))","F",0
770,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3*atan(a*x)**(3/2),x)","c^{3} \left(\int x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 3 a^{2} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 3 a^{4} x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{7} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(x*atan(a*x)**(3/2), x) + Integral(3*a**2*x**3*atan(a*x)**(3/2), x) + Integral(3*a**4*x**5*atan(a*x)**(3/2), x) + Integral(a**6*x**7*atan(a*x)**(3/2), x))","F",0
771,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(3/2),x)","c^{3} \left(\int 3 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 3 a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2*atan(a*x)**(3/2), x) + Integral(3*a**4*x**4*atan(a*x)**(3/2), x) + Integral(a**6*x**6*atan(a*x)**(3/2), x) + Integral(atan(a*x)**(3/2), x))","F",0
772,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(3/2)/x,x)","c^{3} \left(\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x}\, dx + \int 3 a^{2} x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int 3 a^{4} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)**(3/2)/x, x) + Integral(3*a**2*x*atan(a*x)**(3/2), x) + Integral(3*a**4*x**3*atan(a*x)**(3/2), x) + Integral(a**6*x**5*atan(a*x)**(3/2), x))","F",0
773,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(3/2)/x**2,x)","c^{3} \left(\int 3 a^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x^{2}}\, dx + \int 3 a^{4} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*atan(a*x)**(3/2), x) + Integral(atan(a*x)**(3/2)/x**2, x) + Integral(3*a**4*x**2*atan(a*x)**(3/2), x) + Integral(a**6*x**4*atan(a*x)**(3/2), x))","F",0
774,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**(3/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{m} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**m*atan(a*x)**(3/2)/(a**2*x**2 + 1), x)/c","F",0
775,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(3/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**3*atan(a*x)**(3/2)/(a**2*x**2 + 1), x)/c","F",0
776,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(3/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**2*atan(a*x)**(3/2)/(a**2*x**2 + 1), x)/c","F",0
777,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*atan(a*x)**(3/2)/(a**2*x**2 + 1), x)/c","F",0
778,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(atan(a*x)**(3/2)/(a**2*x**2 + 1), x)/c","F",0
779,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{3} + x}\, dx}{c}"," ",0,"Integral(atan(a*x)**(3/2)/(a**2*x**3 + x), x)/c","F",0
780,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**2/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{4} + x^{2}}\, dx}{c}"," ",0,"Integral(atan(a*x)**(3/2)/(a**2*x**4 + x**2), x)/c","F",0
781,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{5} + x^{3}}\, dx}{c}"," ",0,"Integral(atan(a*x)**(3/2)/(a**2*x**5 + x**3), x)/c","F",0
782,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**4/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{2} x^{6} + x^{4}}\, dx}{c}"," ",0,"Integral(atan(a*x)**(3/2)/(a**2*x**6 + x**4), x)/c","F",0
783,0,0,0,0.000000," ","integrate(x**m*atan(a*x)**(3/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{m} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**m*atan(a*x)**(3/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
784,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(3/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**3*atan(a*x)**(3/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
785,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(3/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**2*atan(a*x)**(3/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
786,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x*atan(a*x)**(3/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
787,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**(3/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
788,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{4} x^{5} + 2 a^{2} x^{3} + x}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**(3/2)/(a**4*x**5 + 2*a**2*x**3 + x), x)/c**2","F",0
789,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(3/2)/(a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
790,0,0,0,0.000000," ","integrate(x**5*atan(a*x)**(3/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**5*atan(a*x)**(3/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
791,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**(3/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**4*atan(a*x)**(3/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
792,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(3/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**3*atan(a*x)**(3/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
793,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(3/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**2*atan(a*x)**(3/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
794,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x*atan(a*x)**(3/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
795,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**(3/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
796,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{a^{6} x^{7} + 3 a^{4} x^{5} + 3 a^{2} x^{3} + x}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**(3/2)/(a**6*x**7 + 3*a**4*x**5 + 3*a**2*x**3 + x), x)/c**3","F",0
797,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(3/2)*(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
798,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(3/2)*(a**2*c*x**2+c)**(1/2),x)","\int x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2), x)","F",0
799,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2)*(a**2*c*x**2+c)**(1/2),x)","\int x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2), x)","F",0
800,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2), x)","F",0
801,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)*(a**2*c*x**2+c)**(1/2)/x,x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2)/x, x)","F",0
802,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
805,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
807,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
810,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
811,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
812,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
813,-1,0,0,0.000000," ","integrate(x**3*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*atan(a*x)**(3/2)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
815,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x*atan(a*x)**(3/2)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
816,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
817,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(x*sqrt(c*(a**2*x**2 + 1))), x)","F",0
818,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(x**2*sqrt(c*(a**2*x**2 + 1))), x)","F",0
819,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(x**3*sqrt(c*(a**2*x**2 + 1))), x)","F",0
820,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**4/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x^{4} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(x**4*sqrt(c*(a**2*x**2 + 1))), x)","F",0
821,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate(x**3*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)**(3/2)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
824,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*atan(a*x)**(3/2)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
825,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
826,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(x*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
827,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(x**2*(c*(a**2*x**2 + 1))**(3/2)), x)","F",0
828,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate(x**5*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(x**4*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,-1,0,0,0.000000," ","integrate(x**3*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*atan(a*x)**(3/2)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
833,0,0,0,0.000000," ","integrate(x*atan(a*x)**(3/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*atan(a*x)**(3/2)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
834,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
835,0,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**(3/2)/(x*(c*(a**2*x**2 + 1))**(5/2)), x)","F",0
836,-1,0,0,0.000000," ","integrate(atan(a*x)**(3/2)/x**2/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)*atan(a*x)**(5/2),x)","c \left(\int x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{2} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x**2*atan(a*x)**(5/2), x) + Integral(a**2*x**4*atan(a*x)**(5/2), x))","F",0
839,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)*atan(a*x)**(5/2),x)","c \left(\int x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{2} x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(x*atan(a*x)**(5/2), x) + Integral(a**2*x**3*atan(a*x)**(5/2), x))","F",0
840,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(5/2),x)","c \left(\int a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*atan(a*x)**(5/2), x) + Integral(atan(a*x)**(5/2), x))","F",0
841,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(5/2)/x,x)","c \left(\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{x}\, dx + \int a^{2} x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c*(Integral(atan(a*x)**(5/2)/x, x) + Integral(a**2*x*atan(a*x)**(5/2), x))","F",0
842,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)*atan(a*x)**(5/2)/x**2,x)","c \left(\int a^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{x^{2}}\, dx\right)"," ",0,"c*(Integral(a**2*atan(a*x)**(5/2), x) + Integral(atan(a*x)**(5/2)/x**2, x))","F",0
843,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,0,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**2*atan(a*x)**(5/2),x)","c^{2} \left(\int x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int 2 a^{2} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x**2*atan(a*x)**(5/2), x) + Integral(2*a**2*x**4*atan(a*x)**(5/2), x) + Integral(a**4*x**6*atan(a*x)**(5/2), x))","F",0
845,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2*atan(a*x)**(5/2),x)","c^{2} \left(\int x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int 2 a^{2} x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{5} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(x*atan(a*x)**(5/2), x) + Integral(2*a**2*x**3*atan(a*x)**(5/2), x) + Integral(a**4*x**5*atan(a*x)**(5/2), x))","F",0
846,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(5/2),x)","c^{2} \left(\int 2 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*atan(a*x)**(5/2), x) + Integral(a**4*x**4*atan(a*x)**(5/2), x) + Integral(atan(a*x)**(5/2), x))","F",0
847,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(5/2)/x,x)","c^{2} \left(\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{x}\, dx + \int 2 a^{2} x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{4} x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(atan(a*x)**(5/2)/x, x) + Integral(2*a**2*x*atan(a*x)**(5/2), x) + Integral(a**4*x**3*atan(a*x)**(5/2), x))","F",0
848,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2*atan(a*x)**(5/2)/x**2,x)","c^{2} \left(\int 2 a^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{x^{2}}\, dx + \int a^{4} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*atan(a*x)**(5/2), x) + Integral(atan(a*x)**(5/2)/x**2, x) + Integral(a**4*x**2*atan(a*x)**(5/2), x))","F",0
849,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**3*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(5/2),x)","c^{3} \left(\int 3 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int 3 a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2*atan(a*x)**(5/2), x) + Integral(3*a**4*x**4*atan(a*x)**(5/2), x) + Integral(a**6*x**6*atan(a*x)**(5/2), x) + Integral(atan(a*x)**(5/2), x))","F",0
853,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(5/2)/x,x)","c^{3} \left(\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{x}\, dx + \int 3 a^{2} x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int 3 a^{4} x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{5} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(atan(a*x)**(5/2)/x, x) + Integral(3*a**2*x*atan(a*x)**(5/2), x) + Integral(3*a**4*x**3*atan(a*x)**(5/2), x) + Integral(a**6*x**5*atan(a*x)**(5/2), x))","F",0
854,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3*atan(a*x)**(5/2)/x**2,x)","c^{3} \left(\int 3 a^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{x^{2}}\, dx + \int 3 a^{4} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx + \int a^{6} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*atan(a*x)**(5/2), x) + Integral(atan(a*x)**(5/2)/x**2, x) + Integral(3*a**4*x**2*atan(a*x)**(5/2), x) + Integral(a**6*x**4*atan(a*x)**(5/2), x))","F",0
855,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(5/2)/(a**2*c*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(5/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**3*atan(a*x)**(5/2)/(a**2*x**2 + 1), x)/c","F",0
857,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(5/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**2*atan(a*x)**(5/2)/(a**2*x**2 + 1), x)/c","F",0
858,0,0,0,0.000000," ","integrate(x*atan(a*x)**(5/2)/(a**2*c*x**2+c),x)","\frac{\int \frac{x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*atan(a*x)**(5/2)/(a**2*x**2 + 1), x)/c","F",0
859,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/(a**2*c*x**2+c),x)","\begin{cases} \frac{2 \operatorname{atan}^{\frac{7}{2}}{\left(a x \right)}}{7 a c} & \text{for}\: c \neq 0 \\\tilde{\infty} \int \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*atan(a*x)**(7/2)/(7*a*c), Ne(c, 0)), (zoo*Integral(atan(a*x)**(5/2), x), True))","F",0
860,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{2} x^{3} + x}\, dx}{c}"," ",0,"Integral(atan(a*x)**(5/2)/(a**2*x**3 + x), x)/c","F",0
861,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x**2/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{2} x^{4} + x^{2}}\, dx}{c}"," ",0,"Integral(atan(a*x)**(5/2)/(a**2*x**4 + x**2), x)/c","F",0
862,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{2} x^{5} + x^{3}}\, dx}{c}"," ",0,"Integral(atan(a*x)**(5/2)/(a**2*x**5 + x**3), x)/c","F",0
863,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x**4/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{2} x^{6} + x^{4}}\, dx}{c}"," ",0,"Integral(atan(a*x)**(5/2)/(a**2*x**6 + x**4), x)/c","F",0
864,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(5/2)/(a**2*c*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(5/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**3*atan(a*x)**(5/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
866,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(5/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**2*atan(a*x)**(5/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
867,0,0,0,0.000000," ","integrate(x*atan(a*x)**(5/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x*atan(a*x)**(5/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
868,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**(5/2)/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
869,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{4} x^{5} + 2 a^{2} x^{3} + x}\, dx}{c^{2}}"," ",0,"Integral(atan(a*x)**(5/2)/(a**4*x**5 + 2*a**2*x**3 + x), x)/c**2","F",0
870,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(5/2)/(a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
871,0,0,0,0.000000," ","integrate(x**5*atan(a*x)**(5/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{5} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**5*atan(a*x)**(5/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
872,0,0,0,0.000000," ","integrate(x**4*atan(a*x)**(5/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**4*atan(a*x)**(5/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
873,0,0,0,0.000000," ","integrate(x**3*atan(a*x)**(5/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**3*atan(a*x)**(5/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
874,0,0,0,0.000000," ","integrate(x**2*atan(a*x)**(5/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x**2*atan(a*x)**(5/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
875,0,0,0,0.000000," ","integrate(x*atan(a*x)**(5/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(x*atan(a*x)**(5/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
876,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**(5/2)/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)/c**3","F",0
877,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x/(a**2*c*x**2+c)**3,x)","\frac{\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{a^{6} x^{7} + 3 a^{4} x^{5} + 3 a^{2} x^{3} + x}\, dx}{c^{3}}"," ",0,"Integral(atan(a*x)**(5/2)/(a**6*x**7 + 3*a**4*x**5 + 3*a**2*x**3 + x), x)/c**3","F",0
878,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(5/2)*(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate(x**2*atan(a*x)**(5/2)*(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate(x*atan(a*x)**(5/2)*(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate(atan(a*x)**(5/2)*(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate(atan(a*x)**(5/2)*(a**2*c*x**2+c)**(1/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)*atan(a*x)**(5/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate(x**2*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
891,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)*atan(a*x)**(5/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate(x**3*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,-1,0,0,0.000000," ","integrate(x**2*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate(x*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**(5/2)/sqrt(c*(a**2*x**2 + 1)), x)","F",0
898,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(atan(a*x)**(5/2)/(x*sqrt(c*(a**2*x**2 + 1))), x)","F",0
899,-1,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x**2/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,-1,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x**3/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,-1,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x**4/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate(x**2*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate(x*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atan(a*x)**(5/2)/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
906,-1,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate(x**m*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,-1,0,0,0.000000," ","integrate(x**4*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,-1,0,0,0.000000," ","integrate(x**3*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,-1,0,0,0.000000," ","integrate(x**2*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,-1,0,0,0.000000," ","integrate(x*atan(a*x)**(5/2)/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
912,0,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/(a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atan(a*x)**(5/2)/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
913,-1,0,0,0.000000," ","integrate(atan(a*x)**(5/2)/x/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
914,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)/atan(a*x)**(1/2),x)","c \left(\int \frac{x^{m}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{2} x^{2} x^{m}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c*(Integral(x**m/sqrt(atan(a*x)), x) + Integral(a**2*x**2*x**m/sqrt(atan(a*x)), x))","F",0
915,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)/atan(a*x)**(1/2),x)","c \left(\int \frac{x}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{2} x^{3}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c*(Integral(x/sqrt(atan(a*x)), x) + Integral(a**2*x**3/sqrt(atan(a*x)), x))","F",0
916,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/atan(a*x)**(1/2),x)","c \left(\int \frac{a^{2} x^{2}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{1}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/sqrt(atan(a*x)), x) + Integral(1/sqrt(atan(a*x)), x))","F",0
917,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/x/atan(a*x)**(1/2),x)","c \left(\int \frac{1}{x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{2} x}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c*(Integral(1/(x*sqrt(atan(a*x))), x) + Integral(a**2*x/sqrt(atan(a*x)), x))","F",0
918,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","c^{2} \left(\int \frac{x^{m}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{2 a^{2} x^{2} x^{m}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{4} x^{4} x^{m}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c**2*(Integral(x**m/sqrt(atan(a*x)), x) + Integral(2*a**2*x**2*x**m/sqrt(atan(a*x)), x) + Integral(a**4*x**4*x**m/sqrt(atan(a*x)), x))","F",0
919,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","c^{2} \left(\int \frac{x}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{2 a^{2} x^{3}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{4} x^{5}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c**2*(Integral(x/sqrt(atan(a*x)), x) + Integral(2*a**2*x**3/sqrt(atan(a*x)), x) + Integral(a**4*x**5/sqrt(atan(a*x)), x))","F",0
920,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{4} x^{4}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{1}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/sqrt(atan(a*x)), x) + Integral(a**4*x**4/sqrt(atan(a*x)), x) + Integral(1/sqrt(atan(a*x)), x))","F",0
921,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/x/atan(a*x)**(1/2),x)","c^{2} \left(\int \frac{1}{x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{2 a^{2} x}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{4} x^{3}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c**2*(Integral(1/(x*sqrt(atan(a*x))), x) + Integral(2*a**2*x/sqrt(atan(a*x)), x) + Integral(a**4*x**3/sqrt(atan(a*x)), x))","F",0
922,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
923,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","c^{3} \left(\int \frac{x}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{3 a^{2} x^{3}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{3 a^{4} x^{5}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{6} x^{7}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c**3*(Integral(x/sqrt(atan(a*x)), x) + Integral(3*a**2*x**3/sqrt(atan(a*x)), x) + Integral(3*a**4*x**5/sqrt(atan(a*x)), x) + Integral(a**6*x**7/sqrt(atan(a*x)), x))","F",0
924,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{3 a^{4} x^{4}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{6} x^{6}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{1}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/sqrt(atan(a*x)), x) + Integral(3*a**4*x**4/sqrt(atan(a*x)), x) + Integral(a**6*x**6/sqrt(atan(a*x)), x) + Integral(1/sqrt(atan(a*x)), x))","F",0
925,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/x/atan(a*x)**(1/2),x)","c^{3} \left(\int \frac{1}{x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{3 a^{2} x}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{3 a^{4} x^{3}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx + \int \frac{a^{6} x^{5}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx\right)"," ",0,"c**3*(Integral(1/(x*sqrt(atan(a*x))), x) + Integral(3*a**2*x/sqrt(atan(a*x)), x) + Integral(3*a**4*x**3/sqrt(atan(a*x)), x) + Integral(a**6*x**5/sqrt(atan(a*x)), x))","F",0
926,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{m}}{a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c}"," ",0,"Integral(x**m/(a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c","F",0
927,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)/atan(a*x)**(1/2),x)","\frac{\int \frac{x}{a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c}"," ",0,"Integral(x/(a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c","F",0
928,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/atan(a*x)**(1/2),x)","\begin{cases} \frac{2 \sqrt{\operatorname{atan}{\left(a x \right)}}}{a c} & \text{for}\: c \neq 0 \\\tilde{\infty} \int \frac{1}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(atan(a*x))/(a*c), Ne(c, 0)), (zoo*Integral(1/sqrt(atan(a*x)), x), True))","F",0
929,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)/atan(a*x)**(1/2),x)","\frac{\int \frac{1}{a^{2} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}} + x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**3*sqrt(atan(a*x)) + x*sqrt(atan(a*x))), x)/c","F",0
930,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{m}}{a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 2 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{2}}"," ",0,"Integral(x**m/(a**4*x**4*sqrt(atan(a*x)) + 2*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**2","F",0
931,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{3}}{a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 2 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{2}}"," ",0,"Integral(x**3/(a**4*x**4*sqrt(atan(a*x)) + 2*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**2","F",0
932,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{2}}{a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 2 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{2}}"," ",0,"Integral(x**2/(a**4*x**4*sqrt(atan(a*x)) + 2*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**2","F",0
933,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","\frac{\int \frac{x}{a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 2 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{2}}"," ",0,"Integral(x/(a**4*x**4*sqrt(atan(a*x)) + 2*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**2","F",0
934,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","\frac{\int \frac{1}{a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 2 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*sqrt(atan(a*x)) + 2*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**2","F",0
935,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**2/atan(a*x)**(1/2),x)","\frac{\int \frac{1}{a^{4} x^{5} \sqrt{\operatorname{atan}{\left(a x \right)}} + 2 a^{2} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}} + x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**5*sqrt(atan(a*x)) + 2*a**2*x**3*sqrt(atan(a*x)) + x*sqrt(atan(a*x))), x)/c**2","F",0
936,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
937,0,0,0,0.000000," ","integrate(x**5/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{5}}{a^{6} x^{6} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{3}}"," ",0,"Integral(x**5/(a**6*x**6*sqrt(atan(a*x)) + 3*a**4*x**4*sqrt(atan(a*x)) + 3*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**3","F",0
938,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{4}}{a^{6} x^{6} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{3}}"," ",0,"Integral(x**4/(a**6*x**6*sqrt(atan(a*x)) + 3*a**4*x**4*sqrt(atan(a*x)) + 3*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**3","F",0
939,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{3}}{a^{6} x^{6} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{3}}"," ",0,"Integral(x**3/(a**6*x**6*sqrt(atan(a*x)) + 3*a**4*x**4*sqrt(atan(a*x)) + 3*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**3","F",0
940,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\frac{\int \frac{x^{2}}{a^{6} x^{6} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{3}}"," ",0,"Integral(x**2/(a**6*x**6*sqrt(atan(a*x)) + 3*a**4*x**4*sqrt(atan(a*x)) + 3*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**3","F",0
941,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\frac{\int \frac{x}{a^{6} x^{6} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{3}}"," ",0,"Integral(x/(a**6*x**6*sqrt(atan(a*x)) + 3*a**4*x**4*sqrt(atan(a*x)) + 3*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**3","F",0
942,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\frac{\int \frac{1}{a^{6} x^{6} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{4} x^{4} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{2} x^{2} \sqrt{\operatorname{atan}{\left(a x \right)}} + \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**6*sqrt(atan(a*x)) + 3*a**4*x**4*sqrt(atan(a*x)) + 3*a**2*x**2*sqrt(atan(a*x)) + sqrt(atan(a*x))), x)/c**3","F",0
943,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**3/atan(a*x)**(1/2),x)","\frac{\int \frac{1}{a^{6} x^{7} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{4} x^{5} \sqrt{\operatorname{atan}{\left(a x \right)}} + 3 a^{2} x^{3} \sqrt{\operatorname{atan}{\left(a x \right)}} + x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**7*sqrt(atan(a*x)) + 3*a**4*x**5*sqrt(atan(a*x)) + 3*a**2*x**3*sqrt(atan(a*x)) + x*sqrt(atan(a*x))), x)/c**3","F",0
944,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)/atan(a*x)**(1/2),x)","\int \frac{x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))/sqrt(atan(a*x)), x)","F",0
945,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(1/2)/atan(a*x)**(1/2),x)","\int \frac{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))/sqrt(atan(a*x)), x)","F",0
946,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/atan(a*x)**(1/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/sqrt(atan(a*x)), x)","F",0
947,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/x/atan(a*x)**(1/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/(x*sqrt(atan(a*x))), x)","F",0
948,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
949,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)/sqrt(atan(a*x)), x)","F",0
950,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/sqrt(atan(a*x)), x)","F",0
951,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/x/atan(a*x)**(1/2),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/(x*sqrt(atan(a*x))), x)","F",0
952,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
953,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
954,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
955,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/x/atan(a*x)**(1/2),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}{x \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(5/2)/(x*sqrt(atan(a*x))), x)","F",0
956,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(1/2)/atan(a*x)**(1/2),x)","\int \frac{x^{m}}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**m/(sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x))), x)","F",0
957,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(1/2)/atan(a*x)**(1/2),x)","\int \frac{x}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x/(sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x))), x)","F",0
958,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(1/2)/atan(a*x)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x))), x)","F",0
959,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(1/2)/atan(a*x)**(1/2),x)","\int \frac{1}{x \sqrt{c \left(a^{2} x^{2} + 1\right)} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x*sqrt(c*(a**2*x**2 + 1))*sqrt(atan(a*x))), x)","F",0
960,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
961,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(3/2)*sqrt(atan(a*x))), x)","F",0
962,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(3/2)*sqrt(atan(a*x))), x)","F",0
963,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(3/2)*sqrt(atan(a*x))), x)","F",0
964,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(1/2),x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(3/2)*sqrt(atan(a*x))), x)","F",0
965,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
966,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\int \frac{x^{4}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**4/((c*(a**2*x**2 + 1))**(5/2)*sqrt(atan(a*x))), x)","F",0
967,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(5/2)*sqrt(atan(a*x))), x)","F",0
968,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(5/2)*sqrt(atan(a*x))), x)","F",0
969,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(5/2)*sqrt(atan(a*x))), x)","F",0
970,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(5/2)*sqrt(atan(a*x))), x)","F",0
971,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(1/2),x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}} \sqrt{\operatorname{atan}{\left(a x \right)}}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(5/2)*sqrt(atan(a*x))), x)","F",0
972,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)/atan(a*x)**(3/2),x)","c \left(\int \frac{x^{m}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{2} x^{m}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x**m/atan(a*x)**(3/2), x) + Integral(a**2*x**2*x**m/atan(a*x)**(3/2), x))","F",0
973,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)/atan(a*x)**(3/2),x)","c \left(\int \frac{x}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{3}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x/atan(a*x)**(3/2), x) + Integral(a**2*x**3/atan(a*x)**(3/2), x))","F",0
974,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/atan(a*x)**(3/2),x)","c \left(\int \frac{a^{2} x^{2}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/atan(a*x)**(3/2), x) + Integral(atan(a*x)**(-3/2), x))","F",0
975,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/x/atan(a*x)**(3/2),x)","c \left(\int \frac{1}{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{2} x}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(1/(x*atan(a*x)**(3/2)), x) + Integral(a**2*x/atan(a*x)**(3/2), x))","F",0
976,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","c^{2} \left(\int \frac{x^{m}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{2} x^{m}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4} x^{m}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x**m/atan(a*x)**(3/2), x) + Integral(2*a**2*x**2*x**m/atan(a*x)**(3/2), x) + Integral(a**4*x**4*x**m/atan(a*x)**(3/2), x))","F",0
977,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","c^{2} \left(\int \frac{x}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{3}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{5}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x/atan(a*x)**(3/2), x) + Integral(2*a**2*x**3/atan(a*x)**(3/2), x) + Integral(a**4*x**5/atan(a*x)**(3/2), x))","F",0
978,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/atan(a*x)**(3/2), x) + Integral(a**4*x**4/atan(a*x)**(3/2), x) + Integral(atan(a*x)**(-3/2), x))","F",0
979,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/x/atan(a*x)**(3/2),x)","c^{2} \left(\int \frac{1}{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{3}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(1/(x*atan(a*x)**(3/2)), x) + Integral(2*a**2*x/atan(a*x)**(3/2), x) + Integral(a**4*x**3/atan(a*x)**(3/2), x))","F",0
980,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
981,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","c^{3} \left(\int \frac{x}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{3}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{5}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{7}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x/atan(a*x)**(3/2), x) + Integral(3*a**2*x**3/atan(a*x)**(3/2), x) + Integral(3*a**4*x**5/atan(a*x)**(3/2), x) + Integral(a**6*x**7/atan(a*x)**(3/2), x))","F",0
982,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/atan(a*x)**(3/2), x) + Integral(3*a**4*x**4/atan(a*x)**(3/2), x) + Integral(a**6*x**6/atan(a*x)**(3/2), x) + Integral(atan(a*x)**(-3/2), x))","F",0
983,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/x/atan(a*x)**(3/2),x)","c^{3} \left(\int \frac{1}{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{3}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{5}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(1/(x*atan(a*x)**(3/2)), x) + Integral(3*a**2*x/atan(a*x)**(3/2), x) + Integral(3*a**4*x**3/atan(a*x)**(3/2), x) + Integral(a**6*x**5/atan(a*x)**(3/2), x))","F",0
984,0,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)/atan(a*x)**(3/2),x)","\frac{\int \frac{x^{m}}{a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x**m/(a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c","F",0
985,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)/atan(a*x)**(3/2),x)","\frac{\int \frac{x}{a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x/(a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c","F",0
986,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/atan(a*x)**(3/2),x)","\begin{cases} - \frac{2}{a c \sqrt{\operatorname{atan}{\left(a x \right)}}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int \frac{1}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(a*c*sqrt(atan(a*x))), Ne(c, 0)), (zoo*Integral(atan(a*x)**(-3/2), x), True))","F",0
987,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{2} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**3*atan(a*x)**(3/2) + x*atan(a*x)**(3/2)), x)/c","F",0
988,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
989,0,0,0,0.000000," ","integrate(x**4/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{x^{4}}{a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**4/(a**4*x**4*atan(a*x)**(3/2) + 2*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**2","F",0
990,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{x^{3}}{a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**3/(a**4*x**4*atan(a*x)**(3/2) + 2*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**2","F",0
991,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{x^{2}}{a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**2/(a**4*x**4*atan(a*x)**(3/2) + 2*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**2","F",0
992,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{x}{a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x/(a**4*x**4*atan(a*x)**(3/2) + 2*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**2","F",0
993,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*atan(a*x)**(3/2) + 2*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**2","F",0
994,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{4} x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**5*atan(a*x)**(3/2) + 2*a**2*x**3*atan(a*x)**(3/2) + x*atan(a*x)**(3/2)), x)/c**2","F",0
995,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{4} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**6*atan(a*x)**(3/2) + 2*a**2*x**4*atan(a*x)**(3/2) + x**2*atan(a*x)**(3/2)), x)/c**2","F",0
996,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{4} x^{7} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**7*atan(a*x)**(3/2) + 2*a**2*x**5*atan(a*x)**(3/2) + x**3*atan(a*x)**(3/2)), x)/c**2","F",0
997,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**2/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{4} x^{8} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 2 a^{2} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**8*atan(a*x)**(3/2) + 2*a**2*x**6*atan(a*x)**(3/2) + x**4*atan(a*x)**(3/2)), x)/c**2","F",0
998,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
999,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{x^{3}}{a^{6} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**3/(a**6*x**6*atan(a*x)**(3/2) + 3*a**4*x**4*atan(a*x)**(3/2) + 3*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**3","F",0
1000,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{x^{2}}{a^{6} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**2/(a**6*x**6*atan(a*x)**(3/2) + 3*a**4*x**4*atan(a*x)**(3/2) + 3*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**3","F",0
1001,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{x}{a^{6} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x/(a**6*x**6*atan(a*x)**(3/2) + 3*a**4*x**4*atan(a*x)**(3/2) + 3*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**3","F",0
1002,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{6} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**6*atan(a*x)**(3/2) + 3*a**4*x**4*atan(a*x)**(3/2) + 3*a**2*x**2*atan(a*x)**(3/2) + atan(a*x)**(3/2)), x)/c**3","F",0
1003,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{6} x^{7} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**7*atan(a*x)**(3/2) + 3*a**4*x**5*atan(a*x)**(3/2) + 3*a**2*x**3*atan(a*x)**(3/2) + x*atan(a*x)**(3/2)), x)/c**3","F",0
1004,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{6} x^{8} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x^{2} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**8*atan(a*x)**(3/2) + 3*a**4*x**6*atan(a*x)**(3/2) + 3*a**2*x**4*atan(a*x)**(3/2) + x**2*atan(a*x)**(3/2)), x)/c**3","F",0
1005,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{6} x^{9} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{7} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{5} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x^{3} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**9*atan(a*x)**(3/2) + 3*a**4*x**7*atan(a*x)**(3/2) + 3*a**2*x**5*atan(a*x)**(3/2) + x**3*atan(a*x)**(3/2)), x)/c**3","F",0
1006,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**3/atan(a*x)**(3/2),x)","\frac{\int \frac{1}{a^{6} x^{10} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{4} x^{8} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + 3 a^{2} x^{6} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)} + x^{4} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**10*atan(a*x)**(3/2) + 3*a**4*x**8*atan(a*x)**(3/2) + 3*a**2*x**6*atan(a*x)**(3/2) + x**4*atan(a*x)**(3/2)), x)/c**3","F",0
1007,0,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)/atan(a*x)**(3/2),x)","\int \frac{x^{m} \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*sqrt(c*(a**2*x**2 + 1))/atan(a*x)**(3/2), x)","F",0
1008,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(1/2)/atan(a*x)**(3/2),x)","\int \frac{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))/atan(a*x)**(3/2), x)","F",0
1009,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/atan(a*x)**(3/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/atan(a*x)**(3/2), x)","F",0
1010,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/x/atan(a*x)**(3/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/(x*atan(a*x)**(3/2)), x)","F",0
1011,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1012,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(c*(a**2*x**2 + 1))**(3/2)/atan(a*x)**(3/2), x)","F",0
1013,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{\operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/atan(a*x)**(3/2), x)","F",0
1014,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/x/atan(a*x)**(3/2),x)","\int \frac{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}{x \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)/(x*atan(a*x)**(3/2)), x)","F",0
1015,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1016,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1017,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1018,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/x/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1019,-1,0,0,0.000000," ","integrate(x**m/atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1020,0,0,0,0.000000," ","integrate(x/atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2)), x)","F",0
1021,0,0,0,0.000000," ","integrate(1/atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2)), x)","F",0
1022,0,0,0,0.000000," ","integrate(1/x/atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2)), x)","F",0
1023,0,0,0,0.000000," ","integrate(1/x**2/atan(a*x)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(3/2)), x)","F",0
1024,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{x^{3}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**(3/2)), x)","F",0
1026,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{x^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**(3/2)), x)","F",0
1027,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{x}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**(3/2)), x)","F",0
1028,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{1}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**(3/2)), x)","F",0
1029,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{1}{x \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**(3/2)), x)","F",0
1030,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\int \frac{1}{x^{2} \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(c*(a**2*x**2 + 1))**(3/2)*atan(a*x)**(3/2)), x)","F",0
1031,-1,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1032,-1,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1033,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1034,-1,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1035,-1,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1036,-1,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1037,-1,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1038,-1,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1039,-1,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1040,-1,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1041,-1,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1042,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1043,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)/atan(a*x)**(5/2),x)","c \left(\int \frac{x}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{2} x^{3}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x/atan(a*x)**(5/2), x) + Integral(a**2*x**3/atan(a*x)**(5/2), x))","F",0
1044,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/atan(a*x)**(5/2),x)","c \left(\int \frac{a^{2} x^{2}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2/atan(a*x)**(5/2), x) + Integral(atan(a*x)**(-5/2), x))","F",0
1045,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/x/atan(a*x)**(5/2),x)","c \left(\int \frac{1}{x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{2} x}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(1/(x*atan(a*x)**(5/2)), x) + Integral(a**2*x/atan(a*x)**(5/2), x))","F",0
1046,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1047,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","c^{2} \left(\int \frac{x}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x^{3}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{5}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(x/atan(a*x)**(5/2), x) + Integral(2*a**2*x**3/atan(a*x)**(5/2), x) + Integral(a**4*x**5/atan(a*x)**(5/2), x))","F",0
1048,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","c^{2} \left(\int \frac{2 a^{2} x^{2}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{4}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2/atan(a*x)**(5/2), x) + Integral(a**4*x**4/atan(a*x)**(5/2), x) + Integral(atan(a*x)**(-5/2), x))","F",0
1049,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/x/atan(a*x)**(5/2),x)","c^{2} \left(\int \frac{1}{x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{2 a^{2} x}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{4} x^{3}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(1/(x*atan(a*x)**(5/2)), x) + Integral(2*a**2*x/atan(a*x)**(5/2), x) + Integral(a**4*x**3/atan(a*x)**(5/2), x))","F",0
1050,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1051,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","c^{3} \left(\int \frac{x}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x^{3}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{5}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{7}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(x/atan(a*x)**(5/2), x) + Integral(3*a**2*x**3/atan(a*x)**(5/2), x) + Integral(3*a**4*x**5/atan(a*x)**(5/2), x) + Integral(a**6*x**7/atan(a*x)**(5/2), x))","F",0
1052,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","c^{3} \left(\int \frac{3 a^{2} x^{2}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{4}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{6}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{1}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(3*a**2*x**2/atan(a*x)**(5/2), x) + Integral(3*a**4*x**4/atan(a*x)**(5/2), x) + Integral(a**6*x**6/atan(a*x)**(5/2), x) + Integral(atan(a*x)**(-5/2), x))","F",0
1053,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**3/x/atan(a*x)**(5/2),x)","c^{3} \left(\int \frac{1}{x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{2} x}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{3 a^{4} x^{3}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx + \int \frac{a^{6} x^{5}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx\right)"," ",0,"c**3*(Integral(1/(x*atan(a*x)**(5/2)), x) + Integral(3*a**2*x/atan(a*x)**(5/2), x) + Integral(3*a**4*x**3/atan(a*x)**(5/2), x) + Integral(a**6*x**5/atan(a*x)**(5/2), x))","F",0
1054,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1055,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)/atan(a*x)**(5/2),x)","\frac{\int \frac{x}{a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x/(a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c","F",0
1056,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)/atan(a*x)**(5/2),x)","\begin{cases} - \frac{2}{3 a c \operatorname{atan}^{\frac{3}{2}}{\left(a x \right)}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int \frac{1}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(3*a*c*atan(a*x)**(3/2)), Ne(c, 0)), (zoo*Integral(atan(a*x)**(-5/2), x), True))","F",0
1057,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{2} x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a**2*x**3*atan(a*x)**(5/2) + x*atan(a*x)**(5/2)), x)/c","F",0
1058,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1059,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{x^{3}}{a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**3/(a**4*x**4*atan(a*x)**(5/2) + 2*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**2","F",0
1060,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{x^{2}}{a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x**2/(a**4*x**4*atan(a*x)**(5/2) + 2*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**2","F",0
1061,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{x}{a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(x/(a**4*x**4*atan(a*x)**(5/2) + 2*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**2","F",0
1062,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**4*atan(a*x)**(5/2) + 2*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**2","F",0
1063,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{4} x^{5} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**5*atan(a*x)**(5/2) + 2*a**2*x**3*atan(a*x)**(5/2) + x*atan(a*x)**(5/2)), x)/c**2","F",0
1064,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{4} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**6*atan(a*x)**(5/2) + 2*a**2*x**4*atan(a*x)**(5/2) + x**2*atan(a*x)**(5/2)), x)/c**2","F",0
1065,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{4} x^{7} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{5} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**7*atan(a*x)**(5/2) + 2*a**2*x**5*atan(a*x)**(5/2) + x**3*atan(a*x)**(5/2)), x)/c**2","F",0
1066,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**2/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{4} x^{8} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 2 a^{2} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{2}}"," ",0,"Integral(1/(a**4*x**8*atan(a*x)**(5/2) + 2*a**2*x**6*atan(a*x)**(5/2) + x**4*atan(a*x)**(5/2)), x)/c**2","F",0
1067,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1068,0,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{x^{3}}{a^{6} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**3/(a**6*x**6*atan(a*x)**(5/2) + 3*a**4*x**4*atan(a*x)**(5/2) + 3*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**3","F",0
1069,0,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{x^{2}}{a^{6} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x**2/(a**6*x**6*atan(a*x)**(5/2) + 3*a**4*x**4*atan(a*x)**(5/2) + 3*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**3","F",0
1070,0,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{x}{a^{6} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(x/(a**6*x**6*atan(a*x)**(5/2) + 3*a**4*x**4*atan(a*x)**(5/2) + 3*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**3","F",0
1071,0,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{6} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**6*atan(a*x)**(5/2) + 3*a**4*x**4*atan(a*x)**(5/2) + 3*a**2*x**2*atan(a*x)**(5/2) + atan(a*x)**(5/2)), x)/c**3","F",0
1072,0,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{6} x^{7} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{5} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**7*atan(a*x)**(5/2) + 3*a**4*x**5*atan(a*x)**(5/2) + 3*a**2*x**3*atan(a*x)**(5/2) + x*atan(a*x)**(5/2)), x)/c**3","F",0
1073,0,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{6} x^{8} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x^{2} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**8*atan(a*x)**(5/2) + 3*a**4*x**6*atan(a*x)**(5/2) + 3*a**2*x**4*atan(a*x)**(5/2) + x**2*atan(a*x)**(5/2)), x)/c**3","F",0
1074,0,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{6} x^{9} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{7} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{5} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x^{3} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**9*atan(a*x)**(5/2) + 3*a**4*x**7*atan(a*x)**(5/2) + 3*a**2*x**5*atan(a*x)**(5/2) + x**3*atan(a*x)**(5/2)), x)/c**3","F",0
1075,0,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**3/atan(a*x)**(5/2),x)","\frac{\int \frac{1}{a^{6} x^{10} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{4} x^{8} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + 3 a^{2} x^{6} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)} + x^{4} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx}{c^{3}}"," ",0,"Integral(1/(a**6*x**10*atan(a*x)**(5/2) + 3*a**4*x**8*atan(a*x)**(5/2) + 3*a**2*x**6*atan(a*x)**(5/2) + x**4*atan(a*x)**(5/2)), x)/c**3","F",0
1076,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(1/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1077,0,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(1/2)/atan(a*x)**(5/2),x)","\int \frac{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x*sqrt(c*(a**2*x**2 + 1))/atan(a*x)**(5/2), x)","F",0
1078,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/atan(a*x)**(5/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{\operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/atan(a*x)**(5/2), x)","F",0
1079,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/x/atan(a*x)**(5/2),x)","\int \frac{\sqrt{c \left(a^{2} x^{2} + 1\right)}}{x \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))/(x*atan(a*x)**(5/2)), x)","F",0
1080,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1081,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1082,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1083,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/x/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1084,-1,0,0,0.000000," ","integrate(x**m*(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1085,-1,0,0,0.000000," ","integrate(x*(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1086,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1087,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(5/2)/x/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,-1,0,0,0.000000," ","integrate(x**m/atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1089,0,0,0,0.000000," ","integrate(x/atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(x/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(5/2)), x)","F",0
1090,0,0,0,0.000000," ","integrate(1/atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(5/2)), x)","F",0
1091,0,0,0,0.000000," ","integrate(1/x/atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\int \frac{1}{x \sqrt{c \left(a^{2} x^{2} + 1\right)} \operatorname{atan}^{\frac{5}{2}}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*sqrt(c*(a**2*x**2 + 1))*atan(a*x)**(5/2)), x)","F",0
1092,-1,0,0,0.000000," ","integrate(1/x**2/atan(a*x)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1093,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1094,-1,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1095,-1,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1096,-1,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1097,-1,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1098,-1,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1099,-1,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1100,-1,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1101,-1,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**(3/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1102,-1,0,0,0.000000," ","integrate(x**m/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1103,-1,0,0,0.000000," ","integrate(x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1104,-1,0,0,0.000000," ","integrate(x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1105,-1,0,0,0.000000," ","integrate(x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1106,-1,0,0,0.000000," ","integrate(1/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1107,-1,0,0,0.000000," ","integrate(1/x/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1108,-1,0,0,0.000000," ","integrate(1/x**2/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1109,-1,0,0,0.000000," ","integrate(1/x**3/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,-1,0,0,0.000000," ","integrate(1/x**4/(a**2*c*x**2+c)**(5/2)/atan(a*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1111,0,0,0,0.000000," ","integrate(x*atan(a*x)**n/(a**2*c*x**2+c),x)","\frac{\int \frac{x \operatorname{atan}^{n}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*atan(a*x)**n/(a**2*x**2 + 1), x)/c","F",0
1112,0,0,0,0.000000," ","integrate(atan(a*x)**n/(a**2*c*x**2+c),x)","\frac{\int \frac{\operatorname{atan}^{n}{\left(a x \right)}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(atan(a*x)**n/(a**2*x**2 + 1), x)/c","F",0
1113,-1,0,0,0.000000," ","integrate((f*x)**m*(c**2*d*x**2+d)**q*(a+b*atan(c*x))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1114,1,138,0,2.004925," ","integrate(x**3*(e*x**2+d)*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d x^{4}}{4} + \frac{a e x^{6}}{6} + \frac{b d x^{4} \operatorname{atan}{\left(c x \right)}}{4} + \frac{b e x^{6} \operatorname{atan}{\left(c x \right)}}{6} - \frac{b d x^{3}}{12 c} - \frac{b e x^{5}}{30 c} + \frac{b d x}{4 c^{3}} + \frac{b e x^{3}}{18 c^{3}} - \frac{b d \operatorname{atan}{\left(c x \right)}}{4 c^{4}} - \frac{b e x}{6 c^{5}} + \frac{b e \operatorname{atan}{\left(c x \right)}}{6 c^{6}} & \text{for}\: c \neq 0 \\a \left(\frac{d x^{4}}{4} + \frac{e x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**4/4 + a*e*x**6/6 + b*d*x**4*atan(c*x)/4 + b*e*x**6*atan(c*x)/6 - b*d*x**3/(12*c) - b*e*x**5/(30*c) + b*d*x/(4*c**3) + b*e*x**3/(18*c**3) - b*d*atan(c*x)/(4*c**4) - b*e*x/(6*c**5) + b*e*atan(c*x)/(6*c**6), Ne(c, 0)), (a*(d*x**4/4 + e*x**6/6), True))","A",0
1115,1,128,0,1.378487," ","integrate(x**2*(e*x**2+d)*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d x^{3}}{3} + \frac{a e x^{5}}{5} + \frac{b d x^{3} \operatorname{atan}{\left(c x \right)}}{3} + \frac{b e x^{5} \operatorname{atan}{\left(c x \right)}}{5} - \frac{b d x^{2}}{6 c} - \frac{b e x^{4}}{20 c} + \frac{b d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 c^{3}} + \frac{b e x^{2}}{10 c^{3}} - \frac{b e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10 c^{5}} & \text{for}\: c \neq 0 \\a \left(\frac{d x^{3}}{3} + \frac{e x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**3/3 + a*e*x**5/5 + b*d*x**3*atan(c*x)/3 + b*e*x**5*atan(c*x)/5 - b*d*x**2/(6*c) - b*e*x**4/(20*c) + b*d*log(x**2 + c**(-2))/(6*c**3) + b*e*x**2/(10*c**3) - b*e*log(x**2 + c**(-2))/(10*c**5), Ne(c, 0)), (a*(d*x**3/3 + e*x**5/5), True))","A",0
1116,1,114,0,1.177573," ","integrate(x*(e*x**2+d)*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d x^{2}}{2} + \frac{a e x^{4}}{4} + \frac{b d x^{2} \operatorname{atan}{\left(c x \right)}}{2} + \frac{b e x^{4} \operatorname{atan}{\left(c x \right)}}{4} - \frac{b d x}{2 c} - \frac{b e x^{3}}{12 c} + \frac{b d \operatorname{atan}{\left(c x \right)}}{2 c^{2}} + \frac{b e x}{4 c^{3}} - \frac{b e \operatorname{atan}{\left(c x \right)}}{4 c^{4}} & \text{for}\: c \neq 0 \\a \left(\frac{d x^{2}}{2} + \frac{e x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**2/2 + a*e*x**4/4 + b*d*x**2*atan(c*x)/2 + b*e*x**4*atan(c*x)/4 - b*d*x/(2*c) - b*e*x**3/(12*c) + b*d*atan(c*x)/(2*c**2) + b*e*x/(4*c**3) - b*e*atan(c*x)/(4*c**4), Ne(c, 0)), (a*(d*x**2/2 + e*x**4/4), True))","A",0
1117,1,94,0,0.711678," ","integrate((e*x**2+d)*(a+b*atan(c*x)),x)","\begin{cases} a d x + \frac{a e x^{3}}{3} + b d x \operatorname{atan}{\left(c x \right)} + \frac{b e x^{3} \operatorname{atan}{\left(c x \right)}}{3} - \frac{b d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} - \frac{b e x^{2}}{6 c} + \frac{b e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\a \left(d x + \frac{e x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x**3/3 + b*d*x*atan(c*x) + b*e*x**3*atan(c*x)/3 - b*d*log(x**2 + c**(-2))/(2*c) - b*e*x**2/(6*c) + b*e*log(x**2 + c**(-2))/(6*c**3), Ne(c, 0)), (a*(d*x + e*x**3/3), True))","A",0
1118,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*atan(c*x))/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)/x, x)","F",0
1119,1,80,0,0.953307," ","integrate((e*x**2+d)*(a+b*atan(c*x))/x**2,x)","\begin{cases} - \frac{a d}{x} + a e x + b c d \log{\left(x \right)} - \frac{b c d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d \operatorname{atan}{\left(c x \right)}}{x} + b e x \operatorname{atan}{\left(c x \right)} - \frac{b e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} & \text{for}\: c \neq 0 \\a \left(- \frac{d}{x} + e x\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d/x + a*e*x + b*c*d*log(x) - b*c*d*log(x**2 + c**(-2))/2 - b*d*atan(c*x)/x + b*e*x*atan(c*x) - b*e*log(x**2 + c**(-2))/(2*c), Ne(c, 0)), (a*(-d/x + e*x), True))","A",0
1120,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*atan(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)/x**3, x)","F",0
1121,1,116,0,1.285815," ","integrate((e*x**2+d)*(a+b*atan(c*x))/x**4,x)","\begin{cases} - \frac{a d}{3 x^{3}} - \frac{a e}{x} - \frac{b c^{3} d \log{\left(x \right)}}{3} + \frac{b c^{3} d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6} - \frac{b c d}{6 x^{2}} + b c e \log{\left(x \right)} - \frac{b c e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d \operatorname{atan}{\left(c x \right)}}{3 x^{3}} - \frac{b e \operatorname{atan}{\left(c x \right)}}{x} & \text{for}\: c \neq 0 \\a \left(- \frac{d}{3 x^{3}} - \frac{e}{x}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d/(3*x**3) - a*e/x - b*c**3*d*log(x)/3 + b*c**3*d*log(x**2 + c**(-2))/6 - b*c*d/(6*x**2) + b*c*e*log(x) - b*c*e*log(x**2 + c**(-2))/2 - b*d*atan(c*x)/(3*x**3) - b*e*atan(c*x)/x, Ne(c, 0)), (a*(-d/(3*x**3) - e/x), True))","A",0
1122,1,99,0,1.016453," ","integrate((e*x**2+d)*(a+b*atan(c*x))/x**5,x)","- \frac{a d}{4 x^{4}} - \frac{a e}{2 x^{2}} + \frac{b c^{4} d \operatorname{atan}{\left(c x \right)}}{4} + \frac{b c^{3} d}{4 x} - \frac{b c^{2} e \operatorname{atan}{\left(c x \right)}}{2} - \frac{b c d}{12 x^{3}} - \frac{b c e}{2 x} - \frac{b d \operatorname{atan}{\left(c x \right)}}{4 x^{4}} - \frac{b e \operatorname{atan}{\left(c x \right)}}{2 x^{2}}"," ",0,"-a*d/(4*x**4) - a*e/(2*x**2) + b*c**4*d*atan(c*x)/4 + b*c**3*d/(4*x) - b*c**2*e*atan(c*x)/2 - b*c*d/(12*x**3) - b*c*e/(2*x) - b*d*atan(c*x)/(4*x**4) - b*e*atan(c*x)/(2*x**2)","A",0
1123,1,153,0,2.147136," ","integrate((e*x**2+d)*(a+b*atan(c*x))/x**6,x)","\begin{cases} - \frac{a d}{5 x^{5}} - \frac{a e}{3 x^{3}} + \frac{b c^{5} d \log{\left(x \right)}}{5} - \frac{b c^{5} d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10} + \frac{b c^{3} d}{10 x^{2}} - \frac{b c^{3} e \log{\left(x \right)}}{3} + \frac{b c^{3} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6} - \frac{b c d}{20 x^{4}} - \frac{b c e}{6 x^{2}} - \frac{b d \operatorname{atan}{\left(c x \right)}}{5 x^{5}} - \frac{b e \operatorname{atan}{\left(c x \right)}}{3 x^{3}} & \text{for}\: c \neq 0 \\a \left(- \frac{d}{5 x^{5}} - \frac{e}{3 x^{3}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d/(5*x**5) - a*e/(3*x**3) + b*c**5*d*log(x)/5 - b*c**5*d*log(x**2 + c**(-2))/10 + b*c**3*d/(10*x**2) - b*c**3*e*log(x)/3 + b*c**3*e*log(x**2 + c**(-2))/6 - b*c*d/(20*x**4) - b*c*e/(6*x**2) - b*d*atan(c*x)/(5*x**5) - b*e*atan(c*x)/(3*x**3), Ne(c, 0)), (a*(-d/(5*x**5) - e/(3*x**3)), True))","A",0
1124,1,122,0,1.597555," ","integrate((e*x**2+d)*(a+b*atan(c*x))/x**7,x)","- \frac{a d}{6 x^{6}} - \frac{a e}{4 x^{4}} - \frac{b c^{6} d \operatorname{atan}{\left(c x \right)}}{6} - \frac{b c^{5} d}{6 x} + \frac{b c^{4} e \operatorname{atan}{\left(c x \right)}}{4} + \frac{b c^{3} d}{18 x^{3}} + \frac{b c^{3} e}{4 x} - \frac{b c d}{30 x^{5}} - \frac{b c e}{12 x^{3}} - \frac{b d \operatorname{atan}{\left(c x \right)}}{6 x^{6}} - \frac{b e \operatorname{atan}{\left(c x \right)}}{4 x^{4}}"," ",0,"-a*d/(6*x**6) - a*e/(4*x**4) - b*c**6*d*atan(c*x)/6 - b*c**5*d/(6*x) + b*c**4*e*atan(c*x)/4 + b*c**3*d/(18*x**3) + b*c**3*e/(4*x) - b*c*d/(30*x**5) - b*c*e/(12*x**3) - b*d*atan(c*x)/(6*x**6) - b*e*atan(c*x)/(4*x**4)","A",0
1125,1,260,0,3.801575," ","integrate(x**3*(e*x**2+d)**2*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d^{2} x^{4}}{4} + \frac{a d e x^{6}}{3} + \frac{a e^{2} x^{8}}{8} + \frac{b d^{2} x^{4} \operatorname{atan}{\left(c x \right)}}{4} + \frac{b d e x^{6} \operatorname{atan}{\left(c x \right)}}{3} + \frac{b e^{2} x^{8} \operatorname{atan}{\left(c x \right)}}{8} - \frac{b d^{2} x^{3}}{12 c} - \frac{b d e x^{5}}{15 c} - \frac{b e^{2} x^{7}}{56 c} + \frac{b d^{2} x}{4 c^{3}} + \frac{b d e x^{3}}{9 c^{3}} + \frac{b e^{2} x^{5}}{40 c^{3}} - \frac{b d^{2} \operatorname{atan}{\left(c x \right)}}{4 c^{4}} - \frac{b d e x}{3 c^{5}} - \frac{b e^{2} x^{3}}{24 c^{5}} + \frac{b d e \operatorname{atan}{\left(c x \right)}}{3 c^{6}} + \frac{b e^{2} x}{8 c^{7}} - \frac{b e^{2} \operatorname{atan}{\left(c x \right)}}{8 c^{8}} & \text{for}\: c \neq 0 \\a \left(\frac{d^{2} x^{4}}{4} + \frac{d e x^{6}}{3} + \frac{e^{2} x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x**4/4 + a*d*e*x**6/3 + a*e**2*x**8/8 + b*d**2*x**4*atan(c*x)/4 + b*d*e*x**6*atan(c*x)/3 + b*e**2*x**8*atan(c*x)/8 - b*d**2*x**3/(12*c) - b*d*e*x**5/(15*c) - b*e**2*x**7/(56*c) + b*d**2*x/(4*c**3) + b*d*e*x**3/(9*c**3) + b*e**2*x**5/(40*c**3) - b*d**2*atan(c*x)/(4*c**4) - b*d*e*x/(3*c**5) - b*e**2*x**3/(24*c**5) + b*d*e*atan(c*x)/(3*c**6) + b*e**2*x/(8*c**7) - b*e**2*atan(c*x)/(8*c**8), Ne(c, 0)), (a*(d**2*x**4/4 + d*e*x**6/3 + e**2*x**8/8), True))","A",0
1126,1,245,0,2.744032," ","integrate(x**2*(e*x**2+d)**2*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d^{2} x^{3}}{3} + \frac{2 a d e x^{5}}{5} + \frac{a e^{2} x^{7}}{7} + \frac{b d^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{3} + \frac{2 b d e x^{5} \operatorname{atan}{\left(c x \right)}}{5} + \frac{b e^{2} x^{7} \operatorname{atan}{\left(c x \right)}}{7} - \frac{b d^{2} x^{2}}{6 c} - \frac{b d e x^{4}}{10 c} - \frac{b e^{2} x^{6}}{42 c} + \frac{b d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 c^{3}} + \frac{b d e x^{2}}{5 c^{3}} + \frac{b e^{2} x^{4}}{28 c^{3}} - \frac{b d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{5 c^{5}} - \frac{b e^{2} x^{2}}{14 c^{5}} + \frac{b e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{14 c^{7}} & \text{for}\: c \neq 0 \\a \left(\frac{d^{2} x^{3}}{3} + \frac{2 d e x^{5}}{5} + \frac{e^{2} x^{7}}{7}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x**3/3 + 2*a*d*e*x**5/5 + a*e**2*x**7/7 + b*d**2*x**3*atan(c*x)/3 + 2*b*d*e*x**5*atan(c*x)/5 + b*e**2*x**7*atan(c*x)/7 - b*d**2*x**2/(6*c) - b*d*e*x**4/(10*c) - b*e**2*x**6/(42*c) + b*d**2*log(x**2 + c**(-2))/(6*c**3) + b*d*e*x**2/(5*c**3) + b*e**2*x**4/(28*c**3) - b*d*e*log(x**2 + c**(-2))/(5*c**5) - b*e**2*x**2/(14*c**5) + b*e**2*log(x**2 + c**(-2))/(14*c**7), Ne(c, 0)), (a*(d**2*x**3/3 + 2*d*e*x**5/5 + e**2*x**7/7), True))","A",0
1127,1,219,0,2.502488," ","integrate(x*(e*x**2+d)**2*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d^{2} x^{2}}{2} + \frac{a d e x^{4}}{2} + \frac{a e^{2} x^{6}}{6} + \frac{b d^{2} x^{2} \operatorname{atan}{\left(c x \right)}}{2} + \frac{b d e x^{4} \operatorname{atan}{\left(c x \right)}}{2} + \frac{b e^{2} x^{6} \operatorname{atan}{\left(c x \right)}}{6} - \frac{b d^{2} x}{2 c} - \frac{b d e x^{3}}{6 c} - \frac{b e^{2} x^{5}}{30 c} + \frac{b d^{2} \operatorname{atan}{\left(c x \right)}}{2 c^{2}} + \frac{b d e x}{2 c^{3}} + \frac{b e^{2} x^{3}}{18 c^{3}} - \frac{b d e \operatorname{atan}{\left(c x \right)}}{2 c^{4}} - \frac{b e^{2} x}{6 c^{5}} + \frac{b e^{2} \operatorname{atan}{\left(c x \right)}}{6 c^{6}} & \text{for}\: c \neq 0 \\a \left(\frac{d^{2} x^{2}}{2} + \frac{d e x^{4}}{2} + \frac{e^{2} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x**2/2 + a*d*e*x**4/2 + a*e**2*x**6/6 + b*d**2*x**2*atan(c*x)/2 + b*d*e*x**4*atan(c*x)/2 + b*e**2*x**6*atan(c*x)/6 - b*d**2*x/(2*c) - b*d*e*x**3/(6*c) - b*e**2*x**5/(30*c) + b*d**2*atan(c*x)/(2*c**2) + b*d*e*x/(2*c**3) + b*e**2*x**3/(18*c**3) - b*d*e*atan(c*x)/(2*c**4) - b*e**2*x/(6*c**5) + b*e**2*atan(c*x)/(6*c**6), Ne(c, 0)), (a*(d**2*x**2/2 + d*e*x**4/2 + e**2*x**6/6), True))","A",0
1128,1,194,0,1.627048," ","integrate((e*x**2+d)**2*(a+b*atan(c*x)),x)","\begin{cases} a d^{2} x + \frac{2 a d e x^{3}}{3} + \frac{a e^{2} x^{5}}{5} + b d^{2} x \operatorname{atan}{\left(c x \right)} + \frac{2 b d e x^{3} \operatorname{atan}{\left(c x \right)}}{3} + \frac{b e^{2} x^{5} \operatorname{atan}{\left(c x \right)}}{5} - \frac{b d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} - \frac{b d e x^{2}}{3 c} - \frac{b e^{2} x^{4}}{20 c} + \frac{b d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3 c^{3}} + \frac{b e^{2} x^{2}}{10 c^{3}} - \frac{b e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10 c^{5}} & \text{for}\: c \neq 0 \\a \left(d^{2} x + \frac{2 d e x^{3}}{3} + \frac{e^{2} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x + 2*a*d*e*x**3/3 + a*e**2*x**5/5 + b*d**2*x*atan(c*x) + 2*b*d*e*x**3*atan(c*x)/3 + b*e**2*x**5*atan(c*x)/5 - b*d**2*log(x**2 + c**(-2))/(2*c) - b*d*e*x**2/(3*c) - b*e**2*x**4/(20*c) + b*d*e*log(x**2 + c**(-2))/(3*c**3) + b*e**2*x**2/(10*c**3) - b*e**2*log(x**2 + c**(-2))/(10*c**5), Ne(c, 0)), (a*(d**2*x + 2*d*e*x**3/3 + e**2*x**5/5), True))","A",0
1129,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**2/x, x)","F",0
1130,1,165,0,1.832248," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x**2,x)","\begin{cases} - \frac{a d^{2}}{x} + 2 a d e x + \frac{a e^{2} x^{3}}{3} + b c d^{2} \log{\left(x \right)} - \frac{b c d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d^{2} \operatorname{atan}{\left(c x \right)}}{x} + 2 b d e x \operatorname{atan}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{3} - \frac{b d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{c} - \frac{b e^{2} x^{2}}{6 c} + \frac{b e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{2}}{x} + 2 d e x + \frac{e^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**2/x + 2*a*d*e*x + a*e**2*x**3/3 + b*c*d**2*log(x) - b*c*d**2*log(x**2 + c**(-2))/2 - b*d**2*atan(c*x)/x + 2*b*d*e*x*atan(c*x) + b*e**2*x**3*atan(c*x)/3 - b*d*e*log(x**2 + c**(-2))/c - b*e**2*x**2/(6*c) + b*e**2*log(x**2 + c**(-2))/(6*c**3), Ne(c, 0)), (a*(-d**2/x + 2*d*e*x + e**2*x**3/3), True))","A",0
1131,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**2/x**3, x)","F",0
1132,1,180,0,1.870841," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x**4,x)","\begin{cases} - \frac{a d^{2}}{3 x^{3}} - \frac{2 a d e}{x} + a e^{2} x - \frac{b c^{3} d^{2} \log{\left(x \right)}}{3} + \frac{b c^{3} d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6} - \frac{b c d^{2}}{6 x^{2}} + 2 b c d e \log{\left(x \right)} - b c d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)} - \frac{b d^{2} \operatorname{atan}{\left(c x \right)}}{3 x^{3}} - \frac{2 b d e \operatorname{atan}{\left(c x \right)}}{x} + b e^{2} x \operatorname{atan}{\left(c x \right)} - \frac{b e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{2}}{3 x^{3}} - \frac{2 d e}{x} + e^{2} x\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**2/(3*x**3) - 2*a*d*e/x + a*e**2*x - b*c**3*d**2*log(x)/3 + b*c**3*d**2*log(x**2 + c**(-2))/6 - b*c*d**2/(6*x**2) + 2*b*c*d*e*log(x) - b*c*d*e*log(x**2 + c**(-2)) - b*d**2*atan(c*x)/(3*x**3) - 2*b*d*e*atan(c*x)/x + b*e**2*x*atan(c*x) - b*e**2*log(x**2 + c**(-2))/(2*c), Ne(c, 0)), (a*(-d**2/(3*x**3) - 2*d*e/x + e**2*x), True))","A",0
1133,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x**5,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{2}}{x^{5}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**2/x**5, x)","F",0
1134,1,235,0,2.524132," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x**6,x)","\begin{cases} - \frac{a d^{2}}{5 x^{5}} - \frac{2 a d e}{3 x^{3}} - \frac{a e^{2}}{x} + \frac{b c^{5} d^{2} \log{\left(x \right)}}{5} - \frac{b c^{5} d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10} + \frac{b c^{3} d^{2}}{10 x^{2}} - \frac{2 b c^{3} d e \log{\left(x \right)}}{3} + \frac{b c^{3} d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3} - \frac{b c d^{2}}{20 x^{4}} - \frac{b c d e}{3 x^{2}} + b c e^{2} \log{\left(x \right)} - \frac{b c e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d^{2} \operatorname{atan}{\left(c x \right)}}{5 x^{5}} - \frac{2 b d e \operatorname{atan}{\left(c x \right)}}{3 x^{3}} - \frac{b e^{2} \operatorname{atan}{\left(c x \right)}}{x} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{2}}{5 x^{5}} - \frac{2 d e}{3 x^{3}} - \frac{e^{2}}{x}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**2/(5*x**5) - 2*a*d*e/(3*x**3) - a*e**2/x + b*c**5*d**2*log(x)/5 - b*c**5*d**2*log(x**2 + c**(-2))/10 + b*c**3*d**2/(10*x**2) - 2*b*c**3*d*e*log(x)/3 + b*c**3*d*e*log(x**2 + c**(-2))/3 - b*c*d**2/(20*x**4) - b*c*d*e/(3*x**2) + b*c*e**2*log(x) - b*c*e**2*log(x**2 + c**(-2))/2 - b*d**2*atan(c*x)/(5*x**5) - 2*b*d*e*atan(c*x)/(3*x**3) - b*e**2*atan(c*x)/x, Ne(c, 0)), (a*(-d**2/(5*x**5) - 2*d*e/(3*x**3) - e**2/x), True))","A",0
1135,1,192,0,1.871560," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x**7,x)","- \frac{a d^{2}}{6 x^{6}} - \frac{a d e}{2 x^{4}} - \frac{a e^{2}}{2 x^{2}} - \frac{b c^{6} d^{2} \operatorname{atan}{\left(c x \right)}}{6} - \frac{b c^{5} d^{2}}{6 x} + \frac{b c^{4} d e \operatorname{atan}{\left(c x \right)}}{2} + \frac{b c^{3} d^{2}}{18 x^{3}} + \frac{b c^{3} d e}{2 x} - \frac{b c^{2} e^{2} \operatorname{atan}{\left(c x \right)}}{2} - \frac{b c d^{2}}{30 x^{5}} - \frac{b c d e}{6 x^{3}} - \frac{b c e^{2}}{2 x} - \frac{b d^{2} \operatorname{atan}{\left(c x \right)}}{6 x^{6}} - \frac{b d e \operatorname{atan}{\left(c x \right)}}{2 x^{4}} - \frac{b e^{2} \operatorname{atan}{\left(c x \right)}}{2 x^{2}}"," ",0,"-a*d**2/(6*x**6) - a*d*e/(2*x**4) - a*e**2/(2*x**2) - b*c**6*d**2*atan(c*x)/6 - b*c**5*d**2/(6*x) + b*c**4*d*e*atan(c*x)/2 + b*c**3*d**2/(18*x**3) + b*c**3*d*e/(2*x) - b*c**2*e**2*atan(c*x)/2 - b*c*d**2/(30*x**5) - b*c*d*e/(6*x**3) - b*c*e**2/(2*x) - b*d**2*atan(c*x)/(6*x**6) - b*d*e*atan(c*x)/(2*x**4) - b*e**2*atan(c*x)/(2*x**2)","A",0
1136,1,289,0,3.980927," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))/x**8,x)","\begin{cases} - \frac{a d^{2}}{7 x^{7}} - \frac{2 a d e}{5 x^{5}} - \frac{a e^{2}}{3 x^{3}} - \frac{b c^{7} d^{2} \log{\left(x \right)}}{7} + \frac{b c^{7} d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{14} - \frac{b c^{5} d^{2}}{14 x^{2}} + \frac{2 b c^{5} d e \log{\left(x \right)}}{5} - \frac{b c^{5} d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{5} + \frac{b c^{3} d^{2}}{28 x^{4}} + \frac{b c^{3} d e}{5 x^{2}} - \frac{b c^{3} e^{2} \log{\left(x \right)}}{3} + \frac{b c^{3} e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6} - \frac{b c d^{2}}{42 x^{6}} - \frac{b c d e}{10 x^{4}} - \frac{b c e^{2}}{6 x^{2}} - \frac{b d^{2} \operatorname{atan}{\left(c x \right)}}{7 x^{7}} - \frac{2 b d e \operatorname{atan}{\left(c x \right)}}{5 x^{5}} - \frac{b e^{2} \operatorname{atan}{\left(c x \right)}}{3 x^{3}} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{2}}{7 x^{7}} - \frac{2 d e}{5 x^{5}} - \frac{e^{2}}{3 x^{3}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**2/(7*x**7) - 2*a*d*e/(5*x**5) - a*e**2/(3*x**3) - b*c**7*d**2*log(x)/7 + b*c**7*d**2*log(x**2 + c**(-2))/14 - b*c**5*d**2/(14*x**2) + 2*b*c**5*d*e*log(x)/5 - b*c**5*d*e*log(x**2 + c**(-2))/5 + b*c**3*d**2/(28*x**4) + b*c**3*d*e/(5*x**2) - b*c**3*e**2*log(x)/3 + b*c**3*e**2*log(x**2 + c**(-2))/6 - b*c*d**2/(42*x**6) - b*c*d*e/(10*x**4) - b*c*e**2/(6*x**2) - b*d**2*atan(c*x)/(7*x**7) - 2*b*d*e*atan(c*x)/(5*x**5) - b*e**2*atan(c*x)/(3*x**3), Ne(c, 0)), (a*(-d**2/(7*x**7) - 2*d*e/(5*x**5) - e**2/(3*x**3)), True))","A",0
1137,1,411,0,6.750510," ","integrate(x**3*(e*x**2+d)**3*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d^{3} x^{4}}{4} + \frac{a d^{2} e x^{6}}{2} + \frac{3 a d e^{2} x^{8}}{8} + \frac{a e^{3} x^{10}}{10} + \frac{b d^{3} x^{4} \operatorname{atan}{\left(c x \right)}}{4} + \frac{b d^{2} e x^{6} \operatorname{atan}{\left(c x \right)}}{2} + \frac{3 b d e^{2} x^{8} \operatorname{atan}{\left(c x \right)}}{8} + \frac{b e^{3} x^{10} \operatorname{atan}{\left(c x \right)}}{10} - \frac{b d^{3} x^{3}}{12 c} - \frac{b d^{2} e x^{5}}{10 c} - \frac{3 b d e^{2} x^{7}}{56 c} - \frac{b e^{3} x^{9}}{90 c} + \frac{b d^{3} x}{4 c^{3}} + \frac{b d^{2} e x^{3}}{6 c^{3}} + \frac{3 b d e^{2} x^{5}}{40 c^{3}} + \frac{b e^{3} x^{7}}{70 c^{3}} - \frac{b d^{3} \operatorname{atan}{\left(c x \right)}}{4 c^{4}} - \frac{b d^{2} e x}{2 c^{5}} - \frac{b d e^{2} x^{3}}{8 c^{5}} - \frac{b e^{3} x^{5}}{50 c^{5}} + \frac{b d^{2} e \operatorname{atan}{\left(c x \right)}}{2 c^{6}} + \frac{3 b d e^{2} x}{8 c^{7}} + \frac{b e^{3} x^{3}}{30 c^{7}} - \frac{3 b d e^{2} \operatorname{atan}{\left(c x \right)}}{8 c^{8}} - \frac{b e^{3} x}{10 c^{9}} + \frac{b e^{3} \operatorname{atan}{\left(c x \right)}}{10 c^{10}} & \text{for}\: c \neq 0 \\a \left(\frac{d^{3} x^{4}}{4} + \frac{d^{2} e x^{6}}{2} + \frac{3 d e^{2} x^{8}}{8} + \frac{e^{3} x^{10}}{10}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x**4/4 + a*d**2*e*x**6/2 + 3*a*d*e**2*x**8/8 + a*e**3*x**10/10 + b*d**3*x**4*atan(c*x)/4 + b*d**2*e*x**6*atan(c*x)/2 + 3*b*d*e**2*x**8*atan(c*x)/8 + b*e**3*x**10*atan(c*x)/10 - b*d**3*x**3/(12*c) - b*d**2*e*x**5/(10*c) - 3*b*d*e**2*x**7/(56*c) - b*e**3*x**9/(90*c) + b*d**3*x/(4*c**3) + b*d**2*e*x**3/(6*c**3) + 3*b*d*e**2*x**5/(40*c**3) + b*e**3*x**7/(70*c**3) - b*d**3*atan(c*x)/(4*c**4) - b*d**2*e*x/(2*c**5) - b*d*e**2*x**3/(8*c**5) - b*e**3*x**5/(50*c**5) + b*d**2*e*atan(c*x)/(2*c**6) + 3*b*d*e**2*x/(8*c**7) + b*e**3*x**3/(30*c**7) - 3*b*d*e**2*atan(c*x)/(8*c**8) - b*e**3*x/(10*c**9) + b*e**3*atan(c*x)/(10*c**10), Ne(c, 0)), (a*(d**3*x**4/4 + d**2*e*x**6/2 + 3*d*e**2*x**8/8 + e**3*x**10/10), True))","A",0
1138,1,389,0,4.922252," ","integrate(x**2*(e*x**2+d)**3*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d^{3} x^{3}}{3} + \frac{3 a d^{2} e x^{5}}{5} + \frac{3 a d e^{2} x^{7}}{7} + \frac{a e^{3} x^{9}}{9} + \frac{b d^{3} x^{3} \operatorname{atan}{\left(c x \right)}}{3} + \frac{3 b d^{2} e x^{5} \operatorname{atan}{\left(c x \right)}}{5} + \frac{3 b d e^{2} x^{7} \operatorname{atan}{\left(c x \right)}}{7} + \frac{b e^{3} x^{9} \operatorname{atan}{\left(c x \right)}}{9} - \frac{b d^{3} x^{2}}{6 c} - \frac{3 b d^{2} e x^{4}}{20 c} - \frac{b d e^{2} x^{6}}{14 c} - \frac{b e^{3} x^{8}}{72 c} + \frac{b d^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 c^{3}} + \frac{3 b d^{2} e x^{2}}{10 c^{3}} + \frac{3 b d e^{2} x^{4}}{28 c^{3}} + \frac{b e^{3} x^{6}}{54 c^{3}} - \frac{3 b d^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10 c^{5}} - \frac{3 b d e^{2} x^{2}}{14 c^{5}} - \frac{b e^{3} x^{4}}{36 c^{5}} + \frac{3 b d e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{14 c^{7}} + \frac{b e^{3} x^{2}}{18 c^{7}} - \frac{b e^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{18 c^{9}} & \text{for}\: c \neq 0 \\a \left(\frac{d^{3} x^{3}}{3} + \frac{3 d^{2} e x^{5}}{5} + \frac{3 d e^{2} x^{7}}{7} + \frac{e^{3} x^{9}}{9}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x**3/3 + 3*a*d**2*e*x**5/5 + 3*a*d*e**2*x**7/7 + a*e**3*x**9/9 + b*d**3*x**3*atan(c*x)/3 + 3*b*d**2*e*x**5*atan(c*x)/5 + 3*b*d*e**2*x**7*atan(c*x)/7 + b*e**3*x**9*atan(c*x)/9 - b*d**3*x**2/(6*c) - 3*b*d**2*e*x**4/(20*c) - b*d*e**2*x**6/(14*c) - b*e**3*x**8/(72*c) + b*d**3*log(x**2 + c**(-2))/(6*c**3) + 3*b*d**2*e*x**2/(10*c**3) + 3*b*d*e**2*x**4/(28*c**3) + b*e**3*x**6/(54*c**3) - 3*b*d**2*e*log(x**2 + c**(-2))/(10*c**5) - 3*b*d*e**2*x**2/(14*c**5) - b*e**3*x**4/(36*c**5) + 3*b*d*e**2*log(x**2 + c**(-2))/(14*c**7) + b*e**3*x**2/(18*c**7) - b*e**3*log(x**2 + c**(-2))/(18*c**9), Ne(c, 0)), (a*(d**3*x**3/3 + 3*d**2*e*x**5/5 + 3*d*e**2*x**7/7 + e**3*x**9/9), True))","A",0
1139,1,350,0,4.573403," ","integrate(x*(e*x**2+d)**3*(a+b*atan(c*x)),x)","\begin{cases} \frac{a d^{3} x^{2}}{2} + \frac{3 a d^{2} e x^{4}}{4} + \frac{a d e^{2} x^{6}}{2} + \frac{a e^{3} x^{8}}{8} + \frac{b d^{3} x^{2} \operatorname{atan}{\left(c x \right)}}{2} + \frac{3 b d^{2} e x^{4} \operatorname{atan}{\left(c x \right)}}{4} + \frac{b d e^{2} x^{6} \operatorname{atan}{\left(c x \right)}}{2} + \frac{b e^{3} x^{8} \operatorname{atan}{\left(c x \right)}}{8} - \frac{b d^{3} x}{2 c} - \frac{b d^{2} e x^{3}}{4 c} - \frac{b d e^{2} x^{5}}{10 c} - \frac{b e^{3} x^{7}}{56 c} + \frac{b d^{3} \operatorname{atan}{\left(c x \right)}}{2 c^{2}} + \frac{3 b d^{2} e x}{4 c^{3}} + \frac{b d e^{2} x^{3}}{6 c^{3}} + \frac{b e^{3} x^{5}}{40 c^{3}} - \frac{3 b d^{2} e \operatorname{atan}{\left(c x \right)}}{4 c^{4}} - \frac{b d e^{2} x}{2 c^{5}} - \frac{b e^{3} x^{3}}{24 c^{5}} + \frac{b d e^{2} \operatorname{atan}{\left(c x \right)}}{2 c^{6}} + \frac{b e^{3} x}{8 c^{7}} - \frac{b e^{3} \operatorname{atan}{\left(c x \right)}}{8 c^{8}} & \text{for}\: c \neq 0 \\a \left(\frac{d^{3} x^{2}}{2} + \frac{3 d^{2} e x^{4}}{4} + \frac{d e^{2} x^{6}}{2} + \frac{e^{3} x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x**2/2 + 3*a*d**2*e*x**4/4 + a*d*e**2*x**6/2 + a*e**3*x**8/8 + b*d**3*x**2*atan(c*x)/2 + 3*b*d**2*e*x**4*atan(c*x)/4 + b*d*e**2*x**6*atan(c*x)/2 + b*e**3*x**8*atan(c*x)/8 - b*d**3*x/(2*c) - b*d**2*e*x**3/(4*c) - b*d*e**2*x**5/(10*c) - b*e**3*x**7/(56*c) + b*d**3*atan(c*x)/(2*c**2) + 3*b*d**2*e*x/(4*c**3) + b*d*e**2*x**3/(6*c**3) + b*e**3*x**5/(40*c**3) - 3*b*d**2*e*atan(c*x)/(4*c**4) - b*d*e**2*x/(2*c**5) - b*e**3*x**3/(24*c**5) + b*d*e**2*atan(c*x)/(2*c**6) + b*e**3*x/(8*c**7) - b*e**3*atan(c*x)/(8*c**8), Ne(c, 0)), (a*(d**3*x**2/2 + 3*d**2*e*x**4/4 + d*e**2*x**6/2 + e**3*x**8/8), True))","A",0
1140,1,306,0,3.096125," ","integrate((e*x**2+d)**3*(a+b*atan(c*x)),x)","\begin{cases} a d^{3} x + a d^{2} e x^{3} + \frac{3 a d e^{2} x^{5}}{5} + \frac{a e^{3} x^{7}}{7} + b d^{3} x \operatorname{atan}{\left(c x \right)} + b d^{2} e x^{3} \operatorname{atan}{\left(c x \right)} + \frac{3 b d e^{2} x^{5} \operatorname{atan}{\left(c x \right)}}{5} + \frac{b e^{3} x^{7} \operatorname{atan}{\left(c x \right)}}{7} - \frac{b d^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} - \frac{b d^{2} e x^{2}}{2 c} - \frac{3 b d e^{2} x^{4}}{20 c} - \frac{b e^{3} x^{6}}{42 c} + \frac{b d^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{3}} + \frac{3 b d e^{2} x^{2}}{10 c^{3}} + \frac{b e^{3} x^{4}}{28 c^{3}} - \frac{3 b d e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10 c^{5}} - \frac{b e^{3} x^{2}}{14 c^{5}} + \frac{b e^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{14 c^{7}} & \text{for}\: c \neq 0 \\a \left(d^{3} x + d^{2} e x^{3} + \frac{3 d e^{2} x^{5}}{5} + \frac{e^{3} x^{7}}{7}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x + a*d**2*e*x**3 + 3*a*d*e**2*x**5/5 + a*e**3*x**7/7 + b*d**3*x*atan(c*x) + b*d**2*e*x**3*atan(c*x) + 3*b*d*e**2*x**5*atan(c*x)/5 + b*e**3*x**7*atan(c*x)/7 - b*d**3*log(x**2 + c**(-2))/(2*c) - b*d**2*e*x**2/(2*c) - 3*b*d*e**2*x**4/(20*c) - b*e**3*x**6/(42*c) + b*d**2*e*log(x**2 + c**(-2))/(2*c**3) + 3*b*d*e**2*x**2/(10*c**3) + b*e**3*x**4/(28*c**3) - 3*b*d*e**2*log(x**2 + c**(-2))/(10*c**5) - b*e**3*x**2/(14*c**5) + b*e**3*log(x**2 + c**(-2))/(14*c**7), Ne(c, 0)), (a*(d**3*x + d**2*e*x**3 + 3*d*e**2*x**5/5 + e**3*x**7/7), True))","A",0
1141,0,0,0,0.000000," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**3/x, x)","F",0
1142,1,258,0,3.291609," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**2,x)","\begin{cases} - \frac{a d^{3}}{x} + 3 a d^{2} e x + a d e^{2} x^{3} + \frac{a e^{3} x^{5}}{5} + b c d^{3} \log{\left(x \right)} - \frac{b c d^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d^{3} \operatorname{atan}{\left(c x \right)}}{x} + 3 b d^{2} e x \operatorname{atan}{\left(c x \right)} + b d e^{2} x^{3} \operatorname{atan}{\left(c x \right)} + \frac{b e^{3} x^{5} \operatorname{atan}{\left(c x \right)}}{5} - \frac{3 b d^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} - \frac{b d e^{2} x^{2}}{2 c} - \frac{b e^{3} x^{4}}{20 c} + \frac{b d e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{3}} + \frac{b e^{3} x^{2}}{10 c^{3}} - \frac{b e^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10 c^{5}} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{3}}{x} + 3 d^{2} e x + d e^{2} x^{3} + \frac{e^{3} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**3/x + 3*a*d**2*e*x + a*d*e**2*x**3 + a*e**3*x**5/5 + b*c*d**3*log(x) - b*c*d**3*log(x**2 + c**(-2))/2 - b*d**3*atan(c*x)/x + 3*b*d**2*e*x*atan(c*x) + b*d*e**2*x**3*atan(c*x) + b*e**3*x**5*atan(c*x)/5 - 3*b*d**2*e*log(x**2 + c**(-2))/(2*c) - b*d*e**2*x**2/(2*c) - b*e**3*x**4/(20*c) + b*d*e**2*log(x**2 + c**(-2))/(2*c**3) + b*e**3*x**2/(10*c**3) - b*e**3*log(x**2 + c**(-2))/(10*c**5), Ne(c, 0)), (a*(-d**3/x + 3*d**2*e*x + d*e**2*x**3 + e**3*x**5/5), True))","A",0
1143,0,0,0,0.000000," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**3/x**3, x)","F",0
1144,1,272,0,3.302076," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**4,x)","\begin{cases} - \frac{a d^{3}}{3 x^{3}} - \frac{3 a d^{2} e}{x} + 3 a d e^{2} x + \frac{a e^{3} x^{3}}{3} - \frac{b c^{3} d^{3} \log{\left(x \right)}}{3} + \frac{b c^{3} d^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6} - \frac{b c d^{3}}{6 x^{2}} + 3 b c d^{2} e \log{\left(x \right)} - \frac{3 b c d^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d^{3} \operatorname{atan}{\left(c x \right)}}{3 x^{3}} - \frac{3 b d^{2} e \operatorname{atan}{\left(c x \right)}}{x} + 3 b d e^{2} x \operatorname{atan}{\left(c x \right)} + \frac{b e^{3} x^{3} \operatorname{atan}{\left(c x \right)}}{3} - \frac{3 b d e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} - \frac{b e^{3} x^{2}}{6 c} + \frac{b e^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{3}}{3 x^{3}} - \frac{3 d^{2} e}{x} + 3 d e^{2} x + \frac{e^{3} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**3/(3*x**3) - 3*a*d**2*e/x + 3*a*d*e**2*x + a*e**3*x**3/3 - b*c**3*d**3*log(x)/3 + b*c**3*d**3*log(x**2 + c**(-2))/6 - b*c*d**3/(6*x**2) + 3*b*c*d**2*e*log(x) - 3*b*c*d**2*e*log(x**2 + c**(-2))/2 - b*d**3*atan(c*x)/(3*x**3) - 3*b*d**2*e*atan(c*x)/x + 3*b*d*e**2*x*atan(c*x) + b*e**3*x**3*atan(c*x)/3 - 3*b*d*e**2*log(x**2 + c**(-2))/(2*c) - b*e**3*x**2/(6*c) + b*e**3*log(x**2 + c**(-2))/(6*c**3), Ne(c, 0)), (a*(-d**3/(3*x**3) - 3*d**2*e/x + 3*d*e**2*x + e**3*x**3/3), True))","A",0
1145,0,0,0,0.000000," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**5,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{3}}{x^{5}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**3/x**5, x)","F",0
1146,1,289,0,3.383042," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**6,x)","\begin{cases} - \frac{a d^{3}}{5 x^{5}} - \frac{a d^{2} e}{x^{3}} - \frac{3 a d e^{2}}{x} + a e^{3} x + \frac{b c^{5} d^{3} \log{\left(x \right)}}{5} - \frac{b c^{5} d^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10} + \frac{b c^{3} d^{3}}{10 x^{2}} - b c^{3} d^{2} e \log{\left(x \right)} + \frac{b c^{3} d^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b c d^{3}}{20 x^{4}} - \frac{b c d^{2} e}{2 x^{2}} + 3 b c d e^{2} \log{\left(x \right)} - \frac{3 b c d e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d^{3} \operatorname{atan}{\left(c x \right)}}{5 x^{5}} - \frac{b d^{2} e \operatorname{atan}{\left(c x \right)}}{x^{3}} - \frac{3 b d e^{2} \operatorname{atan}{\left(c x \right)}}{x} + b e^{3} x \operatorname{atan}{\left(c x \right)} - \frac{b e^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{3}}{5 x^{5}} - \frac{d^{2} e}{x^{3}} - \frac{3 d e^{2}}{x} + e^{3} x\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**3/(5*x**5) - a*d**2*e/x**3 - 3*a*d*e**2/x + a*e**3*x + b*c**5*d**3*log(x)/5 - b*c**5*d**3*log(x**2 + c**(-2))/10 + b*c**3*d**3/(10*x**2) - b*c**3*d**2*e*log(x) + b*c**3*d**2*e*log(x**2 + c**(-2))/2 - b*c*d**3/(20*x**4) - b*c*d**2*e/(2*x**2) + 3*b*c*d*e**2*log(x) - 3*b*c*d*e**2*log(x**2 + c**(-2))/2 - b*d**3*atan(c*x)/(5*x**5) - b*d**2*e*atan(c*x)/x**3 - 3*b*d*e**2*atan(c*x)/x + b*e**3*x*atan(c*x) - b*e**3*log(x**2 + c**(-2))/(2*c), Ne(c, 0)), (a*(-d**3/(5*x**5) - d**2*e/x**3 - 3*d*e**2/x + e**3*x), True))","A",0
1147,0,0,0,0.000000," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**7,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{3}}{x^{7}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**3/x**7, x)","F",0
1148,1,362,0,4.420073," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**8,x)","\begin{cases} - \frac{a d^{3}}{7 x^{7}} - \frac{3 a d^{2} e}{5 x^{5}} - \frac{a d e^{2}}{x^{3}} - \frac{a e^{3}}{x} - \frac{b c^{7} d^{3} \log{\left(x \right)}}{7} + \frac{b c^{7} d^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{14} - \frac{b c^{5} d^{3}}{14 x^{2}} + \frac{3 b c^{5} d^{2} e \log{\left(x \right)}}{5} - \frac{3 b c^{5} d^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{10} + \frac{b c^{3} d^{3}}{28 x^{4}} + \frac{3 b c^{3} d^{2} e}{10 x^{2}} - b c^{3} d e^{2} \log{\left(x \right)} + \frac{b c^{3} d e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b c d^{3}}{42 x^{6}} - \frac{3 b c d^{2} e}{20 x^{4}} - \frac{b c d e^{2}}{2 x^{2}} + b c e^{3} \log{\left(x \right)} - \frac{b c e^{3} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2} - \frac{b d^{3} \operatorname{atan}{\left(c x \right)}}{7 x^{7}} - \frac{3 b d^{2} e \operatorname{atan}{\left(c x \right)}}{5 x^{5}} - \frac{b d e^{2} \operatorname{atan}{\left(c x \right)}}{x^{3}} - \frac{b e^{3} \operatorname{atan}{\left(c x \right)}}{x} & \text{for}\: c \neq 0 \\a \left(- \frac{d^{3}}{7 x^{7}} - \frac{3 d^{2} e}{5 x^{5}} - \frac{d e^{2}}{x^{3}} - \frac{e^{3}}{x}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**3/(7*x**7) - 3*a*d**2*e/(5*x**5) - a*d*e**2/x**3 - a*e**3/x - b*c**7*d**3*log(x)/7 + b*c**7*d**3*log(x**2 + c**(-2))/14 - b*c**5*d**3/(14*x**2) + 3*b*c**5*d**2*e*log(x)/5 - 3*b*c**5*d**2*e*log(x**2 + c**(-2))/10 + b*c**3*d**3/(28*x**4) + 3*b*c**3*d**2*e/(10*x**2) - b*c**3*d*e**2*log(x) + b*c**3*d*e**2*log(x**2 + c**(-2))/2 - b*c*d**3/(42*x**6) - 3*b*c*d**2*e/(20*x**4) - b*c*d*e**2/(2*x**2) + b*c*e**3*log(x) - b*c*e**3*log(x**2 + c**(-2))/2 - b*d**3*atan(c*x)/(7*x**7) - 3*b*d**2*e*atan(c*x)/(5*x**5) - b*d*e**2*atan(c*x)/x**3 - b*e**3*atan(c*x)/x, Ne(c, 0)), (a*(-d**3/(7*x**7) - 3*d**2*e/(5*x**5) - d*e**2/x**3 - e**3/x), True))","A",0
1149,1,309,0,3.159245," ","integrate((e*x**2+d)**3*(a+b*atan(c*x))/x**9,x)","- \frac{a d^{3}}{8 x^{8}} - \frac{a d^{2} e}{2 x^{6}} - \frac{3 a d e^{2}}{4 x^{4}} - \frac{a e^{3}}{2 x^{2}} + \frac{b c^{8} d^{3} \operatorname{atan}{\left(c x \right)}}{8} + \frac{b c^{7} d^{3}}{8 x} - \frac{b c^{6} d^{2} e \operatorname{atan}{\left(c x \right)}}{2} - \frac{b c^{5} d^{3}}{24 x^{3}} - \frac{b c^{5} d^{2} e}{2 x} + \frac{3 b c^{4} d e^{2} \operatorname{atan}{\left(c x \right)}}{4} + \frac{b c^{3} d^{3}}{40 x^{5}} + \frac{b c^{3} d^{2} e}{6 x^{3}} + \frac{3 b c^{3} d e^{2}}{4 x} - \frac{b c^{2} e^{3} \operatorname{atan}{\left(c x \right)}}{2} - \frac{b c d^{3}}{56 x^{7}} - \frac{b c d^{2} e}{10 x^{5}} - \frac{b c d e^{2}}{4 x^{3}} - \frac{b c e^{3}}{2 x} - \frac{b d^{3} \operatorname{atan}{\left(c x \right)}}{8 x^{8}} - \frac{b d^{2} e \operatorname{atan}{\left(c x \right)}}{2 x^{6}} - \frac{3 b d e^{2} \operatorname{atan}{\left(c x \right)}}{4 x^{4}} - \frac{b e^{3} \operatorname{atan}{\left(c x \right)}}{2 x^{2}}"," ",0,"-a*d**3/(8*x**8) - a*d**2*e/(2*x**6) - 3*a*d*e**2/(4*x**4) - a*e**3/(2*x**2) + b*c**8*d**3*atan(c*x)/8 + b*c**7*d**3/(8*x) - b*c**6*d**2*e*atan(c*x)/2 - b*c**5*d**3/(24*x**3) - b*c**5*d**2*e/(2*x) + 3*b*c**4*d*e**2*atan(c*x)/4 + b*c**3*d**3/(40*x**5) + b*c**3*d**2*e/(6*x**3) + 3*b*c**3*d*e**2/(4*x) - b*c**2*e**3*atan(c*x)/2 - b*c*d**3/(56*x**7) - b*c*d**2*e/(10*x**5) - b*c*d*e**2/(4*x**3) - b*c*e**3/(2*x) - b*d**3*atan(c*x)/(8*x**8) - b*d**2*e*atan(c*x)/(2*x**6) - 3*b*d*e**2*atan(c*x)/(4*x**4) - b*e**3*atan(c*x)/(2*x**2)","B",0
1150,1,314,0,4.299839," ","integrate((d*x**2+c)**4*atan(a*x),x)","\begin{cases} c^{4} x \operatorname{atan}{\left(a x \right)} + \frac{4 c^{3} d x^{3} \operatorname{atan}{\left(a x \right)}}{3} + \frac{6 c^{2} d^{2} x^{5} \operatorname{atan}{\left(a x \right)}}{5} + \frac{4 c d^{3} x^{7} \operatorname{atan}{\left(a x \right)}}{7} + \frac{d^{4} x^{9} \operatorname{atan}{\left(a x \right)}}{9} - \frac{c^{4} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 a} - \frac{2 c^{3} d x^{2}}{3 a} - \frac{3 c^{2} d^{2} x^{4}}{10 a} - \frac{2 c d^{3} x^{6}}{21 a} - \frac{d^{4} x^{8}}{72 a} + \frac{2 c^{3} d \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3 a^{3}} + \frac{3 c^{2} d^{2} x^{2}}{5 a^{3}} + \frac{c d^{3} x^{4}}{7 a^{3}} + \frac{d^{4} x^{6}}{54 a^{3}} - \frac{3 c^{2} d^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{5 a^{5}} - \frac{2 c d^{3} x^{2}}{7 a^{5}} - \frac{d^{4} x^{4}}{36 a^{5}} + \frac{2 c d^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{7 a^{7}} + \frac{d^{4} x^{2}}{18 a^{7}} - \frac{d^{4} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{18 a^{9}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*x*atan(a*x) + 4*c**3*d*x**3*atan(a*x)/3 + 6*c**2*d**2*x**5*atan(a*x)/5 + 4*c*d**3*x**7*atan(a*x)/7 + d**4*x**9*atan(a*x)/9 - c**4*log(x**2 + a**(-2))/(2*a) - 2*c**3*d*x**2/(3*a) - 3*c**2*d**2*x**4/(10*a) - 2*c*d**3*x**6/(21*a) - d**4*x**8/(72*a) + 2*c**3*d*log(x**2 + a**(-2))/(3*a**3) + 3*c**2*d**2*x**2/(5*a**3) + c*d**3*x**4/(7*a**3) + d**4*x**6/(54*a**3) - 3*c**2*d**2*log(x**2 + a**(-2))/(5*a**5) - 2*c*d**3*x**2/(7*a**5) - d**4*x**4/(36*a**5) + 2*c*d**3*log(x**2 + a**(-2))/(7*a**7) + d**4*x**2/(18*a**7) - d**4*log(x**2 + a**(-2))/(18*a**9), Ne(a, 0)), (0, True))","A",0
1151,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(e*x**2+d),x)","\int \frac{x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))/(d + e*x**2), x)","F",0
1152,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(e*x**2+d),x)","\int \frac{x \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))/(d + e*x**2), x)","F",0
1153,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(e*x**2+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x*(d + e*x**2)), x)","F",0
1154,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(e*x**2+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{3} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**3*(d + e*x**2)), x)","F",0
1155,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(e*x**2+d),x)","\int \frac{x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))/(d + e*x**2), x)","F",0
1156,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/(e*x**2+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{d + e x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(d + e*x**2), x)","F",0
1157,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(e*x**2+d),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{2} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**2*(d + e*x**2)), x)","F",0
1158,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1159,-1,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1160,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1161,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1162,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1163,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1164,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1165,-1,0,0,0.000000," ","integrate(x**5*(a+b*atan(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1166,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1167,-1,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1169,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1170,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1171,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1172,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1173,0,0,0,0.000000," ","integrate(x**3*(e*x**2+d)**(1/2)*(a+b*atan(c*x)),x)","\int x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))*sqrt(d + e*x**2), x)","F",0
1174,0,0,0,0.000000," ","integrate(x**2*(e*x**2+d)**(1/2)*(a+b*atan(c*x)),x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))*sqrt(d + e*x**2), x)","F",0
1175,0,0,0,0.000000," ","integrate(x*(e*x**2+d)**(1/2)*(a+b*atan(c*x)),x)","\int x \left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))*sqrt(d + e*x**2), x)","F",0
1176,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)*(a+b*atan(c*x)),x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))*sqrt(d + e*x**2), x)","F",0
1177,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)*(a+b*atan(c*x))/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))*sqrt(d + e*x**2)/x, x)","F",0
1178,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)*(a+b*atan(c*x))/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))*sqrt(d + e*x**2)/x**2, x)","F",0
1179,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)*(a+b*atan(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))*sqrt(d + e*x**2)/x**3, x)","F",0
1180,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)*(a+b*atan(c*x))/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x))*sqrt(d + e*x**2)/x**4, x)","F",0
1181,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)*(a+b*atan(c*x))/x**5,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{5}}\, dx"," ",0,"Integral((a + b*atan(c*x))*sqrt(d + e*x**2)/x**5, x)","F",0
1182,0,0,0,0.000000," ","integrate((e*x**2+d)**(1/2)*(a+b*atan(c*x))/x**6,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{6}}\, dx"," ",0,"Integral((a + b*atan(c*x))*sqrt(d + e*x**2)/x**6, x)","F",0
1183,0,0,0,0.000000," ","integrate(x**3*(e*x**2+d)**(3/2)*(a+b*atan(c*x)),x)","\int x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))*(d + e*x**2)**(3/2), x)","F",0
1184,0,0,0,0.000000," ","integrate(x**2*(e*x**2+d)**(3/2)*(a+b*atan(c*x)),x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))*(d + e*x**2)**(3/2), x)","F",0
1185,0,0,0,0.000000," ","integrate(x*(e*x**2+d)**(3/2)*(a+b*atan(c*x)),x)","\int x \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))*(d + e*x**2)**(3/2), x)","F",0
1186,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*atan(c*x)),x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(3/2), x)","F",0
1187,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*atan(c*x))/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(3/2)/x, x)","F",0
1188,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*atan(c*x))/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(3/2)/x**2, x)","F",0
1189,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*atan(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(3/2)/x**3, x)","F",0
1190,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*atan(c*x))/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(3/2)/x**4, x)","F",0
1191,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*atan(c*x))/x**5,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(3/2)/x**5, x)","F",0
1192,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*atan(c*x))/x**6,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(3/2)/x**6, x)","F",0
1193,0,0,0,0.000000," ","integrate(x**3*(e*x**2+d)**(5/2)*(a+b*atan(c*x)),x)","\int x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))*(d + e*x**2)**(5/2), x)","F",0
1194,0,0,0,0.000000," ","integrate(x**2*(e*x**2+d)**(5/2)*(a+b*atan(c*x)),x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))*(d + e*x**2)**(5/2), x)","F",0
1195,0,0,0,0.000000," ","integrate(x*(e*x**2+d)**(5/2)*(a+b*atan(c*x)),x)","\int x \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))*(d + e*x**2)**(5/2), x)","F",0
1196,0,0,0,0.000000," ","integrate((e*x**2+d)**(5/2)*(a+b*atan(c*x)),x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(5/2), x)","F",0
1197,0,0,0,0.000000," ","integrate((e*x**2+d)**(5/2)*(a+b*atan(c*x))/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(5/2)/x, x)","F",0
1198,0,0,0,0.000000," ","integrate((e*x**2+d)**(5/2)*(a+b*atan(c*x))/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(5/2)/x**2, x)","F",0
1199,0,0,0,0.000000," ","integrate((e*x**2+d)**(5/2)*(a+b*atan(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(5/2)/x**3, x)","F",0
1200,0,0,0,0.000000," ","integrate((e*x**2+d)**(5/2)*(a+b*atan(c*x))/x**4,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{5}{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*x**2)**(5/2)/x**4, x)","F",0
1201,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))/sqrt(d + e*x**2), x)","F",0
1202,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))/sqrt(d + e*x**2), x)","F",0
1203,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))/sqrt(d + e*x**2), x)","F",0
1204,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/sqrt(d + e*x**2), x)","F",0
1205,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x*sqrt(d + e*x**2)), x)","F",0
1206,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{2} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**2*sqrt(d + e*x**2)), x)","F",0
1207,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{3} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**3*sqrt(d + e*x**2)), x)","F",0
1208,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**4/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{4} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**4*sqrt(d + e*x**2)), x)","F",0
1209,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))/(d + e*x**2)**(3/2), x)","F",0
1210,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))/(d + e*x**2)**(3/2), x)","F",0
1211,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{x \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))/(d + e*x**2)**(3/2), x)","F",0
1212,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(d + e*x**2)**(3/2), x)","F",0
1213,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(e*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x*(d + e*x**2)**(3/2)), x)","F",0
1214,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(e*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{2} \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**2*(d + e*x**2)**(3/2)), x)","F",0
1215,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(e*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{3} \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**3*(d + e*x**2)**(3/2)), x)","F",0
1216,0,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**4/(e*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{atan}{\left(c x \right)}}{x^{4} \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atan(c*x))/(x**4*(d + e*x**2)**(3/2)), x)","F",0
1217,-1,0,0,0.000000," ","integrate(x**4*(a+b*atan(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1218,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))/(e*x**2+d)**(5/2),x)","\int \frac{x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))/(d + e*x**2)**(5/2), x)","F",0
1219,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1220,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))/(e*x**2+d)**(5/2),x)","\int \frac{x \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))/(d + e*x**2)**(5/2), x)","F",0
1221,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1222,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1223,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**2/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1224,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**3/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1225,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))/x**4/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1226,0,0,0,0.000000," ","integrate(atan(a*x)/(d*x**2+c)**(7/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(c + d*x**2)**(7/2), x)","F",0
1227,0,0,0,0.000000," ","integrate(atan(a*x)/(d*x**2+c)**(9/2),x)","\int \frac{\operatorname{atan}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(atan(a*x)/(c + d*x**2)**(9/2), x)","F",0
1228,0,0,0,0.000000," ","integrate(x**m*(e*x**2+d)**3*(a+b*atan(c*x)),x)","\int x^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{3}\, dx"," ",0,"Integral(x**m*(a + b*atan(c*x))*(d + e*x**2)**3, x)","F",0
1229,0,0,0,0.000000," ","integrate(x**m*(e*x**2+d)**2*(a+b*atan(c*x)),x)","\int x^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{2}\, dx"," ",0,"Integral(x**m*(a + b*atan(c*x))*(d + e*x**2)**2, x)","F",0
1230,0,0,0,0.000000," ","integrate(x**m*(e*x**2+d)*(a+b*atan(c*x)),x)","\int x^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x^{2}\right)\, dx"," ",0,"Integral(x**m*(a + b*atan(c*x))*(d + e*x**2), x)","F",0
1231,-1,0,0,0.000000," ","integrate(x**m*(a+b*atan(c*x))/(e*x**2+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1232,-1,0,0,0.000000," ","integrate(x**m*(a+b*atan(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1233,-1,0,0,0.000000," ","integrate(x**m*(e*x**2+d)**(5/2)*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1234,-1,0,0,0.000000," ","integrate(x**m*(e*x**2+d)**(3/2)*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1235,0,0,0,0.000000," ","integrate(x**m*(e*x**2+d)**(1/2)*(a+b*atan(c*x)),x)","\int x^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**m*(a + b*atan(c*x))*sqrt(d + e*x**2), x)","F",0
1236,0,0,0,0.000000," ","integrate(x**m*(a+b*atan(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x^{m} \left(a + b \operatorname{atan}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**m*(a + b*atan(c*x))/sqrt(d + e*x**2), x)","F",0
1237,-1,0,0,0.000000," ","integrate(x**m*(a+b*atan(c*x))/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1238,-1,0,0,0.000000," ","integrate(x**m*(a+b*atan(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1239,-1,0,0,0.000000," ","integrate(x**m*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1240,-1,0,0,0.000000," ","integrate(x**(-2-2*p)*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1241,-1,0,0,0.000000," ","integrate(x**(-3-2*p)*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1242,-1,0,0,0.000000," ","integrate(x**(-4-2*p)*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1243,-1,0,0,0.000000," ","integrate(x**(-5-2*p)*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1244,-1,0,0,0.000000," ","integrate(x**(-6-2*p)*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1245,-1,0,0,0.000000," ","integrate(x**(-7-2*p)*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1246,-1,0,0,0.000000," ","integrate(x**(-8-2*p)*(e*x**2+d)**p*(a+b*atan(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1247,1,398,0,3.685752," ","integrate(x**3*(e*x**2+d)*(a+b*atan(c*x))**2,x)","\begin{cases} \frac{a^{2} d x^{4}}{4} + \frac{a^{2} e x^{6}}{6} + \frac{a b d x^{4} \operatorname{atan}{\left(c x \right)}}{2} + \frac{a b e x^{6} \operatorname{atan}{\left(c x \right)}}{3} - \frac{a b d x^{3}}{6 c} - \frac{a b e x^{5}}{15 c} + \frac{a b d x}{2 c^{3}} + \frac{a b e x^{3}}{9 c^{3}} - \frac{a b d \operatorname{atan}{\left(c x \right)}}{2 c^{4}} - \frac{a b e x}{3 c^{5}} + \frac{a b e \operatorname{atan}{\left(c x \right)}}{3 c^{6}} + \frac{b^{2} d x^{4} \operatorname{atan}^{2}{\left(c x \right)}}{4} + \frac{b^{2} e x^{6} \operatorname{atan}^{2}{\left(c x \right)}}{6} - \frac{b^{2} d x^{3} \operatorname{atan}{\left(c x \right)}}{6 c} - \frac{b^{2} e x^{5} \operatorname{atan}{\left(c x \right)}}{15 c} + \frac{b^{2} d x^{2}}{12 c^{2}} + \frac{b^{2} e x^{4}}{60 c^{2}} + \frac{b^{2} d x \operatorname{atan}{\left(c x \right)}}{2 c^{3}} + \frac{b^{2} e x^{3} \operatorname{atan}{\left(c x \right)}}{9 c^{3}} - \frac{b^{2} d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3 c^{4}} - \frac{b^{2} d \operatorname{atan}^{2}{\left(c x \right)}}{4 c^{4}} - \frac{4 b^{2} e x^{2}}{45 c^{4}} - \frac{b^{2} e x \operatorname{atan}{\left(c x \right)}}{3 c^{5}} + \frac{23 b^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{90 c^{6}} + \frac{b^{2} e \operatorname{atan}^{2}{\left(c x \right)}}{6 c^{6}} & \text{for}\: c \neq 0 \\a^{2} \left(\frac{d x^{4}}{4} + \frac{e x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*x**4/4 + a**2*e*x**6/6 + a*b*d*x**4*atan(c*x)/2 + a*b*e*x**6*atan(c*x)/3 - a*b*d*x**3/(6*c) - a*b*e*x**5/(15*c) + a*b*d*x/(2*c**3) + a*b*e*x**3/(9*c**3) - a*b*d*atan(c*x)/(2*c**4) - a*b*e*x/(3*c**5) + a*b*e*atan(c*x)/(3*c**6) + b**2*d*x**4*atan(c*x)**2/4 + b**2*e*x**6*atan(c*x)**2/6 - b**2*d*x**3*atan(c*x)/(6*c) - b**2*e*x**5*atan(c*x)/(15*c) + b**2*d*x**2/(12*c**2) + b**2*e*x**4/(60*c**2) + b**2*d*x*atan(c*x)/(2*c**3) + b**2*e*x**3*atan(c*x)/(9*c**3) - b**2*d*log(x**2 + c**(-2))/(3*c**4) - b**2*d*atan(c*x)**2/(4*c**4) - 4*b**2*e*x**2/(45*c**4) - b**2*e*x*atan(c*x)/(3*c**5) + 23*b**2*e*log(x**2 + c**(-2))/(90*c**6) + b**2*e*atan(c*x)**2/(6*c**6), Ne(c, 0)), (a**2*(d*x**4/4 + e*x**6/6), True))","A",0
1248,0,0,0,0.000000," ","integrate(x**2*(e*x**2+d)*(a+b*atan(c*x))**2,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))**2*(d + e*x**2), x)","F",0
1249,1,296,0,2.179928," ","integrate(x*(e*x**2+d)*(a+b*atan(c*x))**2,x)","\begin{cases} \frac{a^{2} d x^{2}}{2} + \frac{a^{2} e x^{4}}{4} + a b d x^{2} \operatorname{atan}{\left(c x \right)} + \frac{a b e x^{4} \operatorname{atan}{\left(c x \right)}}{2} - \frac{a b d x}{c} - \frac{a b e x^{3}}{6 c} + \frac{a b d \operatorname{atan}{\left(c x \right)}}{c^{2}} + \frac{a b e x}{2 c^{3}} - \frac{a b e \operatorname{atan}{\left(c x \right)}}{2 c^{4}} + \frac{b^{2} d x^{2} \operatorname{atan}^{2}{\left(c x \right)}}{2} + \frac{b^{2} e x^{4} \operatorname{atan}^{2}{\left(c x \right)}}{4} - \frac{b^{2} d x \operatorname{atan}{\left(c x \right)}}{c} - \frac{b^{2} e x^{3} \operatorname{atan}{\left(c x \right)}}{6 c} + \frac{b^{2} d \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{2}} + \frac{b^{2} d \operatorname{atan}^{2}{\left(c x \right)}}{2 c^{2}} + \frac{b^{2} e x^{2}}{12 c^{2}} + \frac{b^{2} e x \operatorname{atan}{\left(c x \right)}}{2 c^{3}} - \frac{b^{2} e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3 c^{4}} - \frac{b^{2} e \operatorname{atan}^{2}{\left(c x \right)}}{4 c^{4}} & \text{for}\: c \neq 0 \\a^{2} \left(\frac{d x^{2}}{2} + \frac{e x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*x**2/2 + a**2*e*x**4/4 + a*b*d*x**2*atan(c*x) + a*b*e*x**4*atan(c*x)/2 - a*b*d*x/c - a*b*e*x**3/(6*c) + a*b*d*atan(c*x)/c**2 + a*b*e*x/(2*c**3) - a*b*e*atan(c*x)/(2*c**4) + b**2*d*x**2*atan(c*x)**2/2 + b**2*e*x**4*atan(c*x)**2/4 - b**2*d*x*atan(c*x)/c - b**2*e*x**3*atan(c*x)/(6*c) + b**2*d*log(x**2 + c**(-2))/(2*c**2) + b**2*d*atan(c*x)**2/(2*c**2) + b**2*e*x**2/(12*c**2) + b**2*e*x*atan(c*x)/(2*c**3) - b**2*e*log(x**2 + c**(-2))/(3*c**4) - b**2*e*atan(c*x)**2/(4*c**4), Ne(c, 0)), (a**2*(d*x**2/2 + e*x**4/4), True))","A",0
1250,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*atan(c*x))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2), x)","F",0
1251,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*atan(c*x))**2/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2)/x, x)","F",0
1252,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*atan(c*x))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2)/x**2, x)","F",0
1253,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*atan(c*x))**2/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2)/x**3, x)","F",0
1254,1,758,0,7.494646," ","integrate(x**3*(e*x**2+d)**2*(a+b*atan(c*x))**2,x)","\begin{cases} \frac{a^{2} d^{2} x^{4}}{4} + \frac{a^{2} d e x^{6}}{3} + \frac{a^{2} e^{2} x^{8}}{8} + \frac{a b d^{2} x^{4} \operatorname{atan}{\left(c x \right)}}{2} + \frac{2 a b d e x^{6} \operatorname{atan}{\left(c x \right)}}{3} + \frac{a b e^{2} x^{8} \operatorname{atan}{\left(c x \right)}}{4} - \frac{a b d^{2} x^{3}}{6 c} - \frac{2 a b d e x^{5}}{15 c} - \frac{a b e^{2} x^{7}}{28 c} + \frac{a b d^{2} x}{2 c^{3}} + \frac{2 a b d e x^{3}}{9 c^{3}} + \frac{a b e^{2} x^{5}}{20 c^{3}} - \frac{a b d^{2} \operatorname{atan}{\left(c x \right)}}{2 c^{4}} - \frac{2 a b d e x}{3 c^{5}} - \frac{a b e^{2} x^{3}}{12 c^{5}} + \frac{2 a b d e \operatorname{atan}{\left(c x \right)}}{3 c^{6}} + \frac{a b e^{2} x}{4 c^{7}} - \frac{a b e^{2} \operatorname{atan}{\left(c x \right)}}{4 c^{8}} + \frac{b^{2} d^{2} x^{4} \operatorname{atan}^{2}{\left(c x \right)}}{4} + \frac{b^{2} d e x^{6} \operatorname{atan}^{2}{\left(c x \right)}}{3} + \frac{b^{2} e^{2} x^{8} \operatorname{atan}^{2}{\left(c x \right)}}{8} - \frac{b^{2} d^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{6 c} - \frac{2 b^{2} d e x^{5} \operatorname{atan}{\left(c x \right)}}{15 c} - \frac{b^{2} e^{2} x^{7} \operatorname{atan}{\left(c x \right)}}{28 c} + \frac{b^{2} d^{2} x^{2}}{12 c^{2}} + \frac{b^{2} d e x^{4}}{30 c^{2}} + \frac{b^{2} e^{2} x^{6}}{168 c^{2}} + \frac{b^{2} d^{2} x \operatorname{atan}{\left(c x \right)}}{2 c^{3}} + \frac{2 b^{2} d e x^{3} \operatorname{atan}{\left(c x \right)}}{9 c^{3}} + \frac{b^{2} e^{2} x^{5} \operatorname{atan}{\left(c x \right)}}{20 c^{3}} - \frac{b^{2} d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3 c^{4}} - \frac{b^{2} d^{2} \operatorname{atan}^{2}{\left(c x \right)}}{4 c^{4}} - \frac{8 b^{2} d e x^{2}}{45 c^{4}} - \frac{3 b^{2} e^{2} x^{4}}{140 c^{4}} - \frac{2 b^{2} d e x \operatorname{atan}{\left(c x \right)}}{3 c^{5}} - \frac{b^{2} e^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{12 c^{5}} + \frac{23 b^{2} d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{45 c^{6}} + \frac{b^{2} d e \operatorname{atan}^{2}{\left(c x \right)}}{3 c^{6}} + \frac{71 b^{2} e^{2} x^{2}}{840 c^{6}} + \frac{b^{2} e^{2} x \operatorname{atan}{\left(c x \right)}}{4 c^{7}} - \frac{22 b^{2} e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{105 c^{8}} - \frac{b^{2} e^{2} \operatorname{atan}^{2}{\left(c x \right)}}{8 c^{8}} & \text{for}\: c \neq 0 \\a^{2} \left(\frac{d^{2} x^{4}}{4} + \frac{d e x^{6}}{3} + \frac{e^{2} x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**2*x**4/4 + a**2*d*e*x**6/3 + a**2*e**2*x**8/8 + a*b*d**2*x**4*atan(c*x)/2 + 2*a*b*d*e*x**6*atan(c*x)/3 + a*b*e**2*x**8*atan(c*x)/4 - a*b*d**2*x**3/(6*c) - 2*a*b*d*e*x**5/(15*c) - a*b*e**2*x**7/(28*c) + a*b*d**2*x/(2*c**3) + 2*a*b*d*e*x**3/(9*c**3) + a*b*e**2*x**5/(20*c**3) - a*b*d**2*atan(c*x)/(2*c**4) - 2*a*b*d*e*x/(3*c**5) - a*b*e**2*x**3/(12*c**5) + 2*a*b*d*e*atan(c*x)/(3*c**6) + a*b*e**2*x/(4*c**7) - a*b*e**2*atan(c*x)/(4*c**8) + b**2*d**2*x**4*atan(c*x)**2/4 + b**2*d*e*x**6*atan(c*x)**2/3 + b**2*e**2*x**8*atan(c*x)**2/8 - b**2*d**2*x**3*atan(c*x)/(6*c) - 2*b**2*d*e*x**5*atan(c*x)/(15*c) - b**2*e**2*x**7*atan(c*x)/(28*c) + b**2*d**2*x**2/(12*c**2) + b**2*d*e*x**4/(30*c**2) + b**2*e**2*x**6/(168*c**2) + b**2*d**2*x*atan(c*x)/(2*c**3) + 2*b**2*d*e*x**3*atan(c*x)/(9*c**3) + b**2*e**2*x**5*atan(c*x)/(20*c**3) - b**2*d**2*log(x**2 + c**(-2))/(3*c**4) - b**2*d**2*atan(c*x)**2/(4*c**4) - 8*b**2*d*e*x**2/(45*c**4) - 3*b**2*e**2*x**4/(140*c**4) - 2*b**2*d*e*x*atan(c*x)/(3*c**5) - b**2*e**2*x**3*atan(c*x)/(12*c**5) + 23*b**2*d*e*log(x**2 + c**(-2))/(45*c**6) + b**2*d*e*atan(c*x)**2/(3*c**6) + 71*b**2*e**2*x**2/(840*c**6) + b**2*e**2*x*atan(c*x)/(4*c**7) - 22*b**2*e**2*log(x**2 + c**(-2))/(105*c**8) - b**2*e**2*atan(c*x)**2/(8*c**8), Ne(c, 0)), (a**2*(d**2*x**4/4 + d*e*x**6/3 + e**2*x**8/8), True))","A",0
1255,0,0,0,0.000000," ","integrate(x**2*(e*x**2+d)**2*(a+b*atan(c*x))**2,x)","\int x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))**2*(d + e*x**2)**2, x)","F",0
1256,1,575,0,4.794515," ","integrate(x*(e*x**2+d)**2*(a+b*atan(c*x))**2,x)","\begin{cases} \frac{a^{2} d^{2} x^{2}}{2} + \frac{a^{2} d e x^{4}}{2} + \frac{a^{2} e^{2} x^{6}}{6} + a b d^{2} x^{2} \operatorname{atan}{\left(c x \right)} + a b d e x^{4} \operatorname{atan}{\left(c x \right)} + \frac{a b e^{2} x^{6} \operatorname{atan}{\left(c x \right)}}{3} - \frac{a b d^{2} x}{c} - \frac{a b d e x^{3}}{3 c} - \frac{a b e^{2} x^{5}}{15 c} + \frac{a b d^{2} \operatorname{atan}{\left(c x \right)}}{c^{2}} + \frac{a b d e x}{c^{3}} + \frac{a b e^{2} x^{3}}{9 c^{3}} - \frac{a b d e \operatorname{atan}{\left(c x \right)}}{c^{4}} - \frac{a b e^{2} x}{3 c^{5}} + \frac{a b e^{2} \operatorname{atan}{\left(c x \right)}}{3 c^{6}} + \frac{b^{2} d^{2} x^{2} \operatorname{atan}^{2}{\left(c x \right)}}{2} + \frac{b^{2} d e x^{4} \operatorname{atan}^{2}{\left(c x \right)}}{2} + \frac{b^{2} e^{2} x^{6} \operatorname{atan}^{2}{\left(c x \right)}}{6} - \frac{b^{2} d^{2} x \operatorname{atan}{\left(c x \right)}}{c} - \frac{b^{2} d e x^{3} \operatorname{atan}{\left(c x \right)}}{3 c} - \frac{b^{2} e^{2} x^{5} \operatorname{atan}{\left(c x \right)}}{15 c} + \frac{b^{2} d^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{2 c^{2}} + \frac{b^{2} d^{2} \operatorname{atan}^{2}{\left(c x \right)}}{2 c^{2}} + \frac{b^{2} d e x^{2}}{6 c^{2}} + \frac{b^{2} e^{2} x^{4}}{60 c^{2}} + \frac{b^{2} d e x \operatorname{atan}{\left(c x \right)}}{c^{3}} + \frac{b^{2} e^{2} x^{3} \operatorname{atan}{\left(c x \right)}}{9 c^{3}} - \frac{2 b^{2} d e \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{3 c^{4}} - \frac{b^{2} d e \operatorname{atan}^{2}{\left(c x \right)}}{2 c^{4}} - \frac{4 b^{2} e^{2} x^{2}}{45 c^{4}} - \frac{b^{2} e^{2} x \operatorname{atan}{\left(c x \right)}}{3 c^{5}} + \frac{23 b^{2} e^{2} \log{\left(x^{2} + \frac{1}{c^{2}} \right)}}{90 c^{6}} + \frac{b^{2} e^{2} \operatorname{atan}^{2}{\left(c x \right)}}{6 c^{6}} & \text{for}\: c \neq 0 \\a^{2} \left(\frac{d^{2} x^{2}}{2} + \frac{d e x^{4}}{2} + \frac{e^{2} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**2*x**2/2 + a**2*d*e*x**4/2 + a**2*e**2*x**6/6 + a*b*d**2*x**2*atan(c*x) + a*b*d*e*x**4*atan(c*x) + a*b*e**2*x**6*atan(c*x)/3 - a*b*d**2*x/c - a*b*d*e*x**3/(3*c) - a*b*e**2*x**5/(15*c) + a*b*d**2*atan(c*x)/c**2 + a*b*d*e*x/c**3 + a*b*e**2*x**3/(9*c**3) - a*b*d*e*atan(c*x)/c**4 - a*b*e**2*x/(3*c**5) + a*b*e**2*atan(c*x)/(3*c**6) + b**2*d**2*x**2*atan(c*x)**2/2 + b**2*d*e*x**4*atan(c*x)**2/2 + b**2*e**2*x**6*atan(c*x)**2/6 - b**2*d**2*x*atan(c*x)/c - b**2*d*e*x**3*atan(c*x)/(3*c) - b**2*e**2*x**5*atan(c*x)/(15*c) + b**2*d**2*log(x**2 + c**(-2))/(2*c**2) + b**2*d**2*atan(c*x)**2/(2*c**2) + b**2*d*e*x**2/(6*c**2) + b**2*e**2*x**4/(60*c**2) + b**2*d*e*x*atan(c*x)/c**3 + b**2*e**2*x**3*atan(c*x)/(9*c**3) - 2*b**2*d*e*log(x**2 + c**(-2))/(3*c**4) - b**2*d*e*atan(c*x)**2/(2*c**4) - 4*b**2*e**2*x**2/(45*c**4) - b**2*e**2*x*atan(c*x)/(3*c**5) + 23*b**2*e**2*log(x**2 + c**(-2))/(90*c**6) + b**2*e**2*atan(c*x)**2/(6*c**6), Ne(c, 0)), (a**2*(d**2*x**2/2 + d*e*x**4/2 + e**2*x**6/6), True))","A",0
1257,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))**2,x)","\int \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)^{2}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2)**2, x)","F",0
1258,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))**2/x,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2)**2/x, x)","F",0
1259,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2)**2/x**2, x)","F",0
1260,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*atan(c*x))**2/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2} \left(d + e x^{2}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2*(d + e*x**2)**2/x**3, x)","F",0
1261,0,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))**2/(e*x**2+d),x)","\int \frac{x^{3} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x^{2}}\, dx"," ",0,"Integral(x**3*(a + b*atan(c*x))**2/(d + e*x**2), x)","F",0
1262,0,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**2/(e*x**2+d),x)","\int \frac{x^{2} \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x^{2}}\, dx"," ",0,"Integral(x**2*(a + b*atan(c*x))**2/(d + e*x**2), x)","F",0
1263,0,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))**2/(e*x**2+d),x)","\int \frac{x \left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x^{2}}\, dx"," ",0,"Integral(x*(a + b*atan(c*x))**2/(d + e*x**2), x)","F",0
1264,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/(e*x**2+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{d + e x^{2}}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(d + e*x**2), x)","F",0
1265,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x/(e*x**2+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(x*(d + e*x**2)), x)","F",0
1266,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**2/(e*x**2+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x^{2} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(x**2*(d + e*x**2)), x)","F",0
1267,0,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**3/(e*x**2+d),x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right)^{2}}{x^{3} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*atan(c*x))**2/(x**3*(d + e*x**2)), x)","F",0
1268,-1,0,0,0.000000," ","integrate(x**3*(a+b*atan(c*x))**2/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1269,-1,0,0,0.000000," ","integrate(x**2*(a+b*atan(c*x))**2/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1270,-1,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))**2/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1271,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1272,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1273,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**2/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1274,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))**2/x**3/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1275,1,107,0,4.641079," ","integrate(x**4*atan(x)*ln(x**2+1),x)","\frac{x^{5} \log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{5} - \frac{2 x^{5} \operatorname{atan}{\left(x \right)}}{25} - \frac{x^{4} \log{\left(x^{2} + 1 \right)}}{20} + \frac{9 x^{4}}{200} + \frac{2 x^{3} \operatorname{atan}{\left(x \right)}}{15} + \frac{x^{2} \log{\left(x^{2} + 1 \right)}}{10} - \frac{77 x^{2}}{300} - \frac{2 x \operatorname{atan}{\left(x \right)}}{5} - \frac{\log{\left(x^{2} + 1 \right)}^{2}}{20} + \frac{137 \log{\left(x^{2} + 1 \right)}}{300} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{5}"," ",0,"x**5*log(x**2 + 1)*atan(x)/5 - 2*x**5*atan(x)/25 - x**4*log(x**2 + 1)/20 + 9*x**4/200 + 2*x**3*atan(x)/15 + x**2*log(x**2 + 1)/10 - 77*x**2/300 - 2*x*atan(x)/5 - log(x**2 + 1)**2/20 + 137*log(x**2 + 1)/300 + atan(x)**2/5","A",0
1276,1,83,0,2.849709," ","integrate(x**3*atan(x)*ln(x**2+1),x)","\frac{x^{4} \log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{4} - \frac{x^{4} \operatorname{atan}{\left(x \right)}}{8} - \frac{x^{3} \log{\left(x^{2} + 1 \right)}}{12} + \frac{7 x^{3}}{72} + \frac{x^{2} \operatorname{atan}{\left(x \right)}}{4} + \frac{x \log{\left(x^{2} + 1 \right)}}{4} - \frac{25 x}{24} - \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{4} + \frac{25 \operatorname{atan}{\left(x \right)}}{24}"," ",0,"x**4*log(x**2 + 1)*atan(x)/4 - x**4*atan(x)/8 - x**3*log(x**2 + 1)/12 + 7*x**3/72 + x**2*atan(x)/4 + x*log(x**2 + 1)/4 - 25*x/24 - log(x**2 + 1)*atan(x)/4 + 25*atan(x)/24","A",0
1277,1,78,0,1.800615," ","integrate(x**2*atan(x)*ln(x**2+1),x)","\frac{x^{3} \log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{3} - \frac{2 x^{3} \operatorname{atan}{\left(x \right)}}{9} - \frac{x^{2} \log{\left(x^{2} + 1 \right)}}{6} + \frac{5 x^{2}}{18} + \frac{2 x \operatorname{atan}{\left(x \right)}}{3} + \frac{\log{\left(x^{2} + 1 \right)}^{2}}{12} - \frac{11 \log{\left(x^{2} + 1 \right)}}{18} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{3}"," ",0,"x**3*log(x**2 + 1)*atan(x)/3 - 2*x**3*atan(x)/9 - x**2*log(x**2 + 1)/6 + 5*x**2/18 + 2*x*atan(x)/3 + log(x**2 + 1)**2/12 - 11*log(x**2 + 1)/18 - atan(x)**2/3","A",0
1278,1,56,0,1.056387," ","integrate(x*atan(x)*ln(x**2+1),x)","\frac{x^{2} \log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{2} - \frac{x^{2} \operatorname{atan}{\left(x \right)}}{2} - \frac{x \log{\left(x^{2} + 1 \right)}}{2} + \frac{3 x}{2} + \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{2} - \frac{3 \operatorname{atan}{\left(x \right)}}{2}"," ",0,"x**2*log(x**2 + 1)*atan(x)/2 - x**2*atan(x)/2 - x*log(x**2 + 1)/2 + 3*x/2 + log(x**2 + 1)*atan(x)/2 - 3*atan(x)/2","A",0
1279,1,39,0,0.587549," ","integrate(atan(x)*ln(x**2+1),x)","x \log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)} - 2 x \operatorname{atan}{\left(x \right)} - \frac{\log{\left(x^{2} + 1 \right)}^{2}}{4} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}^{2}{\left(x \right)}"," ",0,"x*log(x**2 + 1)*atan(x) - 2*x*atan(x) - log(x**2 + 1)**2/4 + log(x**2 + 1) + atan(x)**2","A",0
1280,0,0,0,0.000000," ","integrate(atan(x)*ln(x**2+1)/x,x)","\int \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{x}\, dx"," ",0,"Integral(log(x**2 + 1)*atan(x)/x, x)","F",0
1281,1,37,0,83.960580," ","integrate(atan(x)*ln(x**2+1)/x**2,x)","- \frac{\log{\left(x^{2} + 1 \right)}^{2}}{4} + \operatorname{atan}^{2}{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(x^{2} e^{i \pi}\right)}{2} - \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{x}"," ",0,"-log(x**2 + 1)**2/4 + atan(x)**2 - polylog(2, x**2*exp_polar(I*pi))/2 - log(x**2 + 1)*atan(x)/x","C",0
1282,0,0,0,0.000000," ","integrate(atan(x)*ln(x**2+1)/x**3,x)","\int \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{x^{3}}\, dx"," ",0,"Integral(log(x**2 + 1)*atan(x)/x**3, x)","F",0
1283,1,97,0,28.087687," ","integrate(atan(x)*ln(x**2+1)/x**4,x)","\frac{2 \log{\left(x \right)}}{3} + \frac{\log{\left(2 x^{2} \right)}}{6} + \frac{\log{\left(x^{2} + 1 \right)}^{2}}{12} - \frac{\log{\left(x^{2} + 1 \right)}}{3} - \frac{\log{\left(2 x^{2} + 2 \right)}}{6} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{3} + \frac{\operatorname{Li}_{2}\left(x^{2} e^{i \pi}\right)}{6} - \frac{2 \operatorname{atan}{\left(x \right)}}{3 x} - \frac{\log{\left(x^{2} + 1 \right)}}{6 x^{2}} - \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{3 x^{3}}"," ",0,"2*log(x)/3 + log(2*x**2)/6 + log(x**2 + 1)**2/12 - log(x**2 + 1)/3 - log(2*x**2 + 2)/6 - atan(x)**2/3 + polylog(2, x**2*exp_polar(I*pi))/6 - 2*atan(x)/(3*x) - log(x**2 + 1)/(6*x**2) - log(x**2 + 1)*atan(x)/(3*x**3)","C",0
1284,0,0,0,0.000000," ","integrate(atan(x)*ln(x**2+1)/x**5,x)","\int \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{x^{5}}\, dx"," ",0,"Integral(log(x**2 + 1)*atan(x)/x**5, x)","F",0
1285,1,134,0,38.321951," ","integrate(atan(x)*ln(x**2+1)/x**6,x)","- \frac{8 \log{\left(x \right)}}{15} - \frac{\log{\left(x^{2} \right)}}{20} - \frac{\log{\left(2 x^{2} \right)}}{10} - \frac{\log{\left(x^{2} + 1 \right)}^{2}}{20} + \frac{19 \log{\left(x^{2} + 1 \right)}}{60} + \frac{\log{\left(2 x^{2} + 2 \right)}}{10} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{5} - \frac{\operatorname{Li}_{2}\left(x^{2} e^{i \pi}\right)}{10} + \frac{2 \operatorname{atan}{\left(x \right)}}{5 x} + \frac{\log{\left(x^{2} + 1 \right)}}{10 x^{2}} - \frac{7}{60 x^{2}} - \frac{2 \operatorname{atan}{\left(x \right)}}{15 x^{3}} - \frac{\log{\left(x^{2} + 1 \right)}}{20 x^{4}} - \frac{\log{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(x \right)}}{5 x^{5}}"," ",0,"-8*log(x)/15 - log(x**2)/20 - log(2*x**2)/10 - log(x**2 + 1)**2/20 + 19*log(x**2 + 1)/60 + log(2*x**2 + 2)/10 + atan(x)**2/5 - polylog(2, x**2*exp_polar(I*pi))/10 + 2*atan(x)/(5*x) + log(x**2 + 1)/(10*x**2) - 7/(60*x**2) - 2*atan(x)/(15*x**3) - log(x**2 + 1)/(20*x**4) - log(x**2 + 1)*atan(x)/(5*x**5)","C",0
1286,1,338,0,13.492618," ","integrate(x**4*(a+b*atan(c*x))*(d+e*ln(c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{5}}{5} + \frac{a e x^{5} \log{\left(c^{2} x^{2} + 1 \right)}}{5} - \frac{2 a e x^{5}}{25} + \frac{2 a e x^{3}}{15 c^{2}} - \frac{2 a e x}{5 c^{4}} + \frac{2 a e \operatorname{atan}{\left(c x \right)}}{5 c^{5}} + \frac{b d x^{5} \operatorname{atan}{\left(c x \right)}}{5} + \frac{b e x^{5} \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{5} - \frac{2 b e x^{5} \operatorname{atan}{\left(c x \right)}}{25} - \frac{b d x^{4}}{20 c} - \frac{b e x^{4} \log{\left(c^{2} x^{2} + 1 \right)}}{20 c} + \frac{9 b e x^{4}}{200 c} + \frac{2 b e x^{3} \operatorname{atan}{\left(c x \right)}}{15 c^{2}} + \frac{b d x^{2}}{10 c^{3}} + \frac{b e x^{2} \log{\left(c^{2} x^{2} + 1 \right)}}{10 c^{3}} - \frac{77 b e x^{2}}{300 c^{3}} - \frac{2 b e x \operatorname{atan}{\left(c x \right)}}{5 c^{4}} - \frac{b d \log{\left(c^{2} x^{2} + 1 \right)}}{10 c^{5}} - \frac{b e \log{\left(c^{2} x^{2} + 1 \right)}^{2}}{20 c^{5}} + \frac{137 b e \log{\left(c^{2} x^{2} + 1 \right)}}{300 c^{5}} + \frac{b e \operatorname{atan}^{2}{\left(c x \right)}}{5 c^{5}} & \text{for}\: c \neq 0 \\\frac{a d x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**5/5 + a*e*x**5*log(c**2*x**2 + 1)/5 - 2*a*e*x**5/25 + 2*a*e*x**3/(15*c**2) - 2*a*e*x/(5*c**4) + 2*a*e*atan(c*x)/(5*c**5) + b*d*x**5*atan(c*x)/5 + b*e*x**5*log(c**2*x**2 + 1)*atan(c*x)/5 - 2*b*e*x**5*atan(c*x)/25 - b*d*x**4/(20*c) - b*e*x**4*log(c**2*x**2 + 1)/(20*c) + 9*b*e*x**4/(200*c) + 2*b*e*x**3*atan(c*x)/(15*c**2) + b*d*x**2/(10*c**3) + b*e*x**2*log(c**2*x**2 + 1)/(10*c**3) - 77*b*e*x**2/(300*c**3) - 2*b*e*x*atan(c*x)/(5*c**4) - b*d*log(c**2*x**2 + 1)/(10*c**5) - b*e*log(c**2*x**2 + 1)**2/(20*c**5) + 137*b*e*log(c**2*x**2 + 1)/(300*c**5) + b*e*atan(c*x)**2/(5*c**5), Ne(c, 0)), (a*d*x**5/5, True))","A",0
1287,1,279,0,8.516618," ","integrate(x**3*(a+b*atan(c*x))*(d+e*ln(c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{4}}{4} + \frac{a e x^{4} \log{\left(c^{2} x^{2} + 1 \right)}}{4} - \frac{a e x^{4}}{8} + \frac{a e x^{2}}{4 c^{2}} - \frac{a e \log{\left(c^{2} x^{2} + 1 \right)}}{4 c^{4}} + \frac{b d x^{4} \operatorname{atan}{\left(c x \right)}}{4} + \frac{b e x^{4} \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{4} - \frac{b e x^{4} \operatorname{atan}{\left(c x \right)}}{8} - \frac{b d x^{3}}{12 c} - \frac{b e x^{3} \log{\left(c^{2} x^{2} + 1 \right)}}{12 c} + \frac{7 b e x^{3}}{72 c} + \frac{b e x^{2} \operatorname{atan}{\left(c x \right)}}{4 c^{2}} + \frac{b d x}{4 c^{3}} + \frac{b e x \log{\left(c^{2} x^{2} + 1 \right)}}{4 c^{3}} - \frac{25 b e x}{24 c^{3}} - \frac{b d \operatorname{atan}{\left(c x \right)}}{4 c^{4}} - \frac{b e \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{4 c^{4}} + \frac{25 b e \operatorname{atan}{\left(c x \right)}}{24 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**4/4 + a*e*x**4*log(c**2*x**2 + 1)/4 - a*e*x**4/8 + a*e*x**2/(4*c**2) - a*e*log(c**2*x**2 + 1)/(4*c**4) + b*d*x**4*atan(c*x)/4 + b*e*x**4*log(c**2*x**2 + 1)*atan(c*x)/4 - b*e*x**4*atan(c*x)/8 - b*d*x**3/(12*c) - b*e*x**3*log(c**2*x**2 + 1)/(12*c) + 7*b*e*x**3/(72*c) + b*e*x**2*atan(c*x)/(4*c**2) + b*d*x/(4*c**3) + b*e*x*log(c**2*x**2 + 1)/(4*c**3) - 25*b*e*x/(24*c**3) - b*d*atan(c*x)/(4*c**4) - b*e*log(c**2*x**2 + 1)*atan(c*x)/(4*c**4) + 25*b*e*atan(c*x)/(24*c**4), Ne(c, 0)), (a*d*x**4/4, True))","A",0
1288,1,258,0,5.699340," ","integrate(x**2*(a+b*atan(c*x))*(d+e*ln(c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{3}}{3} + \frac{a e x^{3} \log{\left(c^{2} x^{2} + 1 \right)}}{3} - \frac{2 a e x^{3}}{9} + \frac{2 a e x}{3 c^{2}} - \frac{2 a e \operatorname{atan}{\left(c x \right)}}{3 c^{3}} + \frac{b d x^{3} \operatorname{atan}{\left(c x \right)}}{3} + \frac{b e x^{3} \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{3} - \frac{2 b e x^{3} \operatorname{atan}{\left(c x \right)}}{9} - \frac{b d x^{2}}{6 c} - \frac{b e x^{2} \log{\left(c^{2} x^{2} + 1 \right)}}{6 c} + \frac{5 b e x^{2}}{18 c} + \frac{2 b e x \operatorname{atan}{\left(c x \right)}}{3 c^{2}} + \frac{b d \log{\left(c^{2} x^{2} + 1 \right)}}{6 c^{3}} + \frac{b e \log{\left(c^{2} x^{2} + 1 \right)}^{2}}{12 c^{3}} - \frac{11 b e \log{\left(c^{2} x^{2} + 1 \right)}}{18 c^{3}} - \frac{b e \operatorname{atan}^{2}{\left(c x \right)}}{3 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**3/3 + a*e*x**3*log(c**2*x**2 + 1)/3 - 2*a*e*x**3/9 + 2*a*e*x/(3*c**2) - 2*a*e*atan(c*x)/(3*c**3) + b*d*x**3*atan(c*x)/3 + b*e*x**3*log(c**2*x**2 + 1)*atan(c*x)/3 - 2*b*e*x**3*atan(c*x)/9 - b*d*x**2/(6*c) - b*e*x**2*log(c**2*x**2 + 1)/(6*c) + 5*b*e*x**2/(18*c) + 2*b*e*x*atan(c*x)/(3*c**2) + b*d*log(c**2*x**2 + 1)/(6*c**3) + b*e*log(c**2*x**2 + 1)**2/(12*c**3) - 11*b*e*log(c**2*x**2 + 1)/(18*c**3) - b*e*atan(c*x)**2/(3*c**3), Ne(c, 0)), (a*d*x**3/3, True))","A",0
1289,1,202,0,3.309990," ","integrate(x*(a+b*atan(c*x))*(d+e*ln(c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{2}}{2} + \frac{a e x^{2} \log{\left(c^{2} x^{2} + 1 \right)}}{2} - \frac{a e x^{2}}{2} + \frac{a e \log{\left(c^{2} x^{2} + 1 \right)}}{2 c^{2}} + \frac{b d x^{2} \operatorname{atan}{\left(c x \right)}}{2} + \frac{b e x^{2} \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{2} - \frac{b e x^{2} \operatorname{atan}{\left(c x \right)}}{2} - \frac{b d x}{2 c} - \frac{b e x \log{\left(c^{2} x^{2} + 1 \right)}}{2 c} + \frac{3 b e x}{2 c} + \frac{b d \operatorname{atan}{\left(c x \right)}}{2 c^{2}} + \frac{b e \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{2 c^{2}} - \frac{3 b e \operatorname{atan}{\left(c x \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**2/2 + a*e*x**2*log(c**2*x**2 + 1)/2 - a*e*x**2/2 + a*e*log(c**2*x**2 + 1)/(2*c**2) + b*d*x**2*atan(c*x)/2 + b*e*x**2*log(c**2*x**2 + 1)*atan(c*x)/2 - b*e*x**2*atan(c*x)/2 - b*d*x/(2*c) - b*e*x*log(c**2*x**2 + 1)/(2*c) + 3*b*e*x/(2*c) + b*d*atan(c*x)/(2*c**2) + b*e*log(c**2*x**2 + 1)*atan(c*x)/(2*c**2) - 3*b*e*atan(c*x)/(2*c**2), Ne(c, 0)), (a*d*x**2/2, True))","A",0
1290,1,148,0,1.941254," ","integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1)),x)","\begin{cases} a d x + a e x \log{\left(c^{2} x^{2} + 1 \right)} - 2 a e x + \frac{2 a e \operatorname{atan}{\left(c x \right)}}{c} + b d x \operatorname{atan}{\left(c x \right)} + b e x \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)} - 2 b e x \operatorname{atan}{\left(c x \right)} - \frac{b d \log{\left(c^{2} x^{2} + 1 \right)}}{2 c} - \frac{b e \log{\left(c^{2} x^{2} + 1 \right)}^{2}}{4 c} + \frac{b e \log{\left(c^{2} x^{2} + 1 \right)}}{c} + \frac{b e \operatorname{atan}^{2}{\left(c x \right)}}{c} & \text{for}\: c \neq 0 \\a d x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x*log(c**2*x**2 + 1) - 2*a*e*x + 2*a*e*atan(c*x)/c + b*d*x*atan(c*x) + b*e*x*log(c**2*x**2 + 1)*atan(c*x) - 2*b*e*x*atan(c*x) - b*d*log(c**2*x**2 + 1)/(2*c) - b*e*log(c**2*x**2 + 1)**2/(4*c) + b*e*log(c**2*x**2 + 1)/c + b*e*atan(c*x)**2/c, Ne(c, 0)), (a*d*x, True))","A",0
1291,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1292,1,160,0,141.613089," ","integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**2,x)","- \frac{a d}{x} + \frac{2 a e \operatorname{atan}{\left(\frac{x}{\sqrt{\frac{1}{c^{2}}}} \right)}}{\sqrt{\frac{1}{c^{2}}}} - \frac{a e \log{\left(c^{2} x^{2} + 1 \right)}}{x} - b c^{3} e \left(\begin{cases} 0 & \text{for}\: c^{2} = 0 \\\frac{\log{\left(c^{2} x^{2} + 1 \right)}^{2}}{4 c^{2}} & \text{otherwise} \end{cases}\right) + 4 b c^{2} e \left(\begin{cases} 0 & \text{for}\: c = 0 \\\frac{\operatorname{atan}^{2}{\left(c x \right)}}{4 c} & \text{otherwise} \end{cases}\right) - \frac{b c d \log{\left(c^{2} + \frac{1}{x^{2}} \right)}}{2} - \frac{b c e \operatorname{Li}_{2}\left(c^{2} x^{2} e^{i \pi}\right)}{2} - \frac{b d \operatorname{atan}{\left(c x \right)}}{x} - \frac{b e \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{x}"," ",0,"-a*d/x + 2*a*e*atan(x/sqrt(c**(-2)))/sqrt(c**(-2)) - a*e*log(c**2*x**2 + 1)/x - b*c**3*e*Piecewise((0, Eq(c**2, 0)), (log(c**2*x**2 + 1)**2/(4*c**2), True)) + 4*b*c**2*e*Piecewise((0, Eq(c, 0)), (atan(c*x)**2/(4*c), True)) - b*c*d*log(c**2 + x**(-2))/2 - b*c*e*polylog(2, c**2*x**2*exp_polar(I*pi))/2 - b*d*atan(c*x)/x - b*e*log(c**2*x**2 + 1)*atan(c*x)/x","A",0
1293,0,0,0,0.000000," ","integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**3,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e \log{\left(c^{2} x^{2} + 1 \right)}\right)}{x^{3}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*log(c**2*x**2 + 1))/x**3, x)","F",0
1294,1,428,0,51.578518," ","integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**4,x)","- \frac{2 a c^{2} e \operatorname{atan}{\left(\frac{x}{\sqrt{\frac{1}{c^{2}}}} \right)}}{3 \sqrt{\frac{1}{c^{2}}}} - \frac{2 a c^{2} e}{3 x} - \frac{a d}{3 x^{3}} - \frac{a e \log{\left(c^{2} x^{2} + 1 \right)}}{3 x^{3}} - 2 b c^{7} e \left(\begin{cases} \frac{x^{2}}{12 c^{2}} - \frac{\log{\left(c^{2} x^{2} + 1 \right)}}{12 c^{4}} & \text{for}\: c = 0 \\\frac{\log{\left(c^{2} x^{2} + 1 \right)}^{2}}{24 c^{4}} & \text{otherwise} \end{cases}\right) + \frac{b c^{5} d \left(\begin{cases} x^{2} & \text{for}\: c^{2} = 0 \\\frac{\log{\left(c^{2} x^{2} + 1 \right)}}{c^{2}} & \text{otherwise} \end{cases}\right)}{6} + \frac{b c^{5} e \left(\begin{cases} x^{2} & \text{for}\: c^{2} = 0 \\\frac{\log{\left(c^{2} x^{2} + 1 \right)}}{c^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c^{2} x^{2} + 1 \right)}}{6} - \frac{b c^{3} d \log{\left(x^{2} \right)}}{6} + \frac{b c^{3} e \log{\left(x \right)}}{3} - \frac{b c^{3} e \log{\left(c^{2} x^{2} + 1 \right)}}{6} - \frac{b c^{3} e \log{\left(6 c^{2} \sqrt{\frac{1}{c^{2}}} + \frac{6 \sqrt{\frac{1}{c^{2}}}}{x^{2}} \right)}}{3} + \frac{b c^{3} e \operatorname{atan}^{2}{\left(\frac{x}{\sqrt{\frac{1}{c^{2}}}} \right)}}{3} + \frac{b c^{3} e \operatorname{Li}_{2}\left(c^{2} x^{2} e^{i \pi}\right)}{6} - \frac{2 b c^{2} e \operatorname{atan}{\left(c x \right)} \operatorname{atan}{\left(\frac{x}{\sqrt{\frac{1}{c^{2}}}} \right)}}{3 \sqrt{\frac{1}{c^{2}}}} - \frac{2 b c^{2} e \operatorname{atan}{\left(c x \right)}}{3 x} - \frac{b c d}{6 x^{2}} - \frac{b c e \log{\left(c^{2} x^{2} + 1 \right)}}{6 x^{2}} - \frac{b d \operatorname{atan}{\left(c x \right)}}{3 x^{3}} - \frac{b e \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{3 x^{3}}"," ",0,"-2*a*c**2*e*atan(x/sqrt(c**(-2)))/(3*sqrt(c**(-2))) - 2*a*c**2*e/(3*x) - a*d/(3*x**3) - a*e*log(c**2*x**2 + 1)/(3*x**3) - 2*b*c**7*e*Piecewise((x**2/(12*c**2) - log(c**2*x**2 + 1)/(12*c**4), Eq(c, 0)), (log(c**2*x**2 + 1)**2/(24*c**4), True)) + b*c**5*d*Piecewise((x**2, Eq(c**2, 0)), (log(c**2*x**2 + 1)/c**2, True))/6 + b*c**5*e*Piecewise((x**2, Eq(c**2, 0)), (log(c**2*x**2 + 1)/c**2, True))*log(c**2*x**2 + 1)/6 - b*c**3*d*log(x**2)/6 + b*c**3*e*log(x)/3 - b*c**3*e*log(c**2*x**2 + 1)/6 - b*c**3*e*log(6*c**2*sqrt(c**(-2)) + 6*sqrt(c**(-2))/x**2)/3 + b*c**3*e*atan(x/sqrt(c**(-2)))**2/3 + b*c**3*e*polylog(2, c**2*x**2*exp_polar(I*pi))/6 - 2*b*c**2*e*atan(c*x)*atan(x/sqrt(c**(-2)))/(3*sqrt(c**(-2))) - 2*b*c**2*e*atan(c*x)/(3*x) - b*c*d/(6*x**2) - b*c*e*log(c**2*x**2 + 1)/(6*x**2) - b*d*atan(c*x)/(3*x**3) - b*e*log(c**2*x**2 + 1)*atan(c*x)/(3*x**3)","A",0
1295,0,0,0,0.000000," ","integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**5,x)","\int \frac{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e \log{\left(c^{2} x^{2} + 1 \right)}\right)}{x^{5}}\, dx"," ",0,"Integral((a + b*atan(c*x))*(d + e*log(c**2*x**2 + 1))/x**5, x)","F",0
1296,1,474,0,66.851076," ","integrate((a+b*atan(c*x))*(d+e*ln(c**2*x**2+1))/x**6,x)","\frac{2 a c^{4} e \operatorname{atan}{\left(\frac{x}{\sqrt{\frac{1}{c^{2}}}} \right)}}{5 \sqrt{\frac{1}{c^{2}}}} + \frac{2 a c^{4} e}{5 x} - \frac{2 a c^{2} e}{15 x^{3}} - \frac{a d}{5 x^{5}} - \frac{a e \log{\left(c^{2} x^{2} + 1 \right)}}{5 x^{5}} + 4 b c^{9} e \left(\begin{cases} \frac{x^{2}}{40 c^{2}} - \frac{\log{\left(c^{2} x^{2} + 1 \right)}}{40 c^{4}} & \text{for}\: c = 0 \\\frac{\log{\left(c^{2} x^{2} + 1 \right)}^{2}}{80 c^{4}} & \text{otherwise} \end{cases}\right) - \frac{b c^{7} d \left(\begin{cases} x^{2} & \text{for}\: c^{2} = 0 \\\frac{\log{\left(c^{2} x^{2} + 1 \right)}}{c^{2}} & \text{otherwise} \end{cases}\right)}{10} - \frac{b c^{7} e \left(\begin{cases} x^{2} & \text{for}\: c^{2} = 0 \\\frac{\log{\left(c^{2} x^{2} + 1 \right)}}{c^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c^{2} x^{2} + 1 \right)}}{10} + \frac{b c^{5} d \log{\left(x^{2} \right)}}{10} - \frac{5 b c^{5} e \log{\left(x \right)}}{6} + \frac{5 b c^{5} e \log{\left(c^{2} x^{2} + 1 \right)}}{12} - \frac{b c^{5} e \operatorname{atan}^{2}{\left(\frac{x}{\sqrt{\frac{1}{c^{2}}}} \right)}}{5} - \frac{b c^{5} e \operatorname{Li}_{2}\left(c^{2} x^{2} e^{i \pi}\right)}{10} + \frac{2 b c^{4} e \operatorname{atan}{\left(c x \right)} \operatorname{atan}{\left(\frac{x}{\sqrt{\frac{1}{c^{2}}}} \right)}}{5 \sqrt{\frac{1}{c^{2}}}} + \frac{2 b c^{4} e \operatorname{atan}{\left(c x \right)}}{5 x} + \frac{b c^{3} d}{10 x^{2}} + \frac{b c^{3} e \log{\left(c^{2} x^{2} + 1 \right)}}{10 x^{2}} - \frac{7 b c^{3} e}{60 x^{2}} - \frac{2 b c^{2} e \operatorname{atan}{\left(c x \right)}}{15 x^{3}} - \frac{b c d}{20 x^{4}} - \frac{b c e \log{\left(c^{2} x^{2} + 1 \right)}}{20 x^{4}} - \frac{b d \operatorname{atan}{\left(c x \right)}}{5 x^{5}} - \frac{b e \log{\left(c^{2} x^{2} + 1 \right)} \operatorname{atan}{\left(c x \right)}}{5 x^{5}}"," ",0,"2*a*c**4*e*atan(x/sqrt(c**(-2)))/(5*sqrt(c**(-2))) + 2*a*c**4*e/(5*x) - 2*a*c**2*e/(15*x**3) - a*d/(5*x**5) - a*e*log(c**2*x**2 + 1)/(5*x**5) + 4*b*c**9*e*Piecewise((x**2/(40*c**2) - log(c**2*x**2 + 1)/(40*c**4), Eq(c, 0)), (log(c**2*x**2 + 1)**2/(80*c**4), True)) - b*c**7*d*Piecewise((x**2, Eq(c**2, 0)), (log(c**2*x**2 + 1)/c**2, True))/10 - b*c**7*e*Piecewise((x**2, Eq(c**2, 0)), (log(c**2*x**2 + 1)/c**2, True))*log(c**2*x**2 + 1)/10 + b*c**5*d*log(x**2)/10 - 5*b*c**5*e*log(x)/6 + 5*b*c**5*e*log(c**2*x**2 + 1)/12 - b*c**5*e*atan(x/sqrt(c**(-2)))**2/5 - b*c**5*e*polylog(2, c**2*x**2*exp_polar(I*pi))/10 + 2*b*c**4*e*atan(c*x)*atan(x/sqrt(c**(-2)))/(5*sqrt(c**(-2))) + 2*b*c**4*e*atan(c*x)/(5*x) + b*c**3*d/(10*x**2) + b*c**3*e*log(c**2*x**2 + 1)/(10*x**2) - 7*b*c**3*e/(60*x**2) - 2*b*c**2*e*atan(c*x)/(15*x**3) - b*c*d/(20*x**4) - b*c*e*log(c**2*x**2 + 1)/(20*x**4) - b*d*atan(c*x)/(5*x**5) - b*e*log(c**2*x**2 + 1)*atan(c*x)/(5*x**5)","A",0
1297,-1,0,0,0.000000," ","integrate(x*(a+b*atan(c*x))*(d+e*ln(g*x**2+f)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))*(d+e*ln(g*x**2+f)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))*(d+e*ln(g*x**2+f))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1300,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))*(d+e*ln(g*x**2+f))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1301,-1,0,0,0.000000," ","integrate((a+b*atan(c*x))*(d+e*ln(g*x**2+f))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
