1,1,138,0,5.023699," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)*x**4,x)","i a \left(\begin{cases} \frac{x^{4} \sqrt{a^{2} x^{2} + 1}}{5 a^{2}} - \frac{4 x^{2} \sqrt{a^{2} x^{2} + 1}}{15 a^{4}} + \frac{8 \sqrt{a^{2} x^{2} + 1}}{15 a^{6}} & \text{for}\: a \neq 0 \\\frac{x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{x^{5}}{4 \sqrt{a^{2} x^{2} + 1}} - \frac{x^{3}}{8 a^{2} \sqrt{a^{2} x^{2} + 1}} - \frac{3 x}{8 a^{4} \sqrt{a^{2} x^{2} + 1}} + \frac{3 \operatorname{asinh}{\left(a x \right)}}{8 a^{5}}"," ",0,"I*a*Piecewise((x**4*sqrt(a**2*x**2 + 1)/(5*a**2) - 4*x**2*sqrt(a**2*x**2 + 1)/(15*a**4) + 8*sqrt(a**2*x**2 + 1)/(15*a**6), Ne(a, 0)), (x**6/6, True)) + x**5/(4*sqrt(a**2*x**2 + 1)) - x**3/(8*a**2*sqrt(a**2*x**2 + 1)) - 3*x/(8*a**4*sqrt(a**2*x**2 + 1)) + 3*asinh(a*x)/(8*a**5)","A",0
2,1,119,0,4.494092," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)*x**3,x)","\frac{i a x^{5}}{4 \sqrt{a^{2} x^{2} + 1}} + \begin{cases} \frac{x^{2} \sqrt{a^{2} x^{2} + 1}}{3 a^{2}} - \frac{2 \sqrt{a^{2} x^{2} + 1}}{3 a^{4}} & \text{for}\: a \neq 0 \\\frac{x^{4}}{4} & \text{otherwise} \end{cases} - \frac{i x^{3}}{8 a \sqrt{a^{2} x^{2} + 1}} - \frac{3 i x}{8 a^{3} \sqrt{a^{2} x^{2} + 1}} + \frac{3 i \operatorname{asinh}{\left(a x \right)}}{8 a^{4}}"," ",0,"I*a*x**5/(4*sqrt(a**2*x**2 + 1)) + Piecewise((x**2*sqrt(a**2*x**2 + 1)/(3*a**2) - 2*sqrt(a**2*x**2 + 1)/(3*a**4), Ne(a, 0)), (x**4/4, True)) - I*x**3/(8*a*sqrt(a**2*x**2 + 1)) - 3*I*x/(8*a**3*sqrt(a**2*x**2 + 1)) + 3*I*asinh(a*x)/(8*a**4)","A",0
3,1,75,0,3.212888," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)*x**2,x)","i a \left(\begin{cases} \frac{x^{2} \sqrt{a^{2} x^{2} + 1}}{3 a^{2}} - \frac{2 \sqrt{a^{2} x^{2} + 1}}{3 a^{4}} & \text{for}\: a \neq 0 \\\frac{x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{x \sqrt{a^{2} x^{2} + 1}}{2 a^{2}} - \frac{\operatorname{asinh}{\left(a x \right)}}{2 a^{3}}"," ",0,"I*a*Piecewise((x**2*sqrt(a**2*x**2 + 1)/(3*a**2) - 2*sqrt(a**2*x**2 + 1)/(3*a**4), Ne(a, 0)), (x**4/4, True)) + x*sqrt(a**2*x**2 + 1)/(2*a**2) - asinh(a*x)/(2*a**3)","A",0
4,1,51,0,3.121550," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)*x,x)","\begin{cases} \frac{x^{2}}{2} & \text{for}\: a^{2} = 0 \\\frac{\sqrt{a^{2} x^{2} + 1}}{a^{2}} & \text{otherwise} \end{cases} + \frac{i x \sqrt{a^{2} x^{2} + 1}}{2 a} - \frac{i \operatorname{asinh}{\left(a x \right)}}{2 a^{2}}"," ",0,"Piecewise((x**2/2, Eq(a**2, 0)), (sqrt(a**2*x**2 + 1)/a**2, True)) + I*x*sqrt(a**2*x**2 + 1)/(2*a) - I*asinh(a*x)/(2*a**2)","A",0
5,1,68,0,1.253127," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2),x)","i a \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: a^{2} = 0 \\\frac{\sqrt{a^{2} x^{2} + 1}}{a^{2}} & \text{otherwise} \end{cases}\right) + \begin{cases} \sqrt{- \frac{1}{a^{2}}} \operatorname{asin}{\left(x \sqrt{- a^{2}} \right)} & \text{for}\: a^{2} < 0 \\\sqrt{\frac{1}{a^{2}}} \operatorname{asinh}{\left(x \sqrt{a^{2}} \right)} & \text{for}\: a^{2} > 0 \end{cases}"," ",0,"I*a*Piecewise((x**2/2, Eq(a**2, 0)), (sqrt(a**2*x**2 + 1)/a**2, True)) + Piecewise((sqrt(-1/a**2)*asin(x*sqrt(-a**2)), a**2 < 0), (sqrt(a**(-2))*asinh(x*sqrt(a**2)), a**2 > 0))","A",0
6,1,53,0,3.345590," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)/x,x)","i a \left(\begin{cases} \sqrt{- \frac{1}{a^{2}}} \operatorname{asin}{\left(x \sqrt{- a^{2}} \right)} & \text{for}\: a^{2} < 0 \\\sqrt{\frac{1}{a^{2}}} \operatorname{asinh}{\left(x \sqrt{a^{2}} \right)} & \text{for}\: a^{2} > 0 \end{cases}\right) - \operatorname{asinh}{\left(\frac{1}{a x} \right)}"," ",0,"I*a*Piecewise((sqrt(-1/a**2)*asin(x*sqrt(-a**2)), a**2 < 0), (sqrt(a**(-2))*asinh(x*sqrt(a**2)), a**2 > 0)) - asinh(1/(a*x))","A",0
7,1,26,0,2.302166," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)/x**2,x)","- a \sqrt{1 + \frac{1}{a^{2} x^{2}}} - i a \operatorname{asinh}{\left(\frac{1}{a x} \right)}"," ",0,"-a*sqrt(1 + 1/(a**2*x**2)) - I*a*asinh(1/(a*x))","A",0
8,1,48,0,2.910982," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)/x**3,x)","- i a^{2} \sqrt{1 + \frac{1}{a^{2} x^{2}}} + \frac{a^{2} \operatorname{asinh}{\left(\frac{1}{a x} \right)}}{2} - \frac{a \sqrt{1 + \frac{1}{a^{2} x^{2}}}}{2 x}"," ",0,"-I*a**2*sqrt(1 + 1/(a**2*x**2)) + a**2*asinh(1/(a*x))/2 - a*sqrt(1 + 1/(a**2*x**2))/(2*x)","A",0
9,1,75,0,3.089714," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)/x**4,x)","\frac{2 a^{3} \sqrt{1 + \frac{1}{a^{2} x^{2}}}}{3} + \frac{i a^{3} \operatorname{asinh}{\left(\frac{1}{a x} \right)}}{2} - \frac{i a^{2} \sqrt{1 + \frac{1}{a^{2} x^{2}}}}{2 x} - \frac{a \sqrt{1 + \frac{1}{a^{2} x^{2}}}}{3 x^{2}}"," ",0,"2*a**3*sqrt(1 + 1/(a**2*x**2))/3 + I*a**3*asinh(1/(a*x))/2 - I*a**2*sqrt(1 + 1/(a**2*x**2))/(2*x) - a*sqrt(1 + 1/(a**2*x**2))/(3*x**2)","A",0
10,1,122,0,4.301355," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)/x**5,x)","\frac{2 i a^{4} \sqrt{1 + \frac{1}{a^{2} x^{2}}}}{3} - \frac{3 a^{4} \operatorname{asinh}{\left(\frac{1}{a x} \right)}}{8} + \frac{3 a^{3}}{8 x \sqrt{1 + \frac{1}{a^{2} x^{2}}}} - \frac{i a^{2} \sqrt{1 + \frac{1}{a^{2} x^{2}}}}{3 x^{2}} + \frac{a}{8 x^{3} \sqrt{1 + \frac{1}{a^{2} x^{2}}}} - \frac{1}{4 a x^{5} \sqrt{1 + \frac{1}{a^{2} x^{2}}}}"," ",0,"2*I*a**4*sqrt(1 + 1/(a**2*x**2))/3 - 3*a**4*asinh(1/(a*x))/8 + 3*a**3/(8*x*sqrt(1 + 1/(a**2*x**2))) - I*a**2*sqrt(1 + 1/(a**2*x**2))/(3*x**2) + a/(8*x**3*sqrt(1 + 1/(a**2*x**2))) - 1/(4*a*x**5*sqrt(1 + 1/(a**2*x**2)))","A",0
11,1,42,0,0.125460," ","integrate((1+I*a*x)**2/(a**2*x**2+1)*x**3,x)","- \frac{x^{4}}{4} + \frac{2 i x^{3}}{3 a} + \frac{x^{2}}{a^{2}} - \frac{2 i x}{a^{3}} - \frac{2 \log{\left(i a x - 1 \right)}}{a^{4}}"," ",0,"-x**4/4 + 2*I*x**3/(3*a) + x**2/a**2 - 2*I*x/a**3 - 2*log(I*a*x - 1)/a**4","A",0
12,1,32,0,0.130450," ","integrate((1+I*a*x)**2/(a**2*x**2+1)*x**2,x)","- \frac{x^{3}}{3} + \frac{i x^{2}}{a} + \frac{2 x}{a^{2}} - \frac{2 i \log{\left(i a x - 1 \right)}}{a^{3}}"," ",0,"-x**3/3 + I*x**2/a + 2*x/a**2 - 2*I*log(I*a*x - 1)/a**3","A",0
13,1,24,0,0.104223," ","integrate((1+I*a*x)**2/(a**2*x**2+1)*x,x)","- \frac{x^{2}}{2} + \frac{2 i x}{a} + \frac{2 \log{\left(i a x - 1 \right)}}{a^{2}}"," ",0,"-x**2/2 + 2*I*x/a + 2*log(I*a*x - 1)/a**2","A",0
14,1,14,0,0.105779," ","integrate((1+I*a*x)**2/(a**2*x**2+1),x)","- x + \frac{2 i \log{\left(i a x - 1 \right)}}{a}"," ",0,"-x + 2*I*log(I*a*x - 1)/a","A",0
15,1,17,0,0.151555," ","integrate((1+I*a*x)**2/(a**2*x**2+1)/x,x)","\log{\left(3 a x \right)} - 2 \log{\left(3 a x + 3 i \right)}"," ",0,"log(3*a*x) - 2*log(3*a*x + 3*I)","A",0
16,1,32,0,0.163499," ","integrate((1+I*a*x)**2/(a**2*x**2+1)/x**2,x)","- 2 a \left(- i \log{\left(4 a^{2} x \right)} + i \log{\left(4 a^{2} x + 4 i a \right)}\right) - \frac{1}{x}"," ",0,"-2*a*(-I*log(4*a**2*x) + I*log(4*a**2*x + 4*I*a)) - 1/x","A",0
17,1,42,0,0.185052," ","integrate((1+I*a*x)**2/(a**2*x**2+1)/x**3,x)","- 2 a^{2} \left(\log{\left(4 a^{3} x \right)} - \log{\left(4 a^{3} x + 4 i a^{2} \right)}\right) - \frac{4 i a x + 1}{2 x^{2}}"," ",0,"-2*a**2*(log(4*a**3*x) - log(4*a**3*x + 4*I*a**2)) - (4*I*a*x + 1)/(2*x**2)","A",0
18,1,54,0,0.205576," ","integrate((1+I*a*x)**2/(a**2*x**2+1)/x**4,x)","- 2 a^{3} \left(i \log{\left(4 a^{4} x \right)} - i \log{\left(4 a^{4} x + 4 i a^{3} \right)}\right) - \frac{- 6 a^{2} x^{2} + 3 i a x + 1}{3 x^{3}}"," ",0,"-2*a**3*(I*log(4*a**4*x) - I*log(4*a**4*x + 4*I*a**3)) - (-6*a**2*x**2 + 3*I*a*x + 1)/(3*x**3)","A",0
19,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)*x**3,x)","- i \left(\int \frac{i x^{3}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x^{4}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{6}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{5}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x**3/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x**4/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**6/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**5/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x))","F",0
20,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)*x**2,x)","- i \left(\int \frac{i x^{2}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x^{3}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{5}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{4}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x**2/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x**3/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**5/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**4/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x))","F",0
21,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)*x,x)","- i \left(\int \frac{i x}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x^{2}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{4}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{3}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x**2/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**4/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**3/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x))","F",0
22,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2),x)","- i \left(\int \frac{i}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**3/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**2/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x))","F",0
23,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)/x,x)","- i \left(\int \frac{i}{a^{2} x^{3} \sqrt{a^{2} x^{2} + 1} + x \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x}{a^{2} x^{3} \sqrt{a^{2} x^{2} + 1} + x \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{2} x^{3} \sqrt{a^{2} x^{2} + 1} + x \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{2} x^{3} \sqrt{a^{2} x^{2} + 1} + x \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**3*sqrt(a**2*x**2 + 1) + x*sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x/(a**2*x**3*sqrt(a**2*x**2 + 1) + x*sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**3/(a**2*x**3*sqrt(a**2*x**2 + 1) + x*sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**2/(a**2*x**3*sqrt(a**2*x**2 + 1) + x*sqrt(a**2*x**2 + 1)), x))","F",0
24,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)/x**2,x)","- i \left(\int \frac{i}{a^{2} x^{4} \sqrt{a^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x}{a^{2} x^{4} \sqrt{a^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{2} x^{4} \sqrt{a^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{2} x^{4} \sqrt{a^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**4*sqrt(a**2*x**2 + 1) + x**2*sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x/(a**2*x**4*sqrt(a**2*x**2 + 1) + x**2*sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**3/(a**2*x**4*sqrt(a**2*x**2 + 1) + x**2*sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**2/(a**2*x**4*sqrt(a**2*x**2 + 1) + x**2*sqrt(a**2*x**2 + 1)), x))","F",0
25,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)/x**3,x)","- i \left(\int \frac{i}{a^{2} x^{5} \sqrt{a^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x}{a^{2} x^{5} \sqrt{a^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{2} x^{5} \sqrt{a^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{2} x^{5} \sqrt{a^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**5*sqrt(a**2*x**2 + 1) + x**3*sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x/(a**2*x**5*sqrt(a**2*x**2 + 1) + x**3*sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**3/(a**2*x**5*sqrt(a**2*x**2 + 1) + x**3*sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**2/(a**2*x**5*sqrt(a**2*x**2 + 1) + x**3*sqrt(a**2*x**2 + 1)), x))","F",0
26,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)/x**4,x)","- i \left(\int \frac{i}{a^{2} x^{6} \sqrt{a^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x}{a^{2} x^{6} \sqrt{a^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{2} x^{6} \sqrt{a^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{2} x^{6} \sqrt{a^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**6*sqrt(a**2*x**2 + 1) + x**4*sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x/(a**2*x**6*sqrt(a**2*x**2 + 1) + x**4*sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**3/(a**2*x**6*sqrt(a**2*x**2 + 1) + x**4*sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**2/(a**2*x**6*sqrt(a**2*x**2 + 1) + x**4*sqrt(a**2*x**2 + 1)), x))","F",0
27,1,56,0,0.238861," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2*x**3,x)","\frac{x^{4}}{4} + \frac{4 i}{a^{5} x + i a^{4}} - \frac{4 i x^{3}}{3 a} - \frac{4 x^{2}}{a^{2}} + \frac{12 i x}{a^{3}} + \frac{16 \log{\left(a x + i \right)}}{a^{4}}"," ",0,"x**4/4 + 4*I/(a**5*x + I*a**4) - 4*I*x**3/(3*a) - 4*x**2/a**2 + 12*I*x/a**3 + 16*log(a*x + I)/a**4","A",0
28,1,44,0,0.235125," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2*x**2,x)","\frac{x^{3}}{3} - \frac{4}{a^{4} x + i a^{3}} - \frac{2 i x^{2}}{a} - \frac{8 x}{a^{2}} + \frac{12 i \log{\left(a x + i \right)}}{a^{3}}"," ",0,"x**3/3 - 4/(a**4*x + I*a**3) - 2*I*x**2/a - 8*x/a**2 + 12*I*log(a*x + I)/a**3","A",0
29,1,36,0,0.189570," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2*x,x)","\frac{x^{2}}{2} - \frac{4 i}{a^{3} x + i a^{2}} - \frac{4 i x}{a} - \frac{8 \log{\left(a x + i \right)}}{a^{2}}"," ",0,"x**2/2 - 4*I/(a**3*x + I*a**2) - 4*I*x/a - 8*log(a*x + I)/a**2","A",0
30,1,22,0,0.173171," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2,x)","x + \frac{4}{a^{2} x + i a} - \frac{4 i \log{\left(a x + i \right)}}{a}"," ",0,"x + 4/(a**2*x + I*a) - 4*I*log(a*x + I)/a","A",0
31,1,10,0,0.211496," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2/x,x)","\log{\left(x \right)} + \frac{4 i}{a x + i}"," ",0,"log(x) + 4*I/(a*x + I)","A",0
32,1,44,0,0.297177," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2/x**2,x)","4 a \left(i \log{\left(8 a^{2} x \right)} - i \log{\left(8 a^{2} x + 8 i a \right)}\right) + \frac{5 a x + i}{- a x^{2} - i x}"," ",0,"4*a*(I*log(8*a**2*x) - I*log(8*a**2*x + 8*I*a)) + (5*a*x + I)/(-a*x**2 - I*x)","A",0
33,1,60,0,0.347179," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2/x**3,x)","8 a^{2} \left(- \log{\left(16 a^{3} x \right)} + \log{\left(16 a^{3} x + 16 i a^{2} \right)}\right) + \frac{16 i a^{2} x^{2} - 7 a x + i}{- 2 a x^{3} - 2 i x^{2}}"," ",0,"8*a**2*(-log(16*a**3*x) + log(16*a**3*x + 16*I*a**2)) + (16*I*a**2*x**2 - 7*a*x + I)/(-2*a*x**3 - 2*I*x**2)","A",0
34,1,71,0,0.381918," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2/x**4,x)","12 a^{3} \left(- i \log{\left(24 a^{4} x \right)} + i \log{\left(24 a^{4} x + 24 i a^{3} \right)}\right) + \frac{- 36 a^{3} x^{3} - 18 i a^{2} x^{2} - 5 a x + i}{- 3 a x^{4} - 3 i x^{3}}"," ",0,"12*a**3*(-I*log(24*a**4*x) + I*log(24*a**4*x + 24*I*a**3)) + (-36*a**3*x**3 - 18*I*a**2*x**2 - 5*a*x + I)/(-3*a*x**4 - 3*I*x**3)","A",0
35,0,0,0,0.000000," ","integrate(x**3/(1+I*a*x)*(a**2*x**2+1)**(1/2),x)","- i \int \frac{x^{3} \sqrt{a^{2} x^{2} + 1}}{a x - i}\, dx"," ",0,"-I*Integral(x**3*sqrt(a**2*x**2 + 1)/(a*x - I), x)","F",0
36,0,0,0,0.000000," ","integrate(x**2/(1+I*a*x)*(a**2*x**2+1)**(1/2),x)","- i \int \frac{x^{2} \sqrt{a^{2} x^{2} + 1}}{a x - i}\, dx"," ",0,"-I*Integral(x**2*sqrt(a**2*x**2 + 1)/(a*x - I), x)","F",0
37,0,0,0,0.000000," ","integrate(x/(1+I*a*x)*(a**2*x**2+1)**(1/2),x)","- i \int \frac{x \sqrt{a^{2} x^{2} + 1}}{a x - i}\, dx"," ",0,"-I*Integral(x*sqrt(a**2*x**2 + 1)/(a*x - I), x)","F",0
38,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2),x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a x - i}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a*x - I), x)","F",0
39,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2)/x,x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a x^{2} - i x}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a*x**2 - I*x), x)","F",0
40,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2)/x**2,x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a x^{3} - i x^{2}}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a*x**3 - I*x**2), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2)/x**3,x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a x^{4} - i x^{3}}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a*x**4 - I*x**3), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2)/x**4,x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a x^{5} - i x^{4}}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a*x**5 - I*x**4), x)","F",0
43,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2)/x**5,x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a x^{6} - i x^{5}}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a*x**6 - I*x**5), x)","F",0
44,1,42,0,0.123654," ","integrate(x**3/(1+I*a*x)**2*(a**2*x**2+1),x)","- \frac{x^{4}}{4} - \frac{2 i x^{3}}{3 a} + \frac{x^{2}}{a^{2}} + \frac{2 i x}{a^{3}} - \frac{2 \log{\left(i a x + 1 \right)}}{a^{4}}"," ",0,"-x**4/4 - 2*I*x**3/(3*a) + x**2/a**2 + 2*I*x/a**3 - 2*log(I*a*x + 1)/a**4","A",0
45,1,32,0,0.127908," ","integrate(x**2/(1+I*a*x)**2*(a**2*x**2+1),x)","- \frac{x^{3}}{3} - \frac{i x^{2}}{a} + \frac{2 x}{a^{2}} + \frac{2 i \log{\left(i a x + 1 \right)}}{a^{3}}"," ",0,"-x**3/3 - I*x**2/a + 2*x/a**2 + 2*I*log(I*a*x + 1)/a**3","A",0
46,1,24,0,0.105834," ","integrate(x/(1+I*a*x)**2*(a**2*x**2+1),x)","- \frac{x^{2}}{2} - \frac{2 i x}{a} + \frac{2 \log{\left(i a x + 1 \right)}}{a^{2}}"," ",0,"-x**2/2 - 2*I*x/a + 2*log(I*a*x + 1)/a**2","A",0
47,1,15,0,0.114364," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1),x)","- x - \frac{2 i \log{\left(i a x + 1 \right)}}{a}"," ",0,"-x - 2*I*log(I*a*x + 1)/a","A",0
48,1,17,0,0.150688," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1)/x,x)","\log{\left(3 a x \right)} - 2 \log{\left(3 a x - 3 i \right)}"," ",0,"log(3*a*x) - 2*log(3*a*x - 3*I)","A",0
49,1,32,0,0.155709," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1)/x**2,x)","- 2 a \left(i \log{\left(4 a^{2} x \right)} - i \log{\left(4 a^{2} x - 4 i a \right)}\right) - \frac{1}{x}"," ",0,"-2*a*(I*log(4*a**2*x) - I*log(4*a**2*x - 4*I*a)) - 1/x","A",0
50,1,42,0,0.181635," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1)/x**3,x)","- 2 a^{2} \left(\log{\left(4 a^{3} x \right)} - \log{\left(4 a^{3} x - 4 i a^{2} \right)}\right) - \frac{- 4 i a x + 1}{2 x^{2}}"," ",0,"-2*a**2*(log(4*a**3*x) - log(4*a**3*x - 4*I*a**2)) - (-4*I*a*x + 1)/(2*x**2)","A",0
51,1,54,0,0.208926," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1)/x**4,x)","- 2 a^{3} \left(- i \log{\left(4 a^{4} x \right)} + i \log{\left(4 a^{4} x - 4 i a^{3} \right)}\right) - \frac{- 6 a^{2} x^{2} - 3 i a x + 1}{3 x^{3}}"," ",0,"-2*a**3*(-I*log(4*a**4*x) + I*log(4*a**4*x - 4*I*a**3)) - (-6*a**2*x**2 - 3*I*a*x + 1)/(3*x**3)","A",0
52,0,0,0,0.000000," ","integrate(x**3/(1+I*a*x)**3*(a**2*x**2+1)**(3/2),x)","i \left(\int \frac{x^{3} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx + \int \frac{a^{2} x^{5} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx\right)"," ",0,"I*(Integral(x**3*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x) + Integral(a**2*x**5*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x))","F",0
53,0,0,0,0.000000," ","integrate(x**2/(1+I*a*x)**3*(a**2*x**2+1)**(3/2),x)","i \left(\int \frac{x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx + \int \frac{a^{2} x^{4} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx\right)"," ",0,"I*(Integral(x**2*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x) + Integral(a**2*x**4*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x))","F",0
54,0,0,0,0.000000," ","integrate(x/(1+I*a*x)**3*(a**2*x**2+1)**(3/2),x)","i \left(\int \frac{x \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx + \int \frac{a^{2} x^{3} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx\right)"," ",0,"I*(Integral(x*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x) + Integral(a**2*x**3*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x))","F",0
55,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2),x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x))","F",0
56,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/x,x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} x^{4} - 3 i a^{2} x^{3} - 3 a x^{2} + i x}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{4} - 3 i a^{2} x^{3} - 3 a x^{2} + i x}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**3*x**4 - 3*I*a**2*x**3 - 3*a*x**2 + I*x), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**3*x**4 - 3*I*a**2*x**3 - 3*a*x**2 + I*x), x))","F",0
57,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/x**2,x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} x^{5} - 3 i a^{2} x^{4} - 3 a x^{3} + i x^{2}}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{5} - 3 i a^{2} x^{4} - 3 a x^{3} + i x^{2}}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**3*x**5 - 3*I*a**2*x**4 - 3*a*x**3 + I*x**2), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**3*x**5 - 3*I*a**2*x**4 - 3*a*x**3 + I*x**2), x))","F",0
58,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/x**3,x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} x^{6} - 3 i a^{2} x^{5} - 3 a x^{4} + i x^{3}}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{6} - 3 i a^{2} x^{5} - 3 a x^{4} + i x^{3}}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**3*x**6 - 3*I*a**2*x**5 - 3*a*x**4 + I*x**3), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**3*x**6 - 3*I*a**2*x**5 - 3*a*x**4 + I*x**3), x))","F",0
59,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/x**4,x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} x^{7} - 3 i a^{2} x^{6} - 3 a x^{5} + i x^{4}}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{7} - 3 i a^{2} x^{6} - 3 a x^{5} + i x^{4}}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**3*x**7 - 3*I*a**2*x**6 - 3*a*x**5 + I*x**4), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**3*x**7 - 3*I*a**2*x**6 - 3*a*x**5 + I*x**4), x))","F",0
60,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/x**5,x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} x^{8} - 3 i a^{2} x^{7} - 3 a x^{6} + i x^{5}}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{8} - 3 i a^{2} x^{7} - 3 a x^{6} + i x^{5}}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**3*x**8 - 3*I*a**2*x**7 - 3*a*x**6 + I*x**5), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**3*x**8 - 3*I*a**2*x**7 - 3*a*x**6 + I*x**5), x))","F",0
61,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)*x**2,x)","\int x^{2} \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}\, dx"," ",0,"Integral(x**2*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1)), x)","F",0
62,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)*x,x)","\int x \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}\, dx"," ",0,"Integral(x*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1)), x)","F",0
63,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2),x)","\int \sqrt{\frac{i a x + 1}{\sqrt{a^{2} x^{2} + 1}}}\, dx"," ",0,"Integral(sqrt((I*a*x + 1)/sqrt(a**2*x**2 + 1)), x)","F",0
64,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x}\, dx"," ",0,"Integral(sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))/x, x)","F",0
65,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**2,x)","\int \frac{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))/x**2, x)","F",0
66,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**3,x)","\int \frac{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))/x**3, x)","F",0
67,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**4,x)","\int \frac{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x^{4}}\, dx"," ",0,"Integral(sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))/x**4, x)","F",0
68,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**5,x)","\int \frac{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x^{5}}\, dx"," ",0,"Integral(sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))/x**5, x)","F",0
69,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**6,x)","\int \frac{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x^{6}}\, dx"," ",0,"Integral(sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))/x**6, x)","F",0
70,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)*x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)*x**2,x)","\int x^{2} \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2), x)","F",0
72,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)*x,x)","\int x \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2), x)","F",0
73,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2),x)","\int \left(\frac{i a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(((I*a*x + 1)/sqrt(a**2*x**2 + 1))**(3/2), x)","F",0
74,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x,x)","\int \frac{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)/x, x)","F",0
75,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**2,x)","\int \frac{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)/x**2, x)","F",0
76,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**3,x)","\int \frac{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)/x**3, x)","F",0
77,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**4,x)","\int \frac{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)/x**4, x)","F",0
78,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)*x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)*x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)*x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x,x)","\int \frac{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}{x}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(5/2)/x, x)","F",0
84,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,0,0,0,0.000000," ","integrate(x**3/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2),x)","\int \frac{x^{3}}{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(x**3/sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1)), x)","F",0
89,0,0,0,0.000000," ","integrate(x**2/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2),x)","\int \frac{x^{2}}{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(x**2/sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1)), x)","F",0
90,0,0,0,0.000000," ","integrate(x/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2),x)","\int \frac{x}{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(x/sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1)), x)","F",0
91,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{\frac{i a x + 1}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(1/sqrt((I*a*x + 1)/sqrt(a**2*x**2 + 1)), x)","F",0
92,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x,x)","\int \frac{1}{x \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(1/(x*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))), x)","F",0
93,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**2,x)","\int \frac{1}{x^{2} \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))), x)","F",0
94,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**3,x)","\int \frac{1}{x^{3} \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))), x)","F",0
95,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**4,x)","\int \frac{1}{x^{4} \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))), x)","F",0
96,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)/x**5,x)","\int \frac{1}{x^{5} \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(1/(x**5*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1))), x)","F",0
97,0,0,0,0.000000," ","integrate(x**3/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2),x)","\int \frac{x^{3}}{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2), x)","F",0
98,0,0,0,0.000000," ","integrate(x**2/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2),x)","\int \frac{x^{2}}{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2), x)","F",0
99,0,0,0,0.000000," ","integrate(x/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2),x)","\int \frac{x}{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2), x)","F",0
100,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2),x)","\int \frac{1}{\left(\frac{i a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((I*a*x + 1)/sqrt(a**2*x**2 + 1))**(-3/2), x)","F",0
101,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x,x)","\int \frac{1}{x \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)), x)","F",0
102,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**2,x)","\int \frac{1}{x^{2} \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)), x)","F",0
103,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**3,x)","\int \frac{1}{x^{3} \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)), x)","F",0
104,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**4,x)","\int \frac{1}{x^{4} \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)), x)","F",0
105,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)/x**5,x)","\int \frac{1}{x^{5} \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**5*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2)), x)","F",0
106,0,0,0,0.000000," ","integrate(x**3/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2),x)","\int \frac{x^{3}}{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(5/2), x)","F",0
107,0,0,0,0.000000," ","integrate(x**2/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2),x)","\int \frac{x^{2}}{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(5/2), x)","F",0
108,0,0,0,0.000000," ","integrate(x/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2),x)","\int \frac{x}{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(5/2), x)","F",0
109,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2),x)","\int \frac{1}{\left(\frac{i a x + 1}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(((I*a*x + 1)/sqrt(a**2*x**2 + 1))**(-5/2), x)","F",0
110,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x,x)","\int \frac{1}{x \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(5/2)), x)","F",0
111,0,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**2,x)","\int \frac{1}{x^{2} \left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(5/2)), x)","F",0
112,-1,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(1/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(1/3)*x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,0,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(1/3)*x,x)","\int x \sqrt[3]{\frac{i \left(x - i\right)}{\sqrt{x^{2} + 1}}}\, dx"," ",0,"Integral(x*(I*(x - I)/sqrt(x**2 + 1))**(1/3), x)","F",0
117,0,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(1/3),x)","\int \sqrt[3]{\frac{i x + 1}{\sqrt{x^{2} + 1}}}\, dx"," ",0,"Integral(((I*x + 1)/sqrt(x**2 + 1))**(1/3), x)","F",0
118,0,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(1/3)/x,x)","\int \frac{\sqrt[3]{\frac{i \left(x - i\right)}{\sqrt{x^{2} + 1}}}}{x}\, dx"," ",0,"Integral((I*(x - I)/sqrt(x**2 + 1))**(1/3)/x, x)","F",0
119,0,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(1/3)/x**2,x)","\int \frac{\sqrt[3]{\frac{i \left(x - i\right)}{\sqrt{x^{2} + 1}}}}{x^{2}}\, dx"," ",0,"Integral((I*(x - I)/sqrt(x**2 + 1))**(1/3)/x**2, x)","F",0
120,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(1/3)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(1/3)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(2/3)*x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(2/3)*x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,0,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(2/3)/x,x)","\int \frac{\left(\frac{i \left(x - i\right)}{\sqrt{x^{2} + 1}}\right)^{\frac{2}{3}}}{x}\, dx"," ",0,"Integral((I*(x - I)/sqrt(x**2 + 1))**(2/3)/x, x)","F",0
126,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(2/3)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate(((1+I*x)/(x**2+1)**(1/2))**(2/3)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/4)*x**2,x)","\int x^{2} \sqrt[4]{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}\, dx"," ",0,"Integral(x**2*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(1/4), x)","F",0
129,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/4)*x,x)","\int x \sqrt[4]{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}\, dx"," ",0,"Integral(x*(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(1/4), x)","F",0
130,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/4),x)","\int \sqrt[4]{\frac{i a x + 1}{\sqrt{a^{2} x^{2} + 1}}}\, dx"," ",0,"Integral(((I*a*x + 1)/sqrt(a**2*x**2 + 1))**(1/4), x)","F",0
131,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/4)/x,x)","\int \frac{\sqrt[4]{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(1/4)/x, x)","F",0
132,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/4)/x**2,x)","\int \frac{\sqrt[4]{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x^{2}}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(1/4)/x**2, x)","F",0
133,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/4)/x**3,x)","\int \frac{\sqrt[4]{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}{x^{3}}\, dx"," ",0,"Integral((I*(a*x - I)/sqrt(a**2*x**2 + 1))**(1/4)/x**3, x)","F",0
134,0,0,0,0.000000," ","integrate((1+I*a*x)**6/(a**2*x**2+1)**3*x**m,x)","- \int \left(- \frac{x^{m}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\right)\, dx - \int \frac{15 a^{2} x^{2} x^{m}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx - \int \left(- \frac{15 a^{4} x^{4} x^{m}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\right)\, dx - \int \frac{a^{6} x^{6} x^{m}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx - \int \left(- \frac{6 i a x x^{m}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\right)\, dx - \int \frac{20 i a^{3} x^{3} x^{m}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\, dx - \int \left(- \frac{6 i a^{5} x^{5} x^{m}}{a^{6} x^{6} + 3 a^{4} x^{4} + 3 a^{2} x^{2} + 1}\right)\, dx"," ",0,"-Integral(-x**m/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x) - Integral(15*a**2*x**2*x**m/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x) - Integral(-15*a**4*x**4*x**m/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x) - Integral(a**6*x**6*x**m/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x) - Integral(-6*I*a*x*x**m/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x) - Integral(20*I*a**3*x**3*x**m/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x) - Integral(-6*I*a**5*x**5*x**m/(a**6*x**6 + 3*a**4*x**4 + 3*a**2*x**2 + 1), x)","F",0
135,0,0,0,0.000000," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2*x**m,x)","\int \frac{x^{m} \left(a x - i\right)^{4}}{\left(a^{2} x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral(x**m*(a*x - I)**4/(a**2*x**2 + 1)**2, x)","F",0
136,1,136,0,3.404140," ","integrate((1+I*a*x)**2/(a**2*x**2+1)*x**m,x)","\frac{i a m x^{2} x^{m} \Phi\left(a x e^{\frac{5 i \pi}{2}}, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} + \frac{2 i a x^{2} x^{m} \Phi\left(a x e^{\frac{5 i \pi}{2}}, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} + \frac{m x x^{m} \Phi\left(a x e^{\frac{5 i \pi}{2}}, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)} + \frac{x x^{m} \Phi\left(a x e^{\frac{5 i \pi}{2}}, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)}"," ",0,"I*a*m*x**2*x**m*lerchphi(a*x*exp_polar(5*I*pi/2), 1, m + 2)*gamma(m + 2)/gamma(m + 3) + 2*I*a*x**2*x**m*lerchphi(a*x*exp_polar(5*I*pi/2), 1, m + 2)*gamma(m + 2)/gamma(m + 3) + m*x*x**m*lerchphi(a*x*exp_polar(5*I*pi/2), 1, m + 1)*gamma(m + 1)/gamma(m + 2) + x*x**m*lerchphi(a*x*exp_polar(5*I*pi/2), 1, m + 1)*gamma(m + 1)/gamma(m + 2)","B",0
137,1,136,0,4.062644," ","integrate(x**m/(1+I*a*x)**2*(a**2*x**2+1),x)","- \frac{i a m x^{2} x^{m} \Phi\left(a x e^{\frac{3 i \pi}{2}}, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} - \frac{2 i a x^{2} x^{m} \Phi\left(a x e^{\frac{3 i \pi}{2}}, 1, m + 2\right) \Gamma\left(m + 2\right)}{\Gamma\left(m + 3\right)} + \frac{m x x^{m} \Phi\left(a x e^{\frac{3 i \pi}{2}}, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)} + \frac{x x^{m} \Phi\left(a x e^{\frac{3 i \pi}{2}}, 1, m + 1\right) \Gamma\left(m + 1\right)}{\Gamma\left(m + 2\right)}"," ",0,"-I*a*m*x**2*x**m*lerchphi(a*x*exp_polar(3*I*pi/2), 1, m + 2)*gamma(m + 2)/gamma(m + 3) - 2*I*a*x**2*x**m*lerchphi(a*x*exp_polar(3*I*pi/2), 1, m + 2)*gamma(m + 2)/gamma(m + 3) + m*x*x**m*lerchphi(a*x*exp_polar(3*I*pi/2), 1, m + 1)*gamma(m + 1)/gamma(m + 2) + x*x**m*lerchphi(a*x*exp_polar(3*I*pi/2), 1, m + 1)*gamma(m + 1)/gamma(m + 2)","B",0
138,0,0,0,0.000000," ","integrate(x**m/(1+I*a*x)**4*(a**2*x**2+1)**2,x)","\int \frac{x^{m} \left(a^{2} x^{2} + 1\right)^{2}}{\left(a x - i\right)^{4}}\, dx"," ",0,"Integral(x**m*(a**2*x**2 + 1)**2/(a*x - I)**4, x)","F",0
139,0,0,0,0.000000," ","integrate(x**m/(1+I*a*x)**6*(a**2*x**2+1)**3,x)","- \int \frac{x^{m}}{a^{6} x^{6} - 6 i a^{5} x^{5} - 15 a^{4} x^{4} + 20 i a^{3} x^{3} + 15 a^{2} x^{2} - 6 i a x - 1}\, dx - \int \frac{3 a^{2} x^{2} x^{m}}{a^{6} x^{6} - 6 i a^{5} x^{5} - 15 a^{4} x^{4} + 20 i a^{3} x^{3} + 15 a^{2} x^{2} - 6 i a x - 1}\, dx - \int \frac{3 a^{4} x^{4} x^{m}}{a^{6} x^{6} - 6 i a^{5} x^{5} - 15 a^{4} x^{4} + 20 i a^{3} x^{3} + 15 a^{2} x^{2} - 6 i a x - 1}\, dx - \int \frac{a^{6} x^{6} x^{m}}{a^{6} x^{6} - 6 i a^{5} x^{5} - 15 a^{4} x^{4} + 20 i a^{3} x^{3} + 15 a^{2} x^{2} - 6 i a x - 1}\, dx"," ",0,"-Integral(x**m/(a**6*x**6 - 6*I*a**5*x**5 - 15*a**4*x**4 + 20*I*a**3*x**3 + 15*a**2*x**2 - 6*I*a*x - 1), x) - Integral(3*a**2*x**2*x**m/(a**6*x**6 - 6*I*a**5*x**5 - 15*a**4*x**4 + 20*I*a**3*x**3 + 15*a**2*x**2 - 6*I*a*x - 1), x) - Integral(3*a**4*x**4*x**m/(a**6*x**6 - 6*I*a**5*x**5 - 15*a**4*x**4 + 20*I*a**3*x**3 + 15*a**2*x**2 - 6*I*a*x - 1), x) - Integral(a**6*x**6*x**m/(a**6*x**6 - 6*I*a**5*x**5 - 15*a**4*x**4 + 20*I*a**3*x**3 + 15*a**2*x**2 - 6*I*a*x - 1), x)","F",0
140,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)*x**m,x)","- i \left(\int \frac{i x^{m}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x x^{m}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{3} x^{m}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{2} x^{m}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x**m/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*a*x*x**m/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(a**3*x**3*x**m/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**2*x**m/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x))","F",0
141,1,95,0,3.130038," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)*x**m,x)","\frac{i a x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {a^{2} x^{2} e^{i \pi}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {a^{2} x^{2} e^{i \pi}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"I*a*x**2*x**m*gamma(m/2 + 1)*hyper((1/2, m/2 + 1), (m/2 + 2,), a**2*x**2*exp_polar(I*pi))/(2*gamma(m/2 + 2)) + x*x**m*gamma(m/2 + 1/2)*hyper((1/2, m/2 + 1/2), (m/2 + 3/2,), a**2*x**2*exp_polar(I*pi))/(2*gamma(m/2 + 3/2))","A",0
142,0,0,0,0.000000," ","integrate(x**m/(1+I*a*x)*(a**2*x**2+1)**(1/2),x)","- i \int \frac{x^{m} \sqrt{a^{2} x^{2} + 1}}{a x - i}\, dx"," ",0,"-I*Integral(x**m*sqrt(a**2*x**2 + 1)/(a*x - I), x)","F",0
143,0,0,0,0.000000," ","integrate(x**m/(1+I*a*x)**3*(a**2*x**2+1)**(3/2),x)","i \left(\int \frac{x^{m} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx + \int \frac{a^{2} x^{2} x^{m} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} - 3 i a^{2} x^{2} - 3 a x + i}\, dx\right)"," ",0,"I*(Integral(x**m*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x) + Integral(a**2*x**2*x**m*sqrt(a**2*x**2 + 1)/(a**3*x**3 - 3*I*a**2*x**2 - 3*a*x + I), x))","F",0
144,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2)*x**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2)*x**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2)*x**m,x)","\int x^{m} \sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}\, dx"," ",0,"Integral(x**m*sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1)), x)","F",0
147,0,0,0,0.000000," ","integrate(x**m/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/2),x)","\int \frac{x^{m}}{\sqrt{\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(x**m/sqrt(I*(a*x - I)/sqrt(a**2*x**2 + 1)), x)","F",0
148,0,0,0,0.000000," ","integrate(x**m/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(3/2),x)","\int \frac{x^{m}}{\left(\frac{i \left(a x - i\right)}{\sqrt{a^{2} x^{2} + 1}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m/(I*(a*x - I)/sqrt(a**2*x**2 + 1))**(3/2), x)","F",0
149,-1,0,0,0.000000," ","integrate(x**m/((1+I*a*x)/(a**2*x**2+1)**(1/2))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,0,0,0,0.000000," ","integrate(exp(2/3*atan(x))*x**m,x)","\int x^{m} e^{\frac{2 \operatorname{atan}{\left(x \right)}}{3}}\, dx"," ",0,"Integral(x**m*exp(2*atan(x)/3), x)","F",0
151,0,0,0,0.000000," ","integrate(exp(1/3*atan(x))*x**m,x)","\int x^{m} e^{\frac{\operatorname{atan}{\left(x \right)}}{3}}\, dx"," ",0,"Integral(x**m*exp(atan(x)/3), x)","F",0
152,-1,0,0,0.000000," ","integrate(((1+I*a*x)/(a**2*x**2+1)**(1/2))**(1/4)*x**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))*x**m,x)","\int x^{m} e^{i n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m*exp(I*n*atan(a*x)), x)","F",0
154,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))*x**3,x)","\int x^{3} e^{i n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3*exp(I*n*atan(a*x)), x)","F",0
155,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))*x**2,x)","\int x^{2} e^{i n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2*exp(I*n*atan(a*x)), x)","F",0
156,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))*x,x)","\int x e^{i n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x*exp(I*n*atan(a*x)), x)","F",0
157,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x)),x)","\int e^{i n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(I*n*atan(a*x)), x)","F",0
158,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))/x,x)","\int \frac{e^{i n \operatorname{atan}{\left(a x \right)}}}{x}\, dx"," ",0,"Integral(exp(I*n*atan(a*x))/x, x)","F",0
159,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))/x**2,x)","\int \frac{e^{i n \operatorname{atan}{\left(a x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(I*n*atan(a*x))/x**2, x)","F",0
160,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))/x**3,x)","\int \frac{e^{i n \operatorname{atan}{\left(a x \right)}}}{x^{3}}\, dx"," ",0,"Integral(exp(I*n*atan(a*x))/x**3, x)","F",0
161,0,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))/x**4,x)","\int \frac{e^{i n \operatorname{atan}{\left(a x \right)}}}{x^{4}}\, dx"," ",0,"Integral(exp(I*n*atan(a*x))/x**4, x)","F",0
162,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)*x**4,x)","i \left(\int \left(- \frac{i x^{4}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a x^{4}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{b x^{5}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(-I*x**4/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(a*x**4/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(b*x**5/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x))","F",0
163,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)*x**3,x)","i \left(\int \left(- \frac{i x^{3}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a x^{3}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{b x^{4}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(-I*x**3/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(a*x**3/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(b*x**4/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x))","F",0
164,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)*x**2,x)","i \left(\int \left(- \frac{i x^{2}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a x^{2}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{b x^{3}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(-I*x**2/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(a*x**2/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(b*x**3/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x))","F",0
165,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)*x,x)","i \left(\int \left(- \frac{i x}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a x}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{b x^{2}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(-I*x/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(a*x/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(b*x**2/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x))","F",0
166,1,36,0,3.414160," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2),x)","\begin{cases} \frac{i \sqrt{\left(a + b x\right)^{2} + 1} + \operatorname{asinh}{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x \left(i a + 1\right)}{\sqrt{a^{2} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((I*sqrt((a + b*x)**2 + 1) + asinh(a + b*x))/b, Ne(b, 0)), (x*(I*a + 1)/sqrt(a**2 + 1), True))","A",0
167,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)/x,x)","i \left(\int \frac{b}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{i}{x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a}{x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(b/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x) + Integral(-I/(x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a/(x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
168,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)/x**2,x)","i \left(\int \left(- \frac{i}{x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a}{x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{b}{x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(-I/(x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a/(x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b/(x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
169,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)/x**3,x)","i \left(\int \left(- \frac{i}{x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a}{x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{b}{x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(-I/(x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a/(x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b/(x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
170,0,0,0,0.000000," ","integrate((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2)/x**4,x)","i \left(\int \left(- \frac{i}{x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a}{x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{b}{x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx\right)"," ",0,"I*(Integral(-I/(x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a/(x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b/(x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
171,1,114,0,0.502010," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)*x**4,x)","- \frac{x^{5}}{5} - x^{3} \left(\frac{2 i a}{3 b^{2}} - \frac{2}{3 b^{2}}\right) - x^{2} \left(- \frac{i a^{2}}{b^{3}} + \frac{2 a}{b^{3}} + \frac{i}{b^{3}}\right) - x \left(\frac{2 i a^{3}}{b^{4}} - \frac{6 a^{2}}{b^{4}} - \frac{6 i a}{b^{4}} + \frac{2}{b^{4}}\right) + \frac{i x^{4}}{2 b} + \frac{2 i \left(a + i\right)^{4} \log{\left(i a + i b x - 1 \right)}}{b^{5}}"," ",0,"-x**5/5 - x**3*(2*I*a/(3*b**2) - 2/(3*b**2)) - x**2*(-I*a**2/b**3 + 2*a/b**3 + I/b**3) - x*(2*I*a**3/b**4 - 6*a**2/b**4 - 6*I*a/b**4 + 2/b**4) + I*x**4/(2*b) + 2*I*(a + I)**4*log(I*a + I*b*x - 1)/b**5","A",0
172,1,78,0,0.379630," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)*x**3,x)","- \frac{x^{4}}{4} - x^{2} \left(\frac{i a}{b^{2}} - \frac{1}{b^{2}}\right) - x \left(- \frac{2 i a^{2}}{b^{3}} + \frac{4 a}{b^{3}} + \frac{2 i}{b^{3}}\right) + \frac{2 i x^{3}}{3 b} - \frac{2 i \left(a + i\right)^{3} \log{\left(i a + i b x - 1 \right)}}{b^{4}}"," ",0,"-x**4/4 - x**2*(I*a/b**2 - 1/b**2) - x*(-2*I*a**2/b**3 + 4*a/b**3 + 2*I/b**3) + 2*I*x**3/(3*b) - 2*I*(a + I)**3*log(I*a + I*b*x - 1)/b**4","A",0
173,1,49,0,0.311052," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)*x**2,x)","- \frac{x^{3}}{3} - x \left(\frac{2 i a}{b^{2}} - \frac{2}{b^{2}}\right) + \frac{i x^{2}}{b} + \frac{2 i \left(a + i\right)^{2} \log{\left(i a + i b x - 1 \right)}}{b^{3}}"," ",0,"-x**3/3 - x*(2*I*a/b**2 - 2/b**2) + I*x**2/b + 2*I*(a + I)**2*log(I*a + I*b*x - 1)/b**3","A",0
174,1,32,0,0.223838," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)*x,x)","- \frac{x^{2}}{2} + \frac{2 i x}{b} - \frac{2 i \left(a + i\right) \log{\left(i a + i b x - 1 \right)}}{b^{2}}"," ",0,"-x**2/2 + 2*I*x/b - 2*I*(a + I)*log(I*a + I*b*x - 1)/b**2","A",0
175,1,17,0,0.156198," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2),x)","- x + \frac{2 i \log{\left(i a + i b x - 1 \right)}}{b}"," ",0,"-x + 2*I*log(I*a + I*b*x - 1)/b","A",0
176,1,107,0,0.796090," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)/x,x)","- \frac{\left(a - i\right) \log{\left(\frac{i a^{2} \left(a - i\right)}{a + i} - i a^{2} - \frac{2 a \left(a - i\right)}{a + i} + x \left(- i a b - 3 b\right) - \frac{i \left(a - i\right)}{a + i} - i \right)}}{a + i} - \frac{2 i \log{\left(- i a^{2} - \frac{2 a^{2}}{a + i} - \frac{4 i a}{a + i} + x \left(- i a b - 3 b\right) - i + \frac{2}{a + i} \right)}}{a + i}"," ",0,"-(a - I)*log(I*a**2*(a - I)/(a + I) - I*a**2 - 2*a*(a - I)/(a + I) + x*(-I*a*b - 3*b) - I*(a - I)/(a + I) - I)/(a + I) - 2*I*log(-I*a**2 - 2*a**2/(a + I) - 4*I*a/(a + I) + x*(-I*a*b - 3*b) - I + 2/(a + I))/(a + I)","B",0
177,1,158,0,0.610114," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)/x**2,x)","- \frac{2 i b \log{\left(- \frac{2 a^{3} b}{\left(a + i\right)^{2}} - \frac{6 i a^{2} b}{\left(a + i\right)^{2}} + 2 a b + \frac{6 a b}{\left(a + i\right)^{2}} + 4 b^{2} x + 2 i b + \frac{2 i b}{\left(a + i\right)^{2}} \right)}}{\left(a + i\right)^{2}} + \frac{2 i b \log{\left(\frac{2 a^{3} b}{\left(a + i\right)^{2}} + \frac{6 i a^{2} b}{\left(a + i\right)^{2}} + 2 a b - \frac{6 a b}{\left(a + i\right)^{2}} + 4 b^{2} x + 2 i b - \frac{2 i b}{\left(a + i\right)^{2}} \right)}}{\left(a + i\right)^{2}} - \frac{a - i}{x \left(- a - i\right)}"," ",0,"-2*I*b*log(-2*a**3*b/(a + I)**2 - 6*I*a**2*b/(a + I)**2 + 2*a*b + 6*a*b/(a + I)**2 + 4*b**2*x + 2*I*b + 2*I*b/(a + I)**2)/(a + I)**2 + 2*I*b*log(2*a**3*b/(a + I)**2 + 6*I*a**2*b/(a + I)**2 + 2*a*b - 6*a*b/(a + I)**2 + 4*b**2*x + 2*I*b - 2*I*b/(a + I)**2)/(a + I)**2 - (a - I)/(x*(-a - I))","B",0
178,1,226,0,0.876499," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)/x**3,x)","\frac{2 i b^{2} \log{\left(- \frac{2 a^{4} b^{2}}{\left(a + i\right)^{3}} - \frac{8 i a^{3} b^{2}}{\left(a + i\right)^{3}} + \frac{12 a^{2} b^{2}}{\left(a + i\right)^{3}} + 2 a b^{2} + \frac{8 i a b^{2}}{\left(a + i\right)^{3}} + 4 b^{3} x + 2 i b^{2} - \frac{2 b^{2}}{\left(a + i\right)^{3}} \right)}}{\left(a + i\right)^{3}} - \frac{2 i b^{2} \log{\left(\frac{2 a^{4} b^{2}}{\left(a + i\right)^{3}} + \frac{8 i a^{3} b^{2}}{\left(a + i\right)^{3}} - \frac{12 a^{2} b^{2}}{\left(a + i\right)^{3}} + 2 a b^{2} - \frac{8 i a b^{2}}{\left(a + i\right)^{3}} + 4 b^{3} x + 2 i b^{2} + \frac{2 b^{2}}{\left(a + i\right)^{3}} \right)}}{\left(a + i\right)^{3}} - \frac{a^{2} + 4 i b x + 1}{x^{2} \left(- 2 a^{2} - 4 i a + 2\right)}"," ",0,"2*I*b**2*log(-2*a**4*b**2/(a + I)**3 - 8*I*a**3*b**2/(a + I)**3 + 12*a**2*b**2/(a + I)**3 + 2*a*b**2 + 8*I*a*b**2/(a + I)**3 + 4*b**3*x + 2*I*b**2 - 2*b**2/(a + I)**3)/(a + I)**3 - 2*I*b**2*log(2*a**4*b**2/(a + I)**3 + 8*I*a**3*b**2/(a + I)**3 - 12*a**2*b**2/(a + I)**3 + 2*a*b**2 - 8*I*a*b**2/(a + I)**3 + 4*b**3*x + 2*I*b**2 + 2*b**2/(a + I)**3)/(a + I)**3 - (a**2 + 4*I*b*x + 1)/(x**2*(-2*a**2 - 4*I*a + 2))","B",0
179,1,286,0,1.153261," ","integrate((1+I*(b*x+a))**2/(1+(b*x+a)**2)/x**4,x)","- \frac{2 i b^{3} \log{\left(- \frac{2 a^{5} b^{3}}{\left(a + i\right)^{4}} - \frac{10 i a^{4} b^{3}}{\left(a + i\right)^{4}} + \frac{20 a^{3} b^{3}}{\left(a + i\right)^{4}} + \frac{20 i a^{2} b^{3}}{\left(a + i\right)^{4}} + 2 a b^{3} - \frac{10 a b^{3}}{\left(a + i\right)^{4}} + 4 b^{4} x + 2 i b^{3} - \frac{2 i b^{3}}{\left(a + i\right)^{4}} \right)}}{\left(a + i\right)^{4}} + \frac{2 i b^{3} \log{\left(\frac{2 a^{5} b^{3}}{\left(a + i\right)^{4}} + \frac{10 i a^{4} b^{3}}{\left(a + i\right)^{4}} - \frac{20 a^{3} b^{3}}{\left(a + i\right)^{4}} - \frac{20 i a^{2} b^{3}}{\left(a + i\right)^{4}} + 2 a b^{3} + \frac{10 a b^{3}}{\left(a + i\right)^{4}} + 4 b^{4} x + 2 i b^{3} + \frac{2 i b^{3}}{\left(a + i\right)^{4}} \right)}}{\left(a + i\right)^{4}} - \frac{- i a^{3} + a^{2} - i a - 6 b^{2} x^{2} + x \left(3 a b + 3 i b\right) + 1}{x^{3} \left(3 i a^{3} - 9 a^{2} - 9 i a + 3\right)}"," ",0,"-2*I*b**3*log(-2*a**5*b**3/(a + I)**4 - 10*I*a**4*b**3/(a + I)**4 + 20*a**3*b**3/(a + I)**4 + 20*I*a**2*b**3/(a + I)**4 + 2*a*b**3 - 10*a*b**3/(a + I)**4 + 4*b**4*x + 2*I*b**3 - 2*I*b**3/(a + I)**4)/(a + I)**4 + 2*I*b**3*log(2*a**5*b**3/(a + I)**4 + 10*I*a**4*b**3/(a + I)**4 - 20*a**3*b**3/(a + I)**4 - 20*I*a**2*b**3/(a + I)**4 + 2*a*b**3 + 10*a*b**3/(a + I)**4 + 4*b**4*x + 2*I*b**3 + 2*I*b**3/(a + I)**4)/(a + I)**4 - (-I*a**3 + a**2 - I*a - 6*b**2*x**2 + x*(3*a*b + 3*I*b) + 1)/(x**3*(3*I*a**3 - 9*a**2 - 9*I*a + 3))","B",0
180,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)*x**4,x)","- i \left(\int \frac{i x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 b x^{5}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{7}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 i b^{2} x^{6}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{6}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x^{5}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x^{5}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x**5/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**7/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**6/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**6/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x**5/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x**5/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
181,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)*x**3,x)","- i \left(\int \frac{i x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 b x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{6}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 i b^{2} x^{5}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{5}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**6/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**5/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**5/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
182,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)*x**2,x)","- i \left(\int \frac{i x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 b x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{5}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 i b^{2} x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**5/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
183,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)*x,x)","- i \left(\int \frac{i x}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a x}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3} x}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 b x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{4}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2} x}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 i b^{2} x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I*x/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a*x/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3*x/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**4/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2*x/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
184,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2),x)","- i \left(\int \frac{i}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 b x}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{3}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i b^{2} x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{2}}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x}{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**3/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**2/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x/(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
185,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)/x,x)","- i \left(\int \frac{i}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3}}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2}}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 b x}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{3}}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i b^{2} x^{2}}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{2}}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x}{a^{2} x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**3/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**2/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**2/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x/(a**2*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
186,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)/x**2,x)","- i \left(\int \frac{i}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3}}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2}}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 b x}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{3}}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i b^{2} x^{2}}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{2}}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x}{a^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**3/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**2/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**2/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x/(a**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
187,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)/x**3,x)","- i \left(\int \frac{i}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3}}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2}}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 b x}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{3}}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i b^{2} x^{2}}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{2}}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x}{a^{2} x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**3/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**2/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**2/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x/(a**2*x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
188,0,0,0,0.000000," ","integrate((1+I*(b*x+a))**3/(1+(b*x+a)**2)**(3/2)/x**4,x)","- i \left(\int \frac{i}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 a}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{a^{3}}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i a^{2}}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \left(- \frac{3 b x}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{b^{3} x^{3}}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{3 i b^{2} x^{2}}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx + \int \frac{3 a b^{2} x^{2}}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \frac{3 a^{2} b x}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx + \int \left(- \frac{6 i a b x}{a^{2} x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + 2 a b x^{5} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + b^{2} x^{6} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1} + x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*a/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(a**3/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*a**2/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*b*x/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(b**3*x**3/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-3*I*b**2*x**2/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a*b**2*x**2/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(3*a**2*b*x/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x) + Integral(-6*I*a*b*x/(a**2*x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + 2*a*b*x**5*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + b**2*x**6*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1) + x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x))","F",0
189,0,0,0,0.000000," ","integrate(x**4/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2),x)","- i \int \frac{x^{4} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a + b x - i}\, dx"," ",0,"-I*Integral(x**4*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a + b*x - I), x)","F",0
190,0,0,0,0.000000," ","integrate(x**3/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2),x)","- i \int \frac{x^{3} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a + b x - i}\, dx"," ",0,"-I*Integral(x**3*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a + b*x - I), x)","F",0
191,0,0,0,0.000000," ","integrate(x**2/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2),x)","- i \int \frac{x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a + b x - i}\, dx"," ",0,"-I*Integral(x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a + b*x - I), x)","F",0
192,0,0,0,0.000000," ","integrate(x/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2),x)","- i \int \frac{x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a + b x - i}\, dx"," ",0,"-I*Integral(x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a + b*x - I), x)","F",0
193,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2),x)","- i \int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a + b x - i}\, dx"," ",0,"-I*Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a + b*x - I), x)","F",0
194,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2)/x,x)","- i \int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a x + b x^{2} - i x}\, dx"," ",0,"-I*Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a*x + b*x**2 - I*x), x)","F",0
195,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2)/x**2,x)","- i \int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a x^{2} + b x^{3} - i x^{2}}\, dx"," ",0,"-I*Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a*x**2 + b*x**3 - I*x**2), x)","F",0
196,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2)/x**3,x)","- i \int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a x^{3} + b x^{4} - i x^{3}}\, dx"," ",0,"-I*Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a*x**3 + b*x**4 - I*x**3), x)","F",0
197,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))*(1+(b*x+a)**2)**(1/2)/x**4,x)","- i \int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a x^{4} + b x^{5} - i x^{4}}\, dx"," ",0,"-I*Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a*x**4 + b*x**5 - I*x**4), x)","F",0
198,1,117,0,0.515845," ","integrate(x**4/(1+I*(b*x+a))**2*(1+(b*x+a)**2),x)","- \frac{x^{5}}{5} - x^{3} \left(- \frac{2 i a}{3 b^{2}} - \frac{2}{3 b^{2}}\right) - x^{2} \left(\frac{i a^{2}}{b^{3}} + \frac{2 a}{b^{3}} - \frac{i}{b^{3}}\right) - x \left(- \frac{2 i a^{3}}{b^{4}} - \frac{6 a^{2}}{b^{4}} + \frac{6 i a}{b^{4}} + \frac{2}{b^{4}}\right) - \frac{i x^{4}}{2 b} - \frac{2 i \left(a - i\right)^{4} \log{\left(i a + i b x + 1 \right)}}{b^{5}}"," ",0,"-x**5/5 - x**3*(-2*I*a/(3*b**2) - 2/(3*b**2)) - x**2*(I*a**2/b**3 + 2*a/b**3 - I/b**3) - x*(-2*I*a**3/b**4 - 6*a**2/b**4 + 6*I*a/b**4 + 2/b**4) - I*x**4/(2*b) - 2*I*(a - I)**4*log(I*a + I*b*x + 1)/b**5","A",0
199,1,80,0,0.485835," ","integrate(x**3/(1+I*(b*x+a))**2*(1+(b*x+a)**2),x)","- \frac{x^{4}}{4} - x^{2} \left(- \frac{i a}{b^{2}} - \frac{1}{b^{2}}\right) - x \left(\frac{2 i a^{2}}{b^{3}} + \frac{4 a}{b^{3}} - \frac{2 i}{b^{3}}\right) - \frac{2 i x^{3}}{3 b} + \frac{2 i \left(a - i\right)^{3} \log{\left(i a + i b x + 1 \right)}}{b^{4}}"," ",0,"-x**4/4 - x**2*(-I*a/b**2 - 1/b**2) - x*(2*I*a**2/b**3 + 4*a/b**3 - 2*I/b**3) - 2*I*x**3/(3*b) + 2*I*(a - I)**3*log(I*a + I*b*x + 1)/b**4","A",0
200,1,53,0,0.359064," ","integrate(x**2/(1+I*(b*x+a))**2*(1+(b*x+a)**2),x)","- \frac{x^{3}}{3} - x \left(- \frac{2 i a}{b^{2}} - \frac{2}{b^{2}}\right) - \frac{i x^{2}}{b} - \frac{2 i \left(a - i\right)^{2} \log{\left(i a + i b x + 1 \right)}}{b^{3}}"," ",0,"-x**3/3 - x*(-2*I*a/b**2 - 2/b**2) - I*x**2/b - 2*I*(a - I)**2*log(I*a + I*b*x + 1)/b**3","A",0
201,1,32,0,0.249096," ","integrate(x/(1+I*(b*x+a))**2*(1+(b*x+a)**2),x)","- \frac{x^{2}}{2} - \frac{2 i x}{b} + \frac{2 i \left(a - i\right) \log{\left(i a + i b x + 1 \right)}}{b^{2}}"," ",0,"-x**2/2 - 2*I*x/b + 2*I*(a - I)*log(I*a + I*b*x + 1)/b**2","A",0
202,1,19,0,0.215934," ","integrate(1/(1+I*(b*x+a))**2*(1+(b*x+a)**2),x)","- x - \frac{2 i \log{\left(i a + i b x + 1 \right)}}{b}"," ",0,"-x - 2*I*log(I*a + I*b*x + 1)/b","A",0
203,1,102,0,0.972221," ","integrate(1/(1+I*(b*x+a))**2*(1+(b*x+a)**2)/x,x)","- \frac{\left(a + i\right) \log{\left(i a^{2} - \frac{i a^{2} \left(a + i\right)}{a - i} - \frac{2 a \left(a + i\right)}{a - i} + x \left(i a b - 3 b\right) + i + \frac{i \left(a + i\right)}{a - i} \right)}}{a - i} + \frac{2 i \log{\left(i a^{2} - \frac{2 a^{2}}{a - i} + \frac{4 i a}{a - i} + x \left(i a b - 3 b\right) + i + \frac{2}{a - i} \right)}}{a - i}"," ",0,"-(a + I)*log(I*a**2 - I*a**2*(a + I)/(a - I) - 2*a*(a + I)/(a - I) + x*(I*a*b - 3*b) + I + I*(a + I)/(a - I))/(a - I) + 2*I*log(I*a**2 - 2*a**2/(a - I) + 4*I*a/(a - I) + x*(I*a*b - 3*b) + I + 2/(a - I))/(a - I)","B",0
204,1,156,0,0.740816," ","integrate(1/(1+I*(b*x+a))**2*(1+(b*x+a)**2)/x**2,x)","\frac{2 i b \log{\left(- \frac{2 a^{3} b}{\left(a - i\right)^{2}} + \frac{6 i a^{2} b}{\left(a - i\right)^{2}} + 2 a b + \frac{6 a b}{\left(a - i\right)^{2}} + 4 b^{2} x - 2 i b - \frac{2 i b}{\left(a - i\right)^{2}} \right)}}{\left(a - i\right)^{2}} - \frac{2 i b \log{\left(\frac{2 a^{3} b}{\left(a - i\right)^{2}} - \frac{6 i a^{2} b}{\left(a - i\right)^{2}} + 2 a b - \frac{6 a b}{\left(a - i\right)^{2}} + 4 b^{2} x - 2 i b + \frac{2 i b}{\left(a - i\right)^{2}} \right)}}{\left(a - i\right)^{2}} - \frac{a + i}{x \left(- a + i\right)}"," ",0,"2*I*b*log(-2*a**3*b/(a - I)**2 + 6*I*a**2*b/(a - I)**2 + 2*a*b + 6*a*b/(a - I)**2 + 4*b**2*x - 2*I*b - 2*I*b/(a - I)**2)/(a - I)**2 - 2*I*b*log(2*a**3*b/(a - I)**2 - 6*I*a**2*b/(a - I)**2 + 2*a*b - 6*a*b/(a - I)**2 + 4*b**2*x - 2*I*b + 2*I*b/(a - I)**2)/(a - I)**2 - (a + I)/(x*(-a + I))","B",0
205,1,226,0,0.958028," ","integrate(1/(1+I*(b*x+a))**2*(1+(b*x+a)**2)/x**3,x)","- \frac{2 i b^{2} \log{\left(- \frac{2 a^{4} b^{2}}{\left(a - i\right)^{3}} + \frac{8 i a^{3} b^{2}}{\left(a - i\right)^{3}} + \frac{12 a^{2} b^{2}}{\left(a - i\right)^{3}} + 2 a b^{2} - \frac{8 i a b^{2}}{\left(a - i\right)^{3}} + 4 b^{3} x - 2 i b^{2} - \frac{2 b^{2}}{\left(a - i\right)^{3}} \right)}}{\left(a - i\right)^{3}} + \frac{2 i b^{2} \log{\left(\frac{2 a^{4} b^{2}}{\left(a - i\right)^{3}} - \frac{8 i a^{3} b^{2}}{\left(a - i\right)^{3}} - \frac{12 a^{2} b^{2}}{\left(a - i\right)^{3}} + 2 a b^{2} + \frac{8 i a b^{2}}{\left(a - i\right)^{3}} + 4 b^{3} x - 2 i b^{2} + \frac{2 b^{2}}{\left(a - i\right)^{3}} \right)}}{\left(a - i\right)^{3}} - \frac{a^{2} - 4 i b x + 1}{x^{2} \left(- 2 a^{2} + 4 i a + 2\right)}"," ",0,"-2*I*b**2*log(-2*a**4*b**2/(a - I)**3 + 8*I*a**3*b**2/(a - I)**3 + 12*a**2*b**2/(a - I)**3 + 2*a*b**2 - 8*I*a*b**2/(a - I)**3 + 4*b**3*x - 2*I*b**2 - 2*b**2/(a - I)**3)/(a - I)**3 + 2*I*b**2*log(2*a**4*b**2/(a - I)**3 - 8*I*a**3*b**2/(a - I)**3 - 12*a**2*b**2/(a - I)**3 + 2*a*b**2 + 8*I*a*b**2/(a - I)**3 + 4*b**3*x - 2*I*b**2 + 2*b**2/(a - I)**3)/(a - I)**3 - (a**2 - 4*I*b*x + 1)/(x**2*(-2*a**2 + 4*I*a + 2))","B",0
206,1,286,0,1.401546," ","integrate(1/(1+I*(b*x+a))**2*(1+(b*x+a)**2)/x**4,x)","\frac{2 i b^{3} \log{\left(- \frac{2 a^{5} b^{3}}{\left(a - i\right)^{4}} + \frac{10 i a^{4} b^{3}}{\left(a - i\right)^{4}} + \frac{20 a^{3} b^{3}}{\left(a - i\right)^{4}} - \frac{20 i a^{2} b^{3}}{\left(a - i\right)^{4}} + 2 a b^{3} - \frac{10 a b^{3}}{\left(a - i\right)^{4}} + 4 b^{4} x - 2 i b^{3} + \frac{2 i b^{3}}{\left(a - i\right)^{4}} \right)}}{\left(a - i\right)^{4}} - \frac{2 i b^{3} \log{\left(\frac{2 a^{5} b^{3}}{\left(a - i\right)^{4}} - \frac{10 i a^{4} b^{3}}{\left(a - i\right)^{4}} - \frac{20 a^{3} b^{3}}{\left(a - i\right)^{4}} + \frac{20 i a^{2} b^{3}}{\left(a - i\right)^{4}} + 2 a b^{3} + \frac{10 a b^{3}}{\left(a - i\right)^{4}} + 4 b^{4} x - 2 i b^{3} - \frac{2 i b^{3}}{\left(a - i\right)^{4}} \right)}}{\left(a - i\right)^{4}} - \frac{- i a^{3} - a^{2} - i a + 6 b^{2} x^{2} + x \left(- 3 a b + 3 i b\right) - 1}{x^{3} \left(3 i a^{3} + 9 a^{2} - 9 i a - 3\right)}"," ",0,"2*I*b**3*log(-2*a**5*b**3/(a - I)**4 + 10*I*a**4*b**3/(a - I)**4 + 20*a**3*b**3/(a - I)**4 - 20*I*a**2*b**3/(a - I)**4 + 2*a*b**3 - 10*a*b**3/(a - I)**4 + 4*b**4*x - 2*I*b**3 + 2*I*b**3/(a - I)**4)/(a - I)**4 - 2*I*b**3*log(2*a**5*b**3/(a - I)**4 - 10*I*a**4*b**3/(a - I)**4 - 20*a**3*b**3/(a - I)**4 + 20*I*a**2*b**3/(a - I)**4 + 2*a*b**3 + 10*a*b**3/(a - I)**4 + 4*b**4*x - 2*I*b**3 - 2*I*b**3/(a - I)**4)/(a - I)**4 - (-I*a**3 - a**2 - I*a + 6*b**2*x**2 + x*(-3*a*b + 3*I*b) - 1)/(x**3*(3*I*a**3 + 9*a**2 - 9*I*a - 3))","B",0
207,-1,0,0,0.000000," ","integrate(x**4/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate(x**3/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate(x**2/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate(x/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2),x)","i \left(\int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} + 3 a^{2} b x - 3 i a^{2} + 3 a b^{2} x^{2} - 6 i a b x - 3 a + b^{3} x^{3} - 3 i b^{2} x^{2} - 3 b x + i}\, dx + \int \frac{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} + 3 a^{2} b x - 3 i a^{2} + 3 a b^{2} x^{2} - 6 i a b x - 3 a + b^{3} x^{3} - 3 i b^{2} x^{2} - 3 b x + i}\, dx + \int \frac{b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} + 3 a^{2} b x - 3 i a^{2} + 3 a b^{2} x^{2} - 6 i a b x - 3 a + b^{3} x^{3} - 3 i b^{2} x^{2} - 3 b x + i}\, dx + \int \frac{2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} + 3 a^{2} b x - 3 i a^{2} + 3 a b^{2} x^{2} - 6 i a b x - 3 a + b^{3} x^{3} - 3 i b^{2} x^{2} - 3 b x + i}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3 + 3*a**2*b*x - 3*I*a**2 + 3*a*b**2*x**2 - 6*I*a*b*x - 3*a + b**3*x**3 - 3*I*b**2*x**2 - 3*b*x + I), x) + Integral(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3 + 3*a**2*b*x - 3*I*a**2 + 3*a*b**2*x**2 - 6*I*a*b*x - 3*a + b**3*x**3 - 3*I*b**2*x**2 - 3*b*x + I), x) + Integral(b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3 + 3*a**2*b*x - 3*I*a**2 + 3*a*b**2*x**2 - 6*I*a*b*x - 3*a + b**3*x**3 - 3*I*b**2*x**2 - 3*b*x + I), x) + Integral(2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3 + 3*a**2*b*x - 3*I*a**2 + 3*a*b**2*x**2 - 6*I*a*b*x - 3*a + b**3*x**3 - 3*I*b**2*x**2 - 3*b*x + I), x))","F",0
212,0,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2)/x,x)","i \left(\int \frac{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} x + 3 a^{2} b x^{2} - 3 i a^{2} x + 3 a b^{2} x^{3} - 6 i a b x^{2} - 3 a x + b^{3} x^{4} - 3 i b^{2} x^{3} - 3 b x^{2} + i x}\, dx + \int \frac{a^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} x + 3 a^{2} b x^{2} - 3 i a^{2} x + 3 a b^{2} x^{3} - 6 i a b x^{2} - 3 a x + b^{3} x^{4} - 3 i b^{2} x^{3} - 3 b x^{2} + i x}\, dx + \int \frac{b^{2} x^{2} \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} x + 3 a^{2} b x^{2} - 3 i a^{2} x + 3 a b^{2} x^{3} - 6 i a b x^{2} - 3 a x + b^{3} x^{4} - 3 i b^{2} x^{3} - 3 b x^{2} + i x}\, dx + \int \frac{2 a b x \sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}{a^{3} x + 3 a^{2} b x^{2} - 3 i a^{2} x + 3 a b^{2} x^{3} - 6 i a b x^{2} - 3 a x + b^{3} x^{4} - 3 i b^{2} x^{3} - 3 b x^{2} + i x}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3*x + 3*a**2*b*x**2 - 3*I*a**2*x + 3*a*b**2*x**3 - 6*I*a*b*x**2 - 3*a*x + b**3*x**4 - 3*I*b**2*x**3 - 3*b*x**2 + I*x), x) + Integral(a**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3*x + 3*a**2*b*x**2 - 3*I*a**2*x + 3*a*b**2*x**3 - 6*I*a*b*x**2 - 3*a*x + b**3*x**4 - 3*I*b**2*x**3 - 3*b*x**2 + I*x), x) + Integral(b**2*x**2*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3*x + 3*a**2*b*x**2 - 3*I*a**2*x + 3*a*b**2*x**3 - 6*I*a*b*x**2 - 3*a*x + b**3*x**4 - 3*I*b**2*x**3 - 3*b*x**2 + I*x), x) + Integral(2*a*b*x*sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)/(a**3*x + 3*a**2*b*x**2 - 3*I*a**2*x + 3*a*b**2*x**3 - 6*I*a*b*x**2 - 3*a*x + b**3*x**4 - 3*I*b**2*x**3 - 3*b*x**2 + I*x), x))","F",0
213,-1,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2)/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate(1/(1+I*(b*x+a))**3*(1+(b*x+a)**2)**(3/2)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2)*x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2)*x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2),x)","\int \sqrt{\frac{i \left(a + b x\right) + 1}{\sqrt{\left(a + b x\right)^{2} + 1}}}\, dx"," ",0,"Integral(sqrt((I*(a + b*x) + 1)/sqrt((a + b*x)**2 + 1)), x)","F",0
219,0,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2)/x,x)","\int \frac{\sqrt{\frac{i \left(a + b x - i\right)}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}}}{x}\, dx"," ",0,"Integral(sqrt(I*(a + b*x - I)/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1))/x, x)","F",0
220,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2)*x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2)*x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate(((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,0,0,0,0.000000," ","integrate(x**2/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2),x)","\int \frac{x^{2}}{\sqrt{\frac{i \left(a + b x - i\right)}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(x**2/sqrt(I*(a + b*x - I)/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
227,0,0,0,0.000000," ","integrate(x/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2),x)","\int \frac{x}{\sqrt{\frac{i \left(a + b x - i\right)}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(x/sqrt(I*(a + b*x - I)/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
228,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{\frac{i \left(a + b x\right) + 1}{\sqrt{\left(a + b x\right)^{2} + 1}}}}\, dx"," ",0,"Integral(1/sqrt((I*(a + b*x) + 1)/sqrt((a + b*x)**2 + 1)), x)","F",0
229,0,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2)/x,x)","\int \frac{1}{x \sqrt{\frac{i \left(a + b x - i\right)}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}}}\, dx"," ",0,"Integral(1/(x*sqrt(I*(a + b*x - I)/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1))), x)","F",0
230,-1,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(1/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(x**2/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate(x/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate(1/((1+I*(b*x+a))/(1+(b*x+a)**2)**(1/2))**(3/2)/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate(exp(n*atan(b*x+a))*x**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate(exp(n*atan(b*x+a))*x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,0,0,0,0.000000," ","integrate(exp(n*atan(b*x+a))*x**2,x)","\int x^{2} e^{n \operatorname{atan}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2*exp(n*atan(a + b*x)), x)","F",0
239,0,0,0,0.000000," ","integrate(exp(n*atan(b*x+a))*x,x)","\int x e^{n \operatorname{atan}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*exp(n*atan(a + b*x)), x)","F",0
240,0,0,0,0.000000," ","integrate(exp(n*atan(b*x+a)),x)","\int e^{n \operatorname{atan}{\left(a + b x \right)}}\, dx"," ",0,"Integral(exp(n*atan(a + b*x)), x)","F",0
241,0,0,0,0.000000," ","integrate(exp(n*atan(b*x+a))/x,x)","\int \frac{e^{n \operatorname{atan}{\left(a + b x \right)}}}{x}\, dx"," ",0,"Integral(exp(n*atan(a + b*x))/x, x)","F",0
242,0,0,0,0.000000," ","integrate(exp(n*atan(b*x+a))/x**2,x)","\int \frac{e^{n \operatorname{atan}{\left(a + b x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(n*atan(a + b*x))/x**2, x)","F",0
243,-1,0,0,0.000000," ","integrate(exp(n*atan(b*x+a))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,0,0,0,0.000000," ","integrate(exp(atan(a*x))*(a**2*c*x**2+c)**p,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{p} e^{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**p*exp(atan(a*x)), x)","F",0
245,0,0,0,0.000000," ","integrate(exp(atan(a*x))*(a**2*c*x**2+c)**2,x)","c^{2} \left(\int 2 a^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{4} e^{\operatorname{atan}{\left(a x \right)}}\, dx + \int e^{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*exp(atan(a*x)), x) + Integral(a**4*x**4*exp(atan(a*x)), x) + Integral(exp(atan(a*x)), x))","F",0
246,0,0,0,0.000000," ","integrate(exp(atan(a*x))*(a**2*c*x**2+c),x)","c \left(\int a^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}}\, dx + \int e^{\operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*exp(atan(a*x)), x) + Integral(exp(atan(a*x)), x))","F",0
247,0,0,0,0.000000," ","integrate(exp(atan(a*x)),x)","\int e^{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(atan(a*x)), x)","F",0
248,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c),x)","\begin{cases} \frac{e^{\operatorname{atan}{\left(a x \right)}}}{a c} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{\operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((exp(atan(a*x))/(a*c), Ne(c, 0)), (zoo*Integral(exp(atan(a*x)), x), True))","F",0
249,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**2,x)","\begin{cases} \frac{2 a^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}}}{5 a^{3} c^{2} x^{2} + 5 a c^{2}} + \frac{2 a x e^{\operatorname{atan}{\left(a x \right)}}}{5 a^{3} c^{2} x^{2} + 5 a c^{2}} + \frac{3 e^{\operatorname{atan}{\left(a x \right)}}}{5 a^{3} c^{2} x^{2} + 5 a c^{2}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{\operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*x**2*exp(atan(a*x))/(5*a**3*c**2*x**2 + 5*a*c**2) + 2*a*x*exp(atan(a*x))/(5*a**3*c**2*x**2 + 5*a*c**2) + 3*exp(atan(a*x))/(5*a**3*c**2*x**2 + 5*a*c**2), Ne(c, 0)), (zoo*Integral(exp(atan(a*x)), x), True))","F",0
250,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**3,x)","\begin{cases} \frac{24 a^{4} x^{4} e^{\operatorname{atan}{\left(a x \right)}}}{85 a^{5} c^{3} x^{4} + 170 a^{3} c^{3} x^{2} + 85 a c^{3}} + \frac{24 a^{3} x^{3} e^{\operatorname{atan}{\left(a x \right)}}}{85 a^{5} c^{3} x^{4} + 170 a^{3} c^{3} x^{2} + 85 a c^{3}} + \frac{60 a^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}}}{85 a^{5} c^{3} x^{4} + 170 a^{3} c^{3} x^{2} + 85 a c^{3}} + \frac{44 a x e^{\operatorname{atan}{\left(a x \right)}}}{85 a^{5} c^{3} x^{4} + 170 a^{3} c^{3} x^{2} + 85 a c^{3}} + \frac{41 e^{\operatorname{atan}{\left(a x \right)}}}{85 a^{5} c^{3} x^{4} + 170 a^{3} c^{3} x^{2} + 85 a c^{3}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{\operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((24*a**4*x**4*exp(atan(a*x))/(85*a**5*c**3*x**4 + 170*a**3*c**3*x**2 + 85*a*c**3) + 24*a**3*x**3*exp(atan(a*x))/(85*a**5*c**3*x**4 + 170*a**3*c**3*x**2 + 85*a*c**3) + 60*a**2*x**2*exp(atan(a*x))/(85*a**5*c**3*x**4 + 170*a**3*c**3*x**2 + 85*a*c**3) + 44*a*x*exp(atan(a*x))/(85*a**5*c**3*x**4 + 170*a**3*c**3*x**2 + 85*a*c**3) + 41*exp(atan(a*x))/(85*a**5*c**3*x**4 + 170*a**3*c**3*x**2 + 85*a*c**3), Ne(c, 0)), (zoo*Integral(exp(atan(a*x)), x), True))","F",0
251,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**4,x)","\begin{cases} \frac{144 a^{6} x^{6} e^{\operatorname{atan}{\left(a x \right)}}}{629 a^{7} c^{4} x^{6} + 1887 a^{5} c^{4} x^{4} + 1887 a^{3} c^{4} x^{2} + 629 a c^{4}} + \frac{144 a^{5} x^{5} e^{\operatorname{atan}{\left(a x \right)}}}{629 a^{7} c^{4} x^{6} + 1887 a^{5} c^{4} x^{4} + 1887 a^{3} c^{4} x^{2} + 629 a c^{4}} + \frac{504 a^{4} x^{4} e^{\operatorname{atan}{\left(a x \right)}}}{629 a^{7} c^{4} x^{6} + 1887 a^{5} c^{4} x^{4} + 1887 a^{3} c^{4} x^{2} + 629 a c^{4}} + \frac{408 a^{3} x^{3} e^{\operatorname{atan}{\left(a x \right)}}}{629 a^{7} c^{4} x^{6} + 1887 a^{5} c^{4} x^{4} + 1887 a^{3} c^{4} x^{2} + 629 a c^{4}} + \frac{606 a^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}}}{629 a^{7} c^{4} x^{6} + 1887 a^{5} c^{4} x^{4} + 1887 a^{3} c^{4} x^{2} + 629 a c^{4}} + \frac{366 a x e^{\operatorname{atan}{\left(a x \right)}}}{629 a^{7} c^{4} x^{6} + 1887 a^{5} c^{4} x^{4} + 1887 a^{3} c^{4} x^{2} + 629 a c^{4}} + \frac{263 e^{\operatorname{atan}{\left(a x \right)}}}{629 a^{7} c^{4} x^{6} + 1887 a^{5} c^{4} x^{4} + 1887 a^{3} c^{4} x^{2} + 629 a c^{4}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{\operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((144*a**6*x**6*exp(atan(a*x))/(629*a**7*c**4*x**6 + 1887*a**5*c**4*x**4 + 1887*a**3*c**4*x**2 + 629*a*c**4) + 144*a**5*x**5*exp(atan(a*x))/(629*a**7*c**4*x**6 + 1887*a**5*c**4*x**4 + 1887*a**3*c**4*x**2 + 629*a*c**4) + 504*a**4*x**4*exp(atan(a*x))/(629*a**7*c**4*x**6 + 1887*a**5*c**4*x**4 + 1887*a**3*c**4*x**2 + 629*a*c**4) + 408*a**3*x**3*exp(atan(a*x))/(629*a**7*c**4*x**6 + 1887*a**5*c**4*x**4 + 1887*a**3*c**4*x**2 + 629*a*c**4) + 606*a**2*x**2*exp(atan(a*x))/(629*a**7*c**4*x**6 + 1887*a**5*c**4*x**4 + 1887*a**3*c**4*x**2 + 629*a*c**4) + 366*a*x*exp(atan(a*x))/(629*a**7*c**4*x**6 + 1887*a**5*c**4*x**4 + 1887*a**3*c**4*x**2 + 629*a*c**4) + 263*exp(atan(a*x))/(629*a**7*c**4*x**6 + 1887*a**5*c**4*x**4 + 1887*a**3*c**4*x**2 + 629*a*c**4), Ne(c, 0)), (zoo*Integral(exp(atan(a*x)), x), True))","F",0
252,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**5,x)","\begin{cases} \frac{8064 a^{8} x^{8} e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{8064 a^{7} x^{7} e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{36288 a^{6} x^{6} e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{30912 a^{5} x^{5} e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{62160 a^{4} x^{4} e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{43344 a^{3} x^{3} e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{48664 a^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{25528 a x e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} + \frac{15357 e^{\operatorname{atan}{\left(a x \right)}}}{40885 a^{9} c^{5} x^{8} + 163540 a^{7} c^{5} x^{6} + 245310 a^{5} c^{5} x^{4} + 163540 a^{3} c^{5} x^{2} + 40885 a c^{5}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{\operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((8064*a**8*x**8*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 8064*a**7*x**7*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 36288*a**6*x**6*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 30912*a**5*x**5*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 62160*a**4*x**4*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 43344*a**3*x**3*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 48664*a**2*x**2*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 25528*a*x*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5) + 15357*exp(atan(a*x))/(40885*a**9*c**5*x**8 + 163540*a**7*c**5*x**6 + 245310*a**5*c**5*x**4 + 163540*a**3*c**5*x**2 + 40885*a*c**5), Ne(c, 0)), (zoo*Integral(exp(atan(a*x)), x), True))","F",0
253,0,0,0,0.000000," ","integrate(exp(atan(a*x))*(a**2*c*x**2+c)**(3/2),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} e^{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*exp(atan(a*x)), x)","F",0
254,0,0,0,0.000000," ","integrate(exp(atan(a*x))*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} e^{\operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*exp(atan(a*x)), x)","F",0
255,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{\operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
256,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**(3/2),x)","\int \frac{e^{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**(5/2),x)","\int \frac{e^{\operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(exp(atan(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
258,-1,0,0,0.000000," ","integrate(exp(atan(a*x))/(a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))*(a**2*c*x**2+c)**p,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{p} e^{2 \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**p*exp(2*atan(a*x)), x)","F",0
260,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))*(a**2*c*x**2+c)**2,x)","c^{2} \left(\int 2 a^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{4} e^{2 \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{2 \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*exp(2*atan(a*x)), x) + Integral(a**4*x**4*exp(2*atan(a*x)), x) + Integral(exp(2*atan(a*x)), x))","F",0
261,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))*(a**2*c*x**2+c),x)","c \left(\int a^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{2 \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*exp(2*atan(a*x)), x) + Integral(exp(2*atan(a*x)), x))","F",0
262,0,0,0,0.000000," ","integrate(exp(2*atan(a*x)),x)","\int e^{2 \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(2*atan(a*x)), x)","F",0
263,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c),x)","\begin{cases} \frac{e^{2 \operatorname{atan}{\left(a x \right)}}}{2 a c} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{2 \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((exp(2*atan(a*x))/(2*a*c), Ne(c, 0)), (zoo*Integral(exp(2*atan(a*x)), x), True))","F",0
264,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c)**2,x)","\begin{cases} \frac{a^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}}}{8 a^{3} c^{2} x^{2} + 8 a c^{2}} + \frac{2 a x e^{2 \operatorname{atan}{\left(a x \right)}}}{8 a^{3} c^{2} x^{2} + 8 a c^{2}} + \frac{3 e^{2 \operatorname{atan}{\left(a x \right)}}}{8 a^{3} c^{2} x^{2} + 8 a c^{2}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{2 \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**2*exp(2*atan(a*x))/(8*a**3*c**2*x**2 + 8*a*c**2) + 2*a*x*exp(2*atan(a*x))/(8*a**3*c**2*x**2 + 8*a*c**2) + 3*exp(2*atan(a*x))/(8*a**3*c**2*x**2 + 8*a*c**2), Ne(c, 0)), (zoo*Integral(exp(2*atan(a*x)), x), True))","F",0
265,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c)**3,x)","\begin{cases} \frac{3 a^{4} x^{4} e^{2 \operatorname{atan}{\left(a x \right)}}}{40 a^{5} c^{3} x^{4} + 80 a^{3} c^{3} x^{2} + 40 a c^{3}} + \frac{6 a^{3} x^{3} e^{2 \operatorname{atan}{\left(a x \right)}}}{40 a^{5} c^{3} x^{4} + 80 a^{3} c^{3} x^{2} + 40 a c^{3}} + \frac{12 a^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}}}{40 a^{5} c^{3} x^{4} + 80 a^{3} c^{3} x^{2} + 40 a c^{3}} + \frac{14 a x e^{2 \operatorname{atan}{\left(a x \right)}}}{40 a^{5} c^{3} x^{4} + 80 a^{3} c^{3} x^{2} + 40 a c^{3}} + \frac{13 e^{2 \operatorname{atan}{\left(a x \right)}}}{40 a^{5} c^{3} x^{4} + 80 a^{3} c^{3} x^{2} + 40 a c^{3}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{2 \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*x**4*exp(2*atan(a*x))/(40*a**5*c**3*x**4 + 80*a**3*c**3*x**2 + 40*a*c**3) + 6*a**3*x**3*exp(2*atan(a*x))/(40*a**5*c**3*x**4 + 80*a**3*c**3*x**2 + 40*a*c**3) + 12*a**2*x**2*exp(2*atan(a*x))/(40*a**5*c**3*x**4 + 80*a**3*c**3*x**2 + 40*a*c**3) + 14*a*x*exp(2*atan(a*x))/(40*a**5*c**3*x**4 + 80*a**3*c**3*x**2 + 40*a*c**3) + 13*exp(2*atan(a*x))/(40*a**5*c**3*x**4 + 80*a**3*c**3*x**2 + 40*a*c**3), Ne(c, 0)), (zoo*Integral(exp(2*atan(a*x)), x), True))","F",0
266,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c)**4,x)","\begin{cases} \frac{9 a^{6} x^{6} e^{2 \operatorname{atan}{\left(a x \right)}}}{160 a^{7} c^{4} x^{6} + 480 a^{5} c^{4} x^{4} + 480 a^{3} c^{4} x^{2} + 160 a c^{4}} + \frac{18 a^{5} x^{5} e^{2 \operatorname{atan}{\left(a x \right)}}}{160 a^{7} c^{4} x^{6} + 480 a^{5} c^{4} x^{4} + 480 a^{3} c^{4} x^{2} + 160 a c^{4}} + \frac{45 a^{4} x^{4} e^{2 \operatorname{atan}{\left(a x \right)}}}{160 a^{7} c^{4} x^{6} + 480 a^{5} c^{4} x^{4} + 480 a^{3} c^{4} x^{2} + 160 a c^{4}} + \frac{60 a^{3} x^{3} e^{2 \operatorname{atan}{\left(a x \right)}}}{160 a^{7} c^{4} x^{6} + 480 a^{5} c^{4} x^{4} + 480 a^{3} c^{4} x^{2} + 160 a c^{4}} + \frac{75 a^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}}}{160 a^{7} c^{4} x^{6} + 480 a^{5} c^{4} x^{4} + 480 a^{3} c^{4} x^{2} + 160 a c^{4}} + \frac{66 a x e^{2 \operatorname{atan}{\left(a x \right)}}}{160 a^{7} c^{4} x^{6} + 480 a^{5} c^{4} x^{4} + 480 a^{3} c^{4} x^{2} + 160 a c^{4}} + \frac{47 e^{2 \operatorname{atan}{\left(a x \right)}}}{160 a^{7} c^{4} x^{6} + 480 a^{5} c^{4} x^{4} + 480 a^{3} c^{4} x^{2} + 160 a c^{4}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{2 \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**6*x**6*exp(2*atan(a*x))/(160*a**7*c**4*x**6 + 480*a**5*c**4*x**4 + 480*a**3*c**4*x**2 + 160*a*c**4) + 18*a**5*x**5*exp(2*atan(a*x))/(160*a**7*c**4*x**6 + 480*a**5*c**4*x**4 + 480*a**3*c**4*x**2 + 160*a*c**4) + 45*a**4*x**4*exp(2*atan(a*x))/(160*a**7*c**4*x**6 + 480*a**5*c**4*x**4 + 480*a**3*c**4*x**2 + 160*a*c**4) + 60*a**3*x**3*exp(2*atan(a*x))/(160*a**7*c**4*x**6 + 480*a**5*c**4*x**4 + 480*a**3*c**4*x**2 + 160*a*c**4) + 75*a**2*x**2*exp(2*atan(a*x))/(160*a**7*c**4*x**6 + 480*a**5*c**4*x**4 + 480*a**3*c**4*x**2 + 160*a*c**4) + 66*a*x*exp(2*atan(a*x))/(160*a**7*c**4*x**6 + 480*a**5*c**4*x**4 + 480*a**3*c**4*x**2 + 160*a*c**4) + 47*exp(2*atan(a*x))/(160*a**7*c**4*x**6 + 480*a**5*c**4*x**4 + 480*a**3*c**4*x**2 + 160*a*c**4), Ne(c, 0)), (zoo*Integral(exp(2*atan(a*x)), x), True))","F",0
267,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))*(a**2*c*x**2+c)**(3/2),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} e^{2 \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*exp(2*atan(a*x)), x)","F",0
268,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} e^{2 \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*exp(2*atan(a*x)), x)","F",0
269,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{2 \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(2*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
270,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c)**(3/2),x)","\int \frac{e^{2 \operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(2*atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
271,0,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c)**(5/2),x)","\int \frac{e^{2 \operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(exp(2*atan(a*x))/(c*(a**2*x**2 + 1))**(5/2), x)","F",0
272,-1,0,0,0.000000," ","integrate(exp(2*atan(a*x))/(a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**p/exp(atan(a*x)),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{p} e^{- \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**p*exp(-atan(a*x)), x)","F",0
274,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/exp(atan(a*x)),x)","c^{2} \left(\int 2 a^{2} x^{2} e^{- \operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{4} e^{- \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{- \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*exp(-atan(a*x)), x) + Integral(a**4*x**4*exp(-atan(a*x)), x) + Integral(exp(-atan(a*x)), x))","F",0
275,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/exp(atan(a*x)),x)","c \left(\int a^{2} x^{2} e^{- \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{- \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*exp(-atan(a*x)), x) + Integral(exp(-atan(a*x)), x))","F",0
276,0,0,0,0.000000," ","integrate(exp(-atan(a*x)),x)","\int e^{- \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(-atan(a*x)), x)","F",0
277,0,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c),x)","\begin{cases} - \frac{e^{- \operatorname{atan}{\left(a x \right)}}}{a c} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{- \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-exp(-atan(a*x))/(a*c), Ne(c, 0)), (zoo*Integral(exp(-atan(a*x)), x), True))","F",0
278,0,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c)**2,x)","\begin{cases} - \frac{2 a^{2} x^{2}}{5 a^{3} c^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}} + 5 a c^{2} e^{\operatorname{atan}{\left(a x \right)}}} + \frac{2 a x}{5 a^{3} c^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}} + 5 a c^{2} e^{\operatorname{atan}{\left(a x \right)}}} - \frac{3}{5 a^{3} c^{2} x^{2} e^{\operatorname{atan}{\left(a x \right)}} + 5 a c^{2} e^{\operatorname{atan}{\left(a x \right)}}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{- \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*x**2/(5*a**3*c**2*x**2*exp(atan(a*x)) + 5*a*c**2*exp(atan(a*x))) + 2*a*x/(5*a**3*c**2*x**2*exp(atan(a*x)) + 5*a*c**2*exp(atan(a*x))) - 3/(5*a**3*c**2*x**2*exp(atan(a*x)) + 5*a*c**2*exp(atan(a*x))), Ne(c, 0)), (zoo*Integral(exp(-atan(a*x)), x), True))","F",0
279,-1,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/exp(atan(a*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/exp(atan(a*x)),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} e^{- \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*exp(-atan(a*x)), x)","F",0
283,0,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{- \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(-atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
284,0,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c)**(3/2),x)","\int \frac{e^{- \operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(-atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
285,-1,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate(1/exp(atan(a*x))/(a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**p/exp(2*atan(a*x)),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{p} e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**p*exp(-2*atan(a*x)), x)","F",0
288,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**2/exp(2*atan(a*x)),x)","c^{2} \left(\int 2 a^{2} x^{2} e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{4} e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*exp(-2*atan(a*x)), x) + Integral(a**4*x**4*exp(-2*atan(a*x)), x) + Integral(exp(-2*atan(a*x)), x))","F",0
289,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)/exp(2*atan(a*x)),x)","c \left(\int a^{2} x^{2} e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*exp(-2*atan(a*x)), x) + Integral(exp(-2*atan(a*x)), x))","F",0
290,0,0,0,0.000000," ","integrate(exp(-2*atan(a*x)),x)","\int e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(-2*atan(a*x)), x)","F",0
291,0,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c),x)","\begin{cases} - \frac{e^{- 2 \operatorname{atan}{\left(a x \right)}}}{2 a c} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-exp(-2*atan(a*x))/(2*a*c), Ne(c, 0)), (zoo*Integral(exp(-2*atan(a*x)), x), True))","F",0
292,0,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c)**2,x)","\begin{cases} - \frac{a^{2} x^{2}}{8 a^{3} c^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}} + 8 a c^{2} e^{2 \operatorname{atan}{\left(a x \right)}}} + \frac{2 a x}{8 a^{3} c^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}} + 8 a c^{2} e^{2 \operatorname{atan}{\left(a x \right)}}} - \frac{3}{8 a^{3} c^{2} x^{2} e^{2 \operatorname{atan}{\left(a x \right)}} + 8 a c^{2} e^{2 \operatorname{atan}{\left(a x \right)}}} & \text{for}\: c \neq 0 \\\tilde{\infty} \int e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**2/(8*a**3*c**2*x**2*exp(2*atan(a*x)) + 8*a*c**2*exp(2*atan(a*x))) + 2*a*x/(8*a**3*c**2*x**2*exp(2*atan(a*x)) + 8*a*c**2*exp(2*atan(a*x))) - 3/(8*a**3*c**2*x**2*exp(2*atan(a*x)) + 8*a*c**2*exp(2*atan(a*x))), Ne(c, 0)), (zoo*Integral(exp(-2*atan(a*x)), x), True))","F",0
293,-1,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,-1,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(3/2)/exp(2*atan(a*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**(1/2)/exp(2*atan(a*x)),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} e^{- 2 \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*exp(-2*atan(a*x)), x)","F",0
297,0,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{- 2 \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(-2*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
298,-1,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate(1/exp(2*atan(a*x))/(a**2*c*x**2+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,1,37,0,0.307738," ","integrate((1+I*a*x)**5/(a**2*x**2+1)**3,x)","- \frac{- 4 a x - 2 i}{- a^{3} x^{2} - 2 i a^{2} x + a} + \frac{i \log{\left(i a x - 1 \right)}}{a}"," ",0,"-(-4*a*x - 2*I)/(-a**3*x**2 - 2*I*a**2*x + a) + I*log(I*a*x - 1)/a","A",0
302,0,0,0,0.000000," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**(5/2),x)","\int \frac{\left(a x - i\right)^{4}}{\left(a^{2} x^{2} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*x - I)**4/(a**2*x**2 + 1)**(5/2), x)","F",0
303,1,19,0,0.162793," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**2,x)","\frac{2}{a^{2} x + i a} - \frac{i \log{\left(a x + i \right)}}{a}"," ",0,"2/(a**2*x + I*a) - I*log(a*x + I)/a","A",0
304,0,0,0,0.000000," ","integrate((1+I*a*x)**2/(a**2*x**2+1)**(3/2),x)","- \int \frac{a^{2} x^{2}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx - \int \left(- \frac{2 i a x}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx - \int \left(- \frac{1}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx"," ",0,"-Integral(a**2*x**2/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) - Integral(-2*I*a*x/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) - Integral(-1/(a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x)","F",0
305,1,10,0,0.058300," ","integrate((1+I*a*x)/(a**2*x**2+1),x)","\frac{i \log{\left(i a x - 1 \right)}}{a}"," ",0,"I*log(I*a*x - 1)/a","A",0
306,1,14,0,0.053904," ","integrate(1/(1+I*a*x),x)","- \frac{i \log{\left(- i a x - 1 \right)}}{a}"," ",0,"-I*log(-I*a*x - 1)/a","A",0
307,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1)**(1/2),x)","- \int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{2} x^{2} - 2 i a x - 1}\, dx"," ",0,"-Integral(sqrt(a**2*x**2 + 1)/(a**2*x**2 - 2*I*a*x - 1), x)","F",0
308,1,19,0,0.157855," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1),x)","\frac{2}{a^{2} x - i a} + \frac{i \log{\left(a x - i \right)}}{a}"," ",0,"2/(a**2*x - I*a) + I*log(a*x - I)/a","A",0
309,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**4*(a**2*x**2+1)**(3/2),x)","\int \frac{\left(a^{2} x^{2} + 1\right)^{\frac{3}{2}}}{\left(a x - i\right)^{4}}\, dx"," ",0,"Integral((a**2*x**2 + 1)**(3/2)/(a*x - I)**4, x)","F",0
310,0,0,0,0.000000," ","integrate((1+I*a*x)**5/(a**2*x**2+1)**(5/2)/(a**2*c*x**2+c)**(1/2),x)","i \left(\int \left(- \frac{i}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{5 a x}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{10 a^{3} x^{3}}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{a^{5} x^{5}}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \frac{10 i a^{2} x^{2}}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{5 i a^{4} x^{4}}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx\right)"," ",0,"I*(Integral(-I/(a**4*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(5*a*x/(a**4*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-10*a**3*x**3/(a**4*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(a**5*x**5/(a**4*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(10*I*a**2*x**2/(a**4*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-5*I*a**4*x**4/(a**4*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x))","F",0
311,0,0,0,0.000000," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\left(a x - i\right)^{4}}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \left(a^{2} x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral((a*x - I)**4/(sqrt(c*(a**2*x**2 + 1))*(a**2*x**2 + 1)**2), x)","F",0
312,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","- i \left(\int \frac{i}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{3 a x}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-3*a*x/(a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(a**3*x**3/(a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-3*I*a**2*x**2/(a**2*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x))","F",0
313,0,0,0,0.000000," ","integrate((1+I*a*x)**2/(a**2*x**2+1)/(a**2*c*x**2+c)**(1/2),x)","- \int \frac{a^{2} x^{2}}{a^{2} x^{2} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} c x^{2} + c}}\, dx - \int \left(- \frac{2 i a x}{a^{2} x^{2} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} c x^{2} + c}}\right)\, dx - \int \left(- \frac{1}{a^{2} x^{2} \sqrt{a^{2} c x^{2} + c} + \sqrt{a^{2} c x^{2} + c}}\right)\, dx"," ",0,"-Integral(a**2*x**2/(a**2*x**2*sqrt(a**2*c*x**2 + c) + sqrt(a**2*c*x**2 + c)), x) - Integral(-2*I*a*x/(a**2*x**2*sqrt(a**2*c*x**2 + c) + sqrt(a**2*c*x**2 + c)), x) - Integral(-1/(a**2*x**2*sqrt(a**2*c*x**2 + c) + sqrt(a**2*c*x**2 + c)), x)","F",0
314,0,0,0,0.000000," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","i \left(\int \left(- \frac{i}{\sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{a x}{\sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx\right)"," ",0,"I*(Integral(-I/(sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(a*x/(sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x))","F",0
315,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2)/(a**2*c*x**2+c)**(1/2),x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a x \sqrt{a^{2} c x^{2} + c} - i \sqrt{a^{2} c x^{2} + c}}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a*x*sqrt(a**2*c*x**2 + c) - I*sqrt(a**2*c*x**2 + c)), x)","F",0
316,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1)/(a**2*c*x**2+c)**(1/2),x)","- \int \frac{a^{2} x^{2}}{a^{2} x^{2} \sqrt{a^{2} c x^{2} + c} - 2 i a x \sqrt{a^{2} c x^{2} + c} - \sqrt{a^{2} c x^{2} + c}}\, dx - \int \frac{1}{a^{2} x^{2} \sqrt{a^{2} c x^{2} + c} - 2 i a x \sqrt{a^{2} c x^{2} + c} - \sqrt{a^{2} c x^{2} + c}}\, dx"," ",0,"-Integral(a**2*x**2/(a**2*x**2*sqrt(a**2*c*x**2 + c) - 2*I*a*x*sqrt(a**2*c*x**2 + c) - sqrt(a**2*c*x**2 + c)), x) - Integral(1/(a**2*x**2*sqrt(a**2*c*x**2 + c) - 2*I*a*x*sqrt(a**2*c*x**2 + c) - sqrt(a**2*c*x**2 + c)), x)","F",0
317,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/(a**2*c*x**2+c)**(1/2),x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} \sqrt{a^{2} c x^{2} + c} - 3 i a^{2} x^{2} \sqrt{a^{2} c x^{2} + c} - 3 a x \sqrt{a^{2} c x^{2} + c} + i \sqrt{a^{2} c x^{2} + c}}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} x^{3} \sqrt{a^{2} c x^{2} + c} - 3 i a^{2} x^{2} \sqrt{a^{2} c x^{2} + c} - 3 a x \sqrt{a^{2} c x^{2} + c} + i \sqrt{a^{2} c x^{2} + c}}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**3*x**3*sqrt(a**2*c*x**2 + c) - 3*I*a**2*x**2*sqrt(a**2*c*x**2 + c) - 3*a*x*sqrt(a**2*c*x**2 + c) + I*sqrt(a**2*c*x**2 + c)), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**3*x**3*sqrt(a**2*c*x**2 + c) - 3*I*a**2*x**2*sqrt(a**2*c*x**2 + c) - 3*a*x*sqrt(a**2*c*x**2 + c) + I*sqrt(a**2*c*x**2 + c)), x))","F",0
318,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**4*(a**2*x**2+1)**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{\left(a^{2} x^{2} + 1\right)^{2}}{\sqrt{c \left(a^{2} x^{2} + 1\right)} \left(a x - i\right)^{4}}\, dx"," ",0,"Integral((a**2*x**2 + 1)**2/(sqrt(c*(a**2*x**2 + 1))*(a*x - I)**4), x)","F",0
319,1,37,0,0.310607," ","integrate((1+I*a*x)**5/(a**2*x**2+1)**4,x)","\frac{3 i a x + 1}{- 6 a^{4} x^{3} - 18 i a^{3} x^{2} + 18 a^{2} x + 6 i a}"," ",0,"(3*I*a*x + 1)/(-6*a**4*x**3 - 18*I*a**3*x**2 + 18*a**2*x + 6*I*a)","A",0
320,0,0,0,0.000000," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**(7/2),x)","\int \frac{\left(a x - i\right)^{4}}{\left(a^{2} x^{2} + 1\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a*x - I)**4/(a**2*x**2 + 1)**(7/2), x)","F",0
321,1,20,0,0.189508," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**3,x)","\frac{i}{2 a^{3} x^{2} + 4 i a^{2} x - 2 a}"," ",0,"I/(2*a**3*x**2 + 4*I*a**2*x - 2*a)","A",0
322,0,0,0,0.000000," ","integrate((1+I*a*x)**2/(a**2*x**2+1)**(5/2),x)","- \int \frac{a^{2} x^{2}}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\, dx - \int \left(- \frac{2 i a x}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx - \int \left(- \frac{1}{a^{4} x^{4} \sqrt{a^{2} x^{2} + 1} + 2 a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} + \sqrt{a^{2} x^{2} + 1}}\right)\, dx"," ",0,"-Integral(a**2*x**2/(a**4*x**4*sqrt(a**2*x**2 + 1) + 2*a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) - Integral(-2*I*a*x/(a**4*x**4*sqrt(a**2*x**2 + 1) + 2*a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x) - Integral(-1/(a**4*x**4*sqrt(a**2*x**2 + 1) + 2*a**2*x**2*sqrt(a**2*x**2 + 1) + sqrt(a**2*x**2 + 1)), x)","F",0
323,1,34,0,0.209548," ","integrate((1+I*a*x)/(a**2*x**2+1)**2,x)","\frac{1}{2 a^{2} x + 2 i a} - \frac{\frac{i \log{\left(x - \frac{i}{a} \right)}}{4} - \frac{i \log{\left(x + \frac{i}{a} \right)}}{4}}{a}"," ",0,"1/(2*a**2*x + 2*I*a) - (I*log(x - I/a)/4 - I*log(x + I/a)/4)/a","A",0
324,1,34,0,0.204024," ","integrate(1/(1+I*a*x)/(a**2*x**2+1),x)","\frac{1}{2 a^{2} x - 2 i a} + \frac{- \frac{i \log{\left(x - \frac{i}{a} \right)}}{4} + \frac{i \log{\left(x + \frac{i}{a} \right)}}{4}}{a}"," ",0,"1/(2*a**2*x - 2*I*a) + (-I*log(x - I/a)/4 + I*log(x + I/a)/4)/a","A",0
325,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**2/(a**2*x**2+1)**(1/2),x)","- \int \frac{1}{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1} - 2 i a x \sqrt{a^{2} x^{2} + 1} - \sqrt{a^{2} x^{2} + 1}}\, dx"," ",0,"-Integral(1/(a**2*x**2*sqrt(a**2*x**2 + 1) - 2*I*a*x*sqrt(a**2*x**2 + 1) - sqrt(a**2*x**2 + 1)), x)","F",0
326,1,22,0,0.172431," ","integrate(1/(1+I*a*x)**3,x)","- \frac{i}{2 a^{3} x^{2} - 4 i a^{2} x - 2 a}"," ",0,"-I/(2*a**3*x**2 - 4*I*a**2*x - 2*a)","A",0
327,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**4*(a**2*x**2+1)**(1/2),x)","\int \frac{\sqrt{a^{2} x^{2} + 1}}{\left(a x - i\right)^{4}}\, dx"," ",0,"Integral(sqrt(a**2*x**2 + 1)/(a*x - I)**4, x)","F",0
328,0,0,0,0.000000," ","integrate((1+I*a*x)**5/(a**2*x**2+1)**(5/2)/(a**2*c*x**2+c)**(3/2),x)","i \left(\int \left(- \frac{i}{a^{6} c x^{6} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{5 a x}{a^{6} c x^{6} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{10 a^{3} x^{3}}{a^{6} c x^{6} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{a^{5} x^{5}}{a^{6} c x^{6} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \frac{10 i a^{2} x^{2}}{a^{6} c x^{6} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{5 i a^{4} x^{4}}{a^{6} c x^{6} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 3 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx\right)"," ",0,"I*(Integral(-I/(a**6*c*x**6*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(5*a*x/(a**6*c*x**6*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-10*a**3*x**3/(a**6*c*x**6*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(a**5*x**5/(a**6*c*x**6*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(10*I*a**2*x**2/(a**6*c*x**6*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-5*I*a**4*x**4/(a**6*c*x**6*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 3*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x))","F",0
329,0,0,0,0.000000," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\left(a x - i\right)^{4}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a^{2} x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral((a*x - I)**4/((c*(a**2*x**2 + 1))**(3/2)*(a**2*x**2 + 1)**2), x)","F",0
330,0,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","- i \left(\int \frac{i}{a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{3 a x}{a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{a^{3} x^{3}}{a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx + \int \left(- \frac{3 i a^{2} x^{2}}{a^{4} c x^{4} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx\right)"," ",0,"-I*(Integral(I/(a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-3*a*x/(a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(a**3*x**3/(a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(-3*I*a**2*x**2/(a**4*c*x**4*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + 2*a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x))","F",0
331,0,0,0,0.000000," ","integrate((1+I*a*x)**2/(a**2*x**2+1)/(a**2*c*x**2+c)**(3/2),x)","- \int \frac{a^{2} x^{2}}{a^{4} c x^{4} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} c x^{2} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} c x^{2} + c}}\, dx - \int \left(- \frac{2 i a x}{a^{4} c x^{4} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} c x^{2} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} c x^{2} + c}}\right)\, dx - \int \left(- \frac{1}{a^{4} c x^{4} \sqrt{a^{2} c x^{2} + c} + 2 a^{2} c x^{2} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} c x^{2} + c}}\right)\, dx"," ",0,"-Integral(a**2*x**2/(a**4*c*x**4*sqrt(a**2*c*x**2 + c) + 2*a**2*c*x**2*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*c*x**2 + c)), x) - Integral(-2*I*a*x/(a**4*c*x**4*sqrt(a**2*c*x**2 + c) + 2*a**2*c*x**2*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*c*x**2 + c)), x) - Integral(-1/(a**4*c*x**4*sqrt(a**2*c*x**2 + c) + 2*a**2*c*x**2*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*c*x**2 + c)), x)","F",0
332,0,0,0,0.000000," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","i \left(\int \left(- \frac{i}{a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{a x}{a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx\right)"," ",0,"I*(Integral(-I/(a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(a*x/(a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x))","F",0
333,0,0,0,0.000000," ","integrate(1/(1+I*a*x)*(a**2*x**2+1)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","- i \int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{3} c x^{3} \sqrt{a^{2} c x^{2} + c} - i a^{2} c x^{2} \sqrt{a^{2} c x^{2} + c} + a c x \sqrt{a^{2} c x^{2} + c} - i c \sqrt{a^{2} c x^{2} + c}}\, dx"," ",0,"-I*Integral(sqrt(a**2*x**2 + 1)/(a**3*c*x**3*sqrt(a**2*c*x**2 + c) - I*a**2*c*x**2*sqrt(a**2*c*x**2 + c) + a*c*x*sqrt(a**2*c*x**2 + c) - I*c*sqrt(a**2*c*x**2 + c)), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**2*(a**2*x**2+1)/(a**2*c*x**2+c)**(3/2),x)","- \int \frac{a^{2} x^{2}}{a^{4} c x^{4} \sqrt{a^{2} c x^{2} + c} - 2 i a^{3} c x^{3} \sqrt{a^{2} c x^{2} + c} - 2 i a c x \sqrt{a^{2} c x^{2} + c} - c \sqrt{a^{2} c x^{2} + c}}\, dx - \int \frac{1}{a^{4} c x^{4} \sqrt{a^{2} c x^{2} + c} - 2 i a^{3} c x^{3} \sqrt{a^{2} c x^{2} + c} - 2 i a c x \sqrt{a^{2} c x^{2} + c} - c \sqrt{a^{2} c x^{2} + c}}\, dx"," ",0,"-Integral(a**2*x**2/(a**4*c*x**4*sqrt(a**2*c*x**2 + c) - 2*I*a**3*c*x**3*sqrt(a**2*c*x**2 + c) - 2*I*a*c*x*sqrt(a**2*c*x**2 + c) - c*sqrt(a**2*c*x**2 + c)), x) - Integral(1/(a**4*c*x**4*sqrt(a**2*c*x**2 + c) - 2*I*a**3*c*x**3*sqrt(a**2*c*x**2 + c) - 2*I*a*c*x*sqrt(a**2*c*x**2 + c) - c*sqrt(a**2*c*x**2 + c)), x)","F",0
335,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/(a**2*c*x**2+c)**(3/2),x)","i \left(\int \frac{\sqrt{a^{2} x^{2} + 1}}{a^{5} c x^{5} \sqrt{a^{2} c x^{2} + c} - 3 i a^{4} c x^{4} \sqrt{a^{2} c x^{2} + c} - 2 a^{3} c x^{3} \sqrt{a^{2} c x^{2} + c} - 2 i a^{2} c x^{2} \sqrt{a^{2} c x^{2} + c} - 3 a c x \sqrt{a^{2} c x^{2} + c} + i c \sqrt{a^{2} c x^{2} + c}}\, dx + \int \frac{a^{2} x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{5} c x^{5} \sqrt{a^{2} c x^{2} + c} - 3 i a^{4} c x^{4} \sqrt{a^{2} c x^{2} + c} - 2 a^{3} c x^{3} \sqrt{a^{2} c x^{2} + c} - 2 i a^{2} c x^{2} \sqrt{a^{2} c x^{2} + c} - 3 a c x \sqrt{a^{2} c x^{2} + c} + i c \sqrt{a^{2} c x^{2} + c}}\, dx\right)"," ",0,"I*(Integral(sqrt(a**2*x**2 + 1)/(a**5*c*x**5*sqrt(a**2*c*x**2 + c) - 3*I*a**4*c*x**4*sqrt(a**2*c*x**2 + c) - 2*a**3*c*x**3*sqrt(a**2*c*x**2 + c) - 2*I*a**2*c*x**2*sqrt(a**2*c*x**2 + c) - 3*a*c*x*sqrt(a**2*c*x**2 + c) + I*c*sqrt(a**2*c*x**2 + c)), x) + Integral(a**2*x**2*sqrt(a**2*x**2 + 1)/(a**5*c*x**5*sqrt(a**2*c*x**2 + c) - 3*I*a**4*c*x**4*sqrt(a**2*c*x**2 + c) - 2*a**3*c*x**3*sqrt(a**2*c*x**2 + c) - 2*I*a**2*c*x**2*sqrt(a**2*c*x**2 + c) - 3*a*c*x*sqrt(a**2*c*x**2 + c) + I*c*sqrt(a**2*c*x**2 + c)), x))","F",0
336,0,0,0,0.000000," ","integrate(1/(1+I*a*x)**4*(a**2*x**2+1)**2/(a**2*c*x**2+c)**(3/2),x)","\int \frac{\left(a^{2} x^{2} + 1\right)^{2}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} \left(a x - i\right)^{4}}\, dx"," ",0,"Integral((a**2*x**2 + 1)**2/((c*(a**2*x**2 + 1))**(3/2)*(a*x - I)**4), x)","F",0
337,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*(a**2*c*x**2+c)**2,x)","c^{2} \left(\int 2 a^{2} x^{2} e^{n \operatorname{atan}{\left(a x \right)}}\, dx + \int a^{4} x^{4} e^{n \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{n \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c**2*(Integral(2*a**2*x**2*exp(n*atan(a*x)), x) + Integral(a**4*x**4*exp(n*atan(a*x)), x) + Integral(exp(n*atan(a*x)), x))","F",0
338,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*(a**2*c*x**2+c),x)","c \left(\int a^{2} x^{2} e^{n \operatorname{atan}{\left(a x \right)}}\, dx + \int e^{n \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(a**2*x**2*exp(n*atan(a*x)), x) + Integral(exp(n*atan(a*x)), x))","F",0
339,0,0,0,0.000000," ","integrate(exp(n*atan(a*x)),x)","\int e^{n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(n*atan(a*x)), x)","F",0
340,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{3} e^{n \operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**3*exp(n*atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
341,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**2/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{2} e^{n \operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**2*exp(n*atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
342,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x/(a**2*c*x**2+c),x)","\frac{\int \frac{x e^{n \operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x*exp(n*atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
343,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/(a**2*c*x**2+c),x)","\begin{cases} \tilde{\infty} x & \text{for}\: c = 0 \wedge n = 0 \\\tilde{\infty} \int e^{n \operatorname{atan}{\left(a x \right)}}\, dx & \text{for}\: c = 0 \\\frac{\operatorname{atan}{\left(a x \right)}}{a c} & \text{for}\: n = 0 \\\frac{e^{n \operatorname{atan}{\left(a x \right)}}}{a c n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(c, 0) & Eq(n, 0)), (zoo*Integral(exp(n*atan(a*x)), x), Eq(c, 0)), (atan(a*x)/(a*c), Eq(n, 0)), (exp(n*atan(a*x))/(a*c*n), True))","F",0
344,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/x/(a**2*c*x**2+c),x)","\frac{\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{a^{2} x^{3} + x}\, dx}{c}"," ",0,"Integral(exp(n*atan(a*x))/(a**2*x**3 + x), x)/c","F",0
345,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/x**2/(a**2*c*x**2+c),x)","\frac{\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{a^{2} x^{4} + x^{2}}\, dx}{c}"," ",0,"Integral(exp(n*atan(a*x))/(a**2*x**4 + x**2), x)/c","F",0
346,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/x**3/(a**2*c*x**2+c),x)","\frac{\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{a^{2} x^{5} + x^{3}}\, dx}{c}"," ",0,"Integral(exp(n*atan(a*x))/(a**2*x**5 + x**3), x)/c","F",0
347,-1,0,0,0.000000," ","integrate(exp(n*atan(a*x))/(a**2*c*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*(a**2*c*x**2+c)**(3/2),x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}} e^{n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(3/2)*exp(n*atan(a*x)), x)","F",0
349,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*(a**2*c*x**2+c)**(1/2),x)","\int \sqrt{c \left(a^{2} x^{2} + 1\right)} e^{n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(c*(a**2*x**2 + 1))*exp(n*atan(a*x)), x)","F",0
350,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
351,-1,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**2*(a**2*c*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**2*(a**2*c*x**2+c)**(1/2),x)","\int x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)} e^{n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2*sqrt(c*(a**2*x**2 + 1))*exp(n*atan(a*x)), x)","F",0
353,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{3} e^{n \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*exp(n*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
354,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{2} e^{n \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**2*exp(n*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
355,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x e^{n \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x*exp(n*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
356,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
357,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/x/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{x \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/(x*sqrt(c*(a**2*x**2 + 1))), x)","F",0
358,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/x**2/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{x^{2} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/(x**2*sqrt(c*(a**2*x**2 + 1))), x)","F",0
359,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/x**3/(a**2*c*x**2+c)**(1/2),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{x^{3} \sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/(x**3*sqrt(c*(a**2*x**2 + 1))), x)","F",0
360,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*(a**2*c*x**2+c)**(1/3),x)","\int \sqrt[3]{c \left(a^{2} x^{2} + 1\right)} e^{n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**(1/3)*exp(n*atan(a*x)), x)","F",0
361,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/(a**2*c*x**2+c)**(1/3),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{\sqrt[3]{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/(c*(a**2*x**2 + 1))**(1/3), x)","F",0
362,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/(a**2*c*x**2+c)**(2/3),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/(c*(a**2*x**2 + 1))**(2/3), x)","F",0
363,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))/(a**2*c*x**2+c)**(4/3),x)","\int \frac{e^{n \operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(exp(n*atan(a*x))/(c*(a**2*x**2 + 1))**(4/3), x)","F",0
364,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**m*(a**2*c*x**2+c),x)","c \left(\int x^{m} e^{n \operatorname{atan}{\left(a x \right)}}\, dx + \int a^{2} x^{2} x^{m} e^{n \operatorname{atan}{\left(a x \right)}}\, dx\right)"," ",0,"c*(Integral(x**m*exp(n*atan(a*x)), x) + Integral(a**2*x**2*x**m*exp(n*atan(a*x)), x))","F",0
365,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**m/(a**2*c*x**2+c),x)","\frac{\int \frac{x^{m} e^{n \operatorname{atan}{\left(a x \right)}}}{a^{2} x^{2} + 1}\, dx}{c}"," ",0,"Integral(x**m*exp(n*atan(a*x))/(a**2*x**2 + 1), x)/c","F",0
366,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**m/(a**2*c*x**2+c)**2,x)","\frac{\int \frac{x^{m} e^{n \operatorname{atan}{\left(a x \right)}}}{a^{4} x^{4} + 2 a^{2} x^{2} + 1}\, dx}{c^{2}}"," ",0,"Integral(x**m*exp(n*atan(a*x))/(a**4*x**4 + 2*a**2*x**2 + 1), x)/c**2","F",0
367,-1,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**m/(a**2*c*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**m/(a**2*c*x**2+c)**(1/2),x)","\int \frac{x^{m} e^{n \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**m*exp(n*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x)","F",0
369,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**m/(a**2*c*x**2+c)**(3/2),x)","\int \frac{x^{m} e^{n \operatorname{atan}{\left(a x \right)}}}{\left(c \left(a^{2} x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*exp(n*atan(a*x))/(c*(a**2*x**2 + 1))**(3/2), x)","F",0
370,-1,0,0,0.000000," ","integrate(exp(n*atan(a*x))*x**m/(a**2*c*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,0,0,0,0.000000," ","integrate(exp(n*atan(a*x))*(a**2*c*x**2+c)**p,x)","\int \left(c \left(a^{2} x^{2} + 1\right)\right)^{p} e^{n \operatorname{atan}{\left(a x \right)}}\, dx"," ",0,"Integral((c*(a**2*x**2 + 1))**p*exp(n*atan(a*x)), x)","F",0
372,0,0,0,0.000000," ","integrate((a**2*c*x**2+c)**p/exp(2*I*p*atan(a*x)),x)","\begin{cases} \frac{x}{\sqrt{c}} & \text{for}\: a = 0 \wedge p = - \frac{1}{2} \\c^{p} x & \text{for}\: a = 0 \\\int \frac{e^{i \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{i a x \left(a^{2} c x^{2} + c\right)^{p}}{2 i a p e^{2 i p \operatorname{atan}{\left(a x \right)}} + i a e^{2 i p \operatorname{atan}{\left(a x \right)}}} - \frac{\left(a^{2} c x^{2} + c\right)^{p}}{2 i a p e^{2 i p \operatorname{atan}{\left(a x \right)}} + i a e^{2 i p \operatorname{atan}{\left(a x \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/sqrt(c), Eq(a, 0) & Eq(p, -1/2)), (c**p*x, Eq(a, 0)), (Integral(exp(I*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x), Eq(p, -1/2)), (I*a*x*(a**2*c*x**2 + c)**p/(2*I*a*p*exp(2*I*p*atan(a*x)) + I*a*exp(2*I*p*atan(a*x))) - (a**2*c*x**2 + c)**p/(2*I*a*p*exp(2*I*p*atan(a*x)) + I*a*exp(2*I*p*atan(a*x))), True))","F",0
373,0,0,0,0.000000," ","integrate(exp(2*I*p*atan(a*x))*(a**2*c*x**2+c)**p,x)","\begin{cases} \frac{x}{\sqrt{c}} & \text{for}\: a = 0 \wedge p = - \frac{1}{2} \\c^{p} x & \text{for}\: a = 0 \\\int \frac{e^{- i \operatorname{atan}{\left(a x \right)}}}{\sqrt{c \left(a^{2} x^{2} + 1\right)}}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a x \left(a^{2} c x^{2} + c\right)^{p} e^{2 i p \operatorname{atan}{\left(a x \right)}}}{2 a p + a} - \frac{i \left(a^{2} c x^{2} + c\right)^{p} e^{2 i p \operatorname{atan}{\left(a x \right)}}}{2 a p + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/sqrt(c), Eq(a, 0) & Eq(p, -1/2)), (c**p*x, Eq(a, 0)), (Integral(exp(-I*atan(a*x))/sqrt(c*(a**2*x**2 + 1)), x), Eq(p, -1/2)), (a*x*(a**2*c*x**2 + c)**p*exp(2*I*p*atan(a*x))/(2*a*p + a) - I*(a**2*c*x**2 + c)**p*exp(2*I*p*atan(a*x))/(2*a*p + a), True))","F",0
374,-1,0,0,0.000000," ","integrate(exp(I*n*atan(a*x))*x**2*(a**2*c*x**2+c)**(-1-1/2*n**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,1,437,0,6.496391," ","integrate((1+I*a*x)**6/(a**2*x**2+1)**3*x**2/(a**2*c*x**2+c)**19,x)","- \frac{6 a x + i}{- 210 a^{39} c^{19} x^{36} - 1260 i a^{38} c^{19} x^{35} - 14700 i a^{36} c^{19} x^{33} + 22050 a^{35} c^{19} x^{32} - 70560 i a^{34} c^{19} x^{31} + 188160 a^{33} c^{19} x^{30} - 151200 i a^{32} c^{19} x^{29} + 819000 a^{31} c^{19} x^{28} + 58800 i a^{30} c^{19} x^{27} + 2257920 a^{29} c^{19} x^{26} + 1375920 i a^{28} c^{19} x^{25} + 4204200 a^{27} c^{19} x^{24} + 4586400 i a^{26} c^{19} x^{23} + 5241600 a^{25} c^{19} x^{22} + 9129120 i a^{24} c^{19} x^{21} + 3783780 a^{23} c^{19} x^{20} + 12612600 i a^{22} c^{19} x^{19} + 12612600 i a^{20} c^{19} x^{17} - 3783780 a^{19} c^{19} x^{16} + 9129120 i a^{18} c^{19} x^{15} - 5241600 a^{17} c^{19} x^{14} + 4586400 i a^{16} c^{19} x^{13} - 4204200 a^{15} c^{19} x^{12} + 1375920 i a^{14} c^{19} x^{11} - 2257920 a^{13} c^{19} x^{10} + 58800 i a^{12} c^{19} x^{9} - 819000 a^{11} c^{19} x^{8} - 151200 i a^{10} c^{19} x^{7} - 188160 a^{9} c^{19} x^{6} - 70560 i a^{8} c^{19} x^{5} - 22050 a^{7} c^{19} x^{4} - 14700 i a^{6} c^{19} x^{3} - 1260 i a^{4} c^{19} x + 210 a^{3} c^{19}}"," ",0,"-(6*a*x + I)/(-210*a**39*c**19*x**36 - 1260*I*a**38*c**19*x**35 - 14700*I*a**36*c**19*x**33 + 22050*a**35*c**19*x**32 - 70560*I*a**34*c**19*x**31 + 188160*a**33*c**19*x**30 - 151200*I*a**32*c**19*x**29 + 819000*a**31*c**19*x**28 + 58800*I*a**30*c**19*x**27 + 2257920*a**29*c**19*x**26 + 1375920*I*a**28*c**19*x**25 + 4204200*a**27*c**19*x**24 + 4586400*I*a**26*c**19*x**23 + 5241600*a**25*c**19*x**22 + 9129120*I*a**24*c**19*x**21 + 3783780*a**23*c**19*x**20 + 12612600*I*a**22*c**19*x**19 + 12612600*I*a**20*c**19*x**17 - 3783780*a**19*c**19*x**16 + 9129120*I*a**18*c**19*x**15 - 5241600*a**17*c**19*x**14 + 4586400*I*a**16*c**19*x**13 - 4204200*a**15*c**19*x**12 + 1375920*I*a**14*c**19*x**11 - 2257920*a**13*c**19*x**10 + 58800*I*a**12*c**19*x**9 - 819000*a**11*c**19*x**8 - 151200*I*a**10*c**19*x**7 - 188160*a**9*c**19*x**6 - 70560*I*a**8*c**19*x**5 - 22050*a**7*c**19*x**4 - 14700*I*a**6*c**19*x**3 - 1260*I*a**4*c**19*x + 210*a**3*c**19)","B",0
376,1,192,0,1.765424," ","integrate((1+I*a*x)**4/(a**2*x**2+1)**2*x**2/(a**2*c*x**2+c)**9,x)","\frac{4 a x + i}{- 60 a^{19} c^{9} x^{16} - 240 i a^{18} c^{9} x^{15} - 1200 i a^{16} c^{9} x^{13} + 1200 a^{15} c^{9} x^{12} - 2160 i a^{14} c^{9} x^{11} + 3840 a^{13} c^{9} x^{10} - 1200 i a^{12} c^{9} x^{9} + 5400 a^{11} c^{9} x^{8} + 1200 i a^{10} c^{9} x^{7} + 3840 a^{9} c^{9} x^{6} + 2160 i a^{8} c^{9} x^{5} + 1200 a^{7} c^{9} x^{4} + 1200 i a^{6} c^{9} x^{3} + 240 i a^{4} c^{9} x - 60 a^{3} c^{9}}"," ",0,"(4*a*x + I)/(-60*a**19*c**9*x**16 - 240*I*a**18*c**9*x**15 - 1200*I*a**16*c**9*x**13 + 1200*a**15*c**9*x**12 - 2160*I*a**14*c**9*x**11 + 3840*a**13*c**9*x**10 - 1200*I*a**12*c**9*x**9 + 5400*a**11*c**9*x**8 + 1200*I*a**10*c**9*x**7 + 3840*a**9*c**9*x**6 + 2160*I*a**8*c**9*x**5 + 1200*a**7*c**9*x**4 + 1200*I*a**6*c**9*x**3 + 240*I*a**4*c**9*x - 60*a**3*c**9)","B",0
377,1,53,0,0.435439," ","integrate((1+I*a*x)**2/(a**2*x**2+1)*x**2/(a**2*c*x**2+c)**3,x)","- \frac{2 a x + i}{- 6 a^{7} c^{3} x^{4} - 12 i a^{6} c^{3} x^{3} - 12 i a^{4} c^{3} x + 6 a^{3} c^{3}}"," ",0,"-(2*a*x + I)/(-6*a**7*c**3*x**4 - 12*I*a**6*c**3*x**3 - 12*I*a**4*c**3*x + 6*a**3*c**3)","A",0
378,1,53,0,0.404368," ","integrate(x**2/(1+I*a*x)**2*(a**2*x**2+1)/(a**2*c*x**2+c)**3,x)","- \frac{2 a x - i}{- 6 a^{7} c^{3} x^{4} + 12 i a^{6} c^{3} x^{3} + 12 i a^{4} c^{3} x + 6 a^{3} c^{3}}"," ",0,"-(2*a*x - I)/(-6*a**7*c**3*x**4 + 12*I*a**6*c**3*x**3 + 12*I*a**4*c**3*x + 6*a**3*c**3)","A",0
379,1,192,0,1.492840," ","integrate(x**2/(1+I*a*x)**4*(a**2*x**2+1)**2/(a**2*c*x**2+c)**9,x)","\frac{4 a x - i}{- 60 a^{19} c^{9} x^{16} + 240 i a^{18} c^{9} x^{15} + 1200 i a^{16} c^{9} x^{13} + 1200 a^{15} c^{9} x^{12} + 2160 i a^{14} c^{9} x^{11} + 3840 a^{13} c^{9} x^{10} + 1200 i a^{12} c^{9} x^{9} + 5400 a^{11} c^{9} x^{8} - 1200 i a^{10} c^{9} x^{7} + 3840 a^{9} c^{9} x^{6} - 2160 i a^{8} c^{9} x^{5} + 1200 a^{7} c^{9} x^{4} - 1200 i a^{6} c^{9} x^{3} - 240 i a^{4} c^{9} x - 60 a^{3} c^{9}}"," ",0,"(4*a*x - I)/(-60*a**19*c**9*x**16 + 240*I*a**18*c**9*x**15 + 1200*I*a**16*c**9*x**13 + 1200*a**15*c**9*x**12 + 2160*I*a**14*c**9*x**11 + 3840*a**13*c**9*x**10 + 1200*I*a**12*c**9*x**9 + 5400*a**11*c**9*x**8 - 1200*I*a**10*c**9*x**7 + 3840*a**9*c**9*x**6 - 2160*I*a**8*c**9*x**5 + 1200*a**7*c**9*x**4 - 1200*I*a**6*c**9*x**3 - 240*I*a**4*c**9*x - 60*a**3*c**9)","B",0
380,-1,0,0,0.000000," ","integrate((1+I*a*x)**5/(a**2*x**2+1)**(5/2)*x**2/(a**2*c*x**2+c)**(27/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((1+I*a*x)**3/(a**2*x**2+1)**(3/2)*x**2/(a**2*c*x**2+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,0,0,0,0.000000," ","integrate((1+I*a*x)/(a**2*x**2+1)**(1/2)*x**2/(a**2*c*x**2+c)**(3/2),x)","i \left(\int \left(- \frac{i x^{2}}{a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\right)\, dx + \int \frac{a x^{3}}{a^{2} c x^{2} \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c} + c \sqrt{a^{2} x^{2} + 1} \sqrt{a^{2} c x^{2} + c}}\, dx\right)"," ",0,"I*(Integral(-I*x**2/(a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x) + Integral(a*x**3/(a**2*c*x**2*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c) + c*sqrt(a**2*x**2 + 1)*sqrt(a**2*c*x**2 + c)), x))","F",0
383,0,0,0,0.000000," ","integrate(x**2/(1+I*a*x)*(a**2*x**2+1)**(1/2)/(a**2*c*x**2+c)**(3/2),x)","- i \int \frac{x^{2} \sqrt{a^{2} x^{2} + 1}}{a^{3} c x^{3} \sqrt{a^{2} c x^{2} + c} - i a^{2} c x^{2} \sqrt{a^{2} c x^{2} + c} + a c x \sqrt{a^{2} c x^{2} + c} - i c \sqrt{a^{2} c x^{2} + c}}\, dx"," ",0,"-I*Integral(x**2*sqrt(a**2*x**2 + 1)/(a**3*c*x**3*sqrt(a**2*c*x**2 + c) - I*a**2*c*x**2*sqrt(a**2*c*x**2 + c) + a*c*x*sqrt(a**2*c*x**2 + c) - I*c*sqrt(a**2*c*x**2 + c)), x)","F",0
384,-1,0,0,0.000000," ","integrate(x**2/(1+I*a*x)**3*(a**2*x**2+1)**(3/2)/(a**2*c*x**2+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(x**2/(1+I*a*x)**5*(a**2*x**2+1)**(5/2)/(a**2*c*x**2+c)**(27/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
