1,1,221,0,8.460583," ","integrate(x**6*(a+b*asec(c*x)),x)","\frac{a x^{7}}{7} + \frac{b x^{7} \operatorname{asec}{\left(c x \right)}}{7} - \frac{b \left(\begin{cases} \frac{c x^{7}}{6 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{5}}{24 c \sqrt{c^{2} x^{2} - 1}} + \frac{5 x^{3}}{48 c^{3} \sqrt{c^{2} x^{2} - 1}} - \frac{5 x}{16 c^{5} \sqrt{c^{2} x^{2} - 1}} + \frac{5 \operatorname{acosh}{\left(c x \right)}}{16 c^{6}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{7}}{6 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{5}}{24 c \sqrt{- c^{2} x^{2} + 1}} - \frac{5 i x^{3}}{48 c^{3} \sqrt{- c^{2} x^{2} + 1}} + \frac{5 i x}{16 c^{5} \sqrt{- c^{2} x^{2} + 1}} - \frac{5 i \operatorname{asin}{\left(c x \right)}}{16 c^{6}} & \text{otherwise} \end{cases}\right)}{7 c}"," ",0,"a*x**7/7 + b*x**7*asec(c*x)/7 - b*Piecewise((c*x**7/(6*sqrt(c**2*x**2 - 1)) + x**5/(24*c*sqrt(c**2*x**2 - 1)) + 5*x**3/(48*c**3*sqrt(c**2*x**2 - 1)) - 5*x/(16*c**5*sqrt(c**2*x**2 - 1)) + 5*acosh(c*x)/(16*c**6), Abs(c**2*x**2) > 1), (-I*c*x**7/(6*sqrt(-c**2*x**2 + 1)) - I*x**5/(24*c*sqrt(-c**2*x**2 + 1)) - 5*I*x**3/(48*c**3*sqrt(-c**2*x**2 + 1)) + 5*I*x/(16*c**5*sqrt(-c**2*x**2 + 1)) - 5*I*asin(c*x)/(16*c**6), True))/(7*c)","A",0
2,1,153,0,4.192448," ","integrate(x**5*(a+b*asec(c*x)),x)","\frac{a x^{6}}{6} + \frac{b x^{6} \operatorname{asec}{\left(c x \right)}}{6} - \frac{b \left(\begin{cases} \frac{x^{4} \sqrt{c^{2} x^{2} - 1}}{5 c} + \frac{4 x^{2} \sqrt{c^{2} x^{2} - 1}}{15 c^{3}} + \frac{8 \sqrt{c^{2} x^{2} - 1}}{15 c^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{4} \sqrt{- c^{2} x^{2} + 1}}{5 c} + \frac{4 i x^{2} \sqrt{- c^{2} x^{2} + 1}}{15 c^{3}} + \frac{8 i \sqrt{- c^{2} x^{2} + 1}}{15 c^{5}} & \text{otherwise} \end{cases}\right)}{6 c}"," ",0,"a*x**6/6 + b*x**6*asec(c*x)/6 - b*Piecewise((x**4*sqrt(c**2*x**2 - 1)/(5*c) + 4*x**2*sqrt(c**2*x**2 - 1)/(15*c**3) + 8*sqrt(c**2*x**2 - 1)/(15*c**5), Abs(c**2*x**2) > 1), (I*x**4*sqrt(-c**2*x**2 + 1)/(5*c) + 4*I*x**2*sqrt(-c**2*x**2 + 1)/(15*c**3) + 8*I*sqrt(-c**2*x**2 + 1)/(15*c**5), True))/(6*c)","A",0
3,1,175,0,5.400934," ","integrate(x**4*(a+b*asec(c*x)),x)","\frac{a x^{5}}{5} + \frac{b x^{5} \operatorname{asec}{\left(c x \right)}}{5} - \frac{b \left(\begin{cases} \frac{c x^{5}}{4 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{3}}{8 c \sqrt{c^{2} x^{2} - 1}} - \frac{3 x}{8 c^{3} \sqrt{c^{2} x^{2} - 1}} + \frac{3 \operatorname{acosh}{\left(c x \right)}}{8 c^{4}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{5}}{4 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{3}}{8 c \sqrt{- c^{2} x^{2} + 1}} + \frac{3 i x}{8 c^{3} \sqrt{- c^{2} x^{2} + 1}} - \frac{3 i \operatorname{asin}{\left(c x \right)}}{8 c^{4}} & \text{otherwise} \end{cases}\right)}{5 c}"," ",0,"a*x**5/5 + b*x**5*asec(c*x)/5 - b*Piecewise((c*x**5/(4*sqrt(c**2*x**2 - 1)) + x**3/(8*c*sqrt(c**2*x**2 - 1)) - 3*x/(8*c**3*sqrt(c**2*x**2 - 1)) + 3*acosh(c*x)/(8*c**4), Abs(c**2*x**2) > 1), (-I*c*x**5/(4*sqrt(-c**2*x**2 + 1)) - I*x**3/(8*c*sqrt(-c**2*x**2 + 1)) + 3*I*x/(8*c**3*sqrt(-c**2*x**2 + 1)) - 3*I*asin(c*x)/(8*c**4), True))/(5*c)","A",0
4,1,107,0,2.789357," ","integrate(x**3*(a+b*asec(c*x)),x)","\frac{a x^{4}}{4} + \frac{b x^{4} \operatorname{asec}{\left(c x \right)}}{4} - \frac{b \left(\begin{cases} \frac{x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} + \frac{2 \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{2 i \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} & \text{otherwise} \end{cases}\right)}{4 c}"," ",0,"a*x**4/4 + b*x**4*asec(c*x)/4 - b*Piecewise((x**2*sqrt(c**2*x**2 - 1)/(3*c) + 2*sqrt(c**2*x**2 - 1)/(3*c**3), Abs(c**2*x**2) > 1), (I*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 2*I*sqrt(-c**2*x**2 + 1)/(3*c**3), True))/(4*c)","A",0
5,1,107,0,3.286447," ","integrate(x**2*(a+b*asec(c*x)),x)","\frac{a x^{3}}{3} + \frac{b x^{3} \operatorname{asec}{\left(c x \right)}}{3} - \frac{b \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"a*x**3/3 + b*x**3*asec(c*x)/3 - b*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/(3*c)","A",0
6,1,58,0,1.991776," ","integrate(x*(a+b*asec(c*x)),x)","\frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{asec}{\left(c x \right)}}{2} - \frac{b \left(\begin{cases} \frac{\sqrt{c^{2} x^{2} - 1}}{c} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{- c^{2} x^{2} + 1}}{c} & \text{otherwise} \end{cases}\right)}{2 c}"," ",0,"a*x**2/2 + b*x**2*asec(c*x)/2 - b*Piecewise((sqrt(c**2*x**2 - 1)/c, Abs(c**2*x**2) > 1), (I*sqrt(-c**2*x**2 + 1)/c, True))/(2*c)","A",0
7,1,32,0,2.325623," ","integrate(a+b*asec(c*x),x)","a x + b \left(x \operatorname{asec}{\left(c x \right)} - \frac{\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}}{c}\right)"," ",0,"a*x + b*(x*asec(c*x) - Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c)","A",0
8,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x,x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x}\, dx"," ",0,"Integral((a + b*asec(c*x))/x, x)","F",0
9,1,36,0,1.773074," ","integrate((a+b*asec(c*x))/x**2,x)","\begin{cases} - \frac{a}{x} + b c \sqrt{1 - \frac{1}{c^{2} x^{2}}} - \frac{b \operatorname{asec}{\left(c x \right)}}{x} & \text{for}\: c \neq 0 \\- \frac{a + \tilde{\infty} b}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x + b*c*sqrt(1 - 1/(c**2*x**2)) - b*asec(c*x)/x, Ne(c, 0)), (-(a + zoo*b)/x, True))","A",0
10,1,119,0,3.138511," ","integrate((a+b*asec(c*x))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{b \operatorname{asec}{\left(c x \right)}}{2 x^{2}} + \frac{b \left(\begin{cases} \frac{i c^{3} \operatorname{acosh}{\left(\frac{1}{c x} \right)}}{2} + \frac{i c^{2} \sqrt{-1 + \frac{1}{c^{2} x^{2}}}}{2 x} & \text{for}\: \frac{1}{\left|{c^{2} x^{2}}\right|} > 1 \\- \frac{c^{3} \operatorname{asin}{\left(\frac{1}{c x} \right)}}{2} + \frac{c^{2}}{2 x \sqrt{1 - \frac{1}{c^{2} x^{2}}}} - \frac{1}{2 x^{3} \sqrt{1 - \frac{1}{c^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{2 c}"," ",0,"-a/(2*x**2) - b*asec(c*x)/(2*x**2) + b*Piecewise((I*c**3*acosh(1/(c*x))/2 + I*c**2*sqrt(-1 + 1/(c**2*x**2))/(2*x), 1/Abs(c**2*x**2) > 1), (-c**3*asin(1/(c*x))/2 + c**2/(2*x*sqrt(1 - 1/(c**2*x**2))) - 1/(2*x**3*sqrt(1 - 1/(c**2*x**2))), True))/(2*c)","A",0
11,1,110,0,2.930093," ","integrate((a+b*asec(c*x))/x**4,x)","- \frac{a}{3 x^{3}} - \frac{b \operatorname{asec}{\left(c x \right)}}{3 x^{3}} + \frac{b \left(\begin{cases} \frac{2 c^{3} \sqrt{c^{2} x^{2} - 1}}{3 x} + \frac{c \sqrt{c^{2} x^{2} - 1}}{3 x^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{2 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{3 x} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{3 x^{3}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"-a/(3*x**3) - b*asec(c*x)/(3*x**3) + b*Piecewise((2*c**3*sqrt(c**2*x**2 - 1)/(3*x) + c*sqrt(c**2*x**2 - 1)/(3*x**3), Abs(c**2*x**2) > 1), (2*I*c**3*sqrt(-c**2*x**2 + 1)/(3*x) + I*c*sqrt(-c**2*x**2 + 1)/(3*x**3), True))/(3*c)","A",0
12,1,192,0,5.234849," ","integrate((a+b*asec(c*x))/x**5,x)","- \frac{a}{4 x^{4}} - \frac{b \operatorname{asec}{\left(c x \right)}}{4 x^{4}} + \frac{b \left(\begin{cases} \frac{3 i c^{5} \operatorname{acosh}{\left(\frac{1}{c x} \right)}}{8} - \frac{3 i c^{4}}{8 x \sqrt{-1 + \frac{1}{c^{2} x^{2}}}} + \frac{i c^{2}}{8 x^{3} \sqrt{-1 + \frac{1}{c^{2} x^{2}}}} + \frac{i}{4 x^{5} \sqrt{-1 + \frac{1}{c^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{c^{2} x^{2}}\right|} > 1 \\- \frac{3 c^{5} \operatorname{asin}{\left(\frac{1}{c x} \right)}}{8} + \frac{3 c^{4}}{8 x \sqrt{1 - \frac{1}{c^{2} x^{2}}}} - \frac{c^{2}}{8 x^{3} \sqrt{1 - \frac{1}{c^{2} x^{2}}}} - \frac{1}{4 x^{5} \sqrt{1 - \frac{1}{c^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{4 c}"," ",0,"-a/(4*x**4) - b*asec(c*x)/(4*x**4) + b*Piecewise((3*I*c**5*acosh(1/(c*x))/8 - 3*I*c**4/(8*x*sqrt(-1 + 1/(c**2*x**2))) + I*c**2/(8*x**3*sqrt(-1 + 1/(c**2*x**2))) + I/(4*x**5*sqrt(-1 + 1/(c**2*x**2))), 1/Abs(c**2*x**2) > 1), (-3*c**5*asin(1/(c*x))/8 + 3*c**4/(8*x*sqrt(1 - 1/(c**2*x**2))) - c**2/(8*x**3*sqrt(1 - 1/(c**2*x**2))) - 1/(4*x**5*sqrt(1 - 1/(c**2*x**2))), True))/(4*c)","A",0
13,1,156,0,6.985382," ","integrate((a+b*asec(c*x))/x**6,x)","- \frac{a}{5 x^{5}} - \frac{b \operatorname{asec}{\left(c x \right)}}{5 x^{5}} + \frac{b \left(\begin{cases} \frac{8 c^{5} \sqrt{c^{2} x^{2} - 1}}{15 x} + \frac{4 c^{3} \sqrt{c^{2} x^{2} - 1}}{15 x^{3}} + \frac{c \sqrt{c^{2} x^{2} - 1}}{5 x^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{8 i c^{5} \sqrt{- c^{2} x^{2} + 1}}{15 x} + \frac{4 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{15 x^{3}} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{5 x^{5}} & \text{otherwise} \end{cases}\right)}{5 c}"," ",0,"-a/(5*x**5) - b*asec(c*x)/(5*x**5) + b*Piecewise((8*c**5*sqrt(c**2*x**2 - 1)/(15*x) + 4*c**3*sqrt(c**2*x**2 - 1)/(15*x**3) + c*sqrt(c**2*x**2 - 1)/(5*x**5), Abs(c**2*x**2) > 1), (8*I*c**5*sqrt(-c**2*x**2 + 1)/(15*x) + 4*I*c**3*sqrt(-c**2*x**2 + 1)/(15*x**3) + I*c*sqrt(-c**2*x**2 + 1)/(5*x**5), True))/(5*c)","A",0
14,1,241,0,8.433362," ","integrate((a+b*asec(c*x))/x**7,x)","- \frac{a}{6 x^{6}} - \frac{b \operatorname{asec}{\left(c x \right)}}{6 x^{6}} + \frac{b \left(\begin{cases} \frac{5 i c^{7} \operatorname{acosh}{\left(\frac{1}{c x} \right)}}{16} - \frac{5 i c^{6}}{16 x \sqrt{-1 + \frac{1}{c^{2} x^{2}}}} + \frac{5 i c^{4}}{48 x^{3} \sqrt{-1 + \frac{1}{c^{2} x^{2}}}} + \frac{i c^{2}}{24 x^{5} \sqrt{-1 + \frac{1}{c^{2} x^{2}}}} + \frac{i}{6 x^{7} \sqrt{-1 + \frac{1}{c^{2} x^{2}}}} & \text{for}\: \frac{1}{\left|{c^{2} x^{2}}\right|} > 1 \\- \frac{5 c^{7} \operatorname{asin}{\left(\frac{1}{c x} \right)}}{16} + \frac{5 c^{6}}{16 x \sqrt{1 - \frac{1}{c^{2} x^{2}}}} - \frac{5 c^{4}}{48 x^{3} \sqrt{1 - \frac{1}{c^{2} x^{2}}}} - \frac{c^{2}}{24 x^{5} \sqrt{1 - \frac{1}{c^{2} x^{2}}}} - \frac{1}{6 x^{7} \sqrt{1 - \frac{1}{c^{2} x^{2}}}} & \text{otherwise} \end{cases}\right)}{6 c}"," ",0,"-a/(6*x**6) - b*asec(c*x)/(6*x**6) + b*Piecewise((5*I*c**7*acosh(1/(c*x))/16 - 5*I*c**6/(16*x*sqrt(-1 + 1/(c**2*x**2))) + 5*I*c**4/(48*x**3*sqrt(-1 + 1/(c**2*x**2))) + I*c**2/(24*x**5*sqrt(-1 + 1/(c**2*x**2))) + I/(6*x**7*sqrt(-1 + 1/(c**2*x**2))), 1/Abs(c**2*x**2) > 1), (-5*c**7*asin(1/(c*x))/16 + 5*c**6/(16*x*sqrt(1 - 1/(c**2*x**2))) - 5*c**4/(48*x**3*sqrt(1 - 1/(c**2*x**2))) - c**2/(24*x**5*sqrt(1 - 1/(c**2*x**2))) - 1/(6*x**7*sqrt(1 - 1/(c**2*x**2))), True))/(6*c)","A",0
15,0,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))**2,x)","\int x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**3*(a + b*asec(c*x))**2, x)","F",0
16,0,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))**2,x)","\int x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*asec(c*x))**2, x)","F",0
17,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))**2,x)","\int x \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))**2, x)","F",0
18,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**2,x)","\int \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*asec(c*x))**2, x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**2/x,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*asec(c*x))**2/x, x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**2/x**2,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))**2/x**2, x)","F",0
21,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**2/x**3,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))**2/x**3, x)","F",0
22,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**2/x**4,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*asec(c*x))**2/x**4, x)","F",0
23,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**2/x**5,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}{x^{5}}\, dx"," ",0,"Integral((a + b*asec(c*x))**2/x**5, x)","F",0
24,0,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))**3,x)","\int x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*asec(c*x))**3, x)","F",0
25,0,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))**3,x)","\int x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*asec(c*x))**3, x)","F",0
26,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))**3,x)","\int x \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))**3, x)","F",0
27,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**3,x)","\int \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*asec(c*x))**3, x)","F",0
28,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**3/x,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*asec(c*x))**3/x, x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**3/x**2,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))**3/x**2, x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**3/x**3,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))**3/x**3, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**3/x**4,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}{x^{4}}\, dx"," ",0,"Integral((a + b*asec(c*x))**3/x**4, x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*asec(c*x))**3/x**5,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}{x^{5}}\, dx"," ",0,"Integral((a + b*asec(c*x))**3/x**5, x)","F",0
33,0,0,0,0.000000," ","integrate(x/(a+b*asec(c*x)),x)","\int \frac{x}{a + b \operatorname{asec}{\left(c x \right)}}\, dx"," ",0,"Integral(x/(a + b*asec(c*x)), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(a+b*asec(c*x)),x)","\int \frac{1}{a + b \operatorname{asec}{\left(c x \right)}}\, dx"," ",0,"Integral(1/(a + b*asec(c*x)), x)","F",0
35,0,0,0,0.000000," ","integrate(1/x/(a+b*asec(c*x)),x)","\int \frac{1}{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(1/(x*(a + b*asec(c*x))), x)","F",0
36,0,0,0,0.000000," ","integrate(1/x**2/(a+b*asec(c*x)),x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(1/(x**2*(a + b*asec(c*x))), x)","F",0
37,0,0,0,0.000000," ","integrate(1/x**3/(a+b*asec(c*x)),x)","\int \frac{1}{x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(1/(x**3*(a + b*asec(c*x))), x)","F",0
38,0,0,0,0.000000," ","integrate(1/x**4/(a+b*asec(c*x)),x)","\int \frac{1}{x^{4} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(1/(x**4*(a + b*asec(c*x))), x)","F",0
39,0,0,0,0.000000," ","integrate(x/(a+b*asec(c*x))**2,x)","\int \frac{x}{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(x/(a + b*asec(c*x))**2, x)","F",0
40,0,0,0,0.000000," ","integrate(1/(a+b*asec(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))**(-2), x)","F",0
41,0,0,0,0.000000," ","integrate(1/x/(a+b*asec(c*x))**2,x)","\int \frac{1}{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(x*(a + b*asec(c*x))**2), x)","F",0
42,0,0,0,0.000000," ","integrate(1/x**2/(a+b*asec(c*x))**2,x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*(a + b*asec(c*x))**2), x)","F",0
43,0,0,0,0.000000," ","integrate(1/x**3/(a+b*asec(c*x))**2,x)","\int \frac{1}{x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(x**3*(a + b*asec(c*x))**2), x)","F",0
44,0,0,0,0.000000," ","integrate(1/x**4/(a+b*asec(c*x))**2,x)","\int \frac{1}{x^{4} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(x**4*(a + b*asec(c*x))**2), x)","F",0
45,0,0,0,0.000000," ","integrate(x/(a+b*asec(c*x))**3,x)","\int \frac{x}{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}\, dx"," ",0,"Integral(x/(a + b*asec(c*x))**3, x)","F",0
46,0,0,0,0.000000," ","integrate(1/(a+b*asec(c*x))**3,x)","\int \frac{1}{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))**(-3), x)","F",0
47,0,0,0,0.000000," ","integrate(1/x/(a+b*asec(c*x))**3,x)","\int \frac{1}{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(x*(a + b*asec(c*x))**3), x)","F",0
48,0,0,0,0.000000," ","integrate(1/x**2/(a+b*asec(c*x))**3,x)","\int \frac{1}{x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(x**2*(a + b*asec(c*x))**3), x)","F",0
49,0,0,0,0.000000," ","integrate(1/x**3/(a+b*asec(c*x))**3,x)","\int \frac{1}{x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(x**3*(a + b*asec(c*x))**3), x)","F",0
50,0,0,0,0.000000," ","integrate(1/x**4/(a+b*asec(c*x))**3,x)","\int \frac{1}{x^{4} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(x**4*(a + b*asec(c*x))**3), x)","F",0
51,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*asec(c*x))**3,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral((d*x)**m*(a + b*asec(c*x))**3, x)","F",0
52,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*asec(c*x))**2,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((d*x)**m*(a + b*asec(c*x))**2, x)","F",0
53,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*asec(c*x)),x)","\int \left(d x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right)\, dx"," ",0,"Integral((d*x)**m*(a + b*asec(c*x)), x)","F",0
54,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*asec(c*x)),x)","\int \frac{\left(d x\right)^{m}}{a + b \operatorname{asec}{\left(c x \right)}}\, dx"," ",0,"Integral((d*x)**m/(a + b*asec(c*x)), x)","F",0
55,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*asec(c*x))**2,x)","\int \frac{\left(d x\right)^{m}}{\left(a + b \operatorname{asec}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d*x)**m/(a + b*asec(c*x))**2, x)","F",0
56,1,362,0,7.875526," ","integrate((e*x+d)**3*(a+b*asec(c*x)),x)","a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + a d e^{2} x^{3} + \frac{a e^{3} x^{4}}{4} + b d^{3} x \operatorname{asec}{\left(c x \right)} + \frac{3 b d^{2} e x^{2} \operatorname{asec}{\left(c x \right)}}{2} + b d e^{2} x^{3} \operatorname{asec}{\left(c x \right)} + \frac{b e^{3} x^{4} \operatorname{asec}{\left(c x \right)}}{4} - \frac{b d^{3} \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c} - \frac{3 b d^{2} e \left(\begin{cases} \frac{\sqrt{c^{2} x^{2} - 1}}{c} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{- c^{2} x^{2} + 1}}{c} & \text{otherwise} \end{cases}\right)}{2 c} - \frac{b d e^{2} \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{c} - \frac{b e^{3} \left(\begin{cases} \frac{x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} + \frac{2 \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{2 i \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} & \text{otherwise} \end{cases}\right)}{4 c}"," ",0,"a*d**3*x + 3*a*d**2*e*x**2/2 + a*d*e**2*x**3 + a*e**3*x**4/4 + b*d**3*x*asec(c*x) + 3*b*d**2*e*x**2*asec(c*x)/2 + b*d*e**2*x**3*asec(c*x) + b*e**3*x**4*asec(c*x)/4 - b*d**3*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c - 3*b*d**2*e*Piecewise((sqrt(c**2*x**2 - 1)/c, Abs(c**2*x**2) > 1), (I*sqrt(-c**2*x**2 + 1)/c, True))/(2*c) - b*d*e**2*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/c - b*e**3*Piecewise((x**2*sqrt(c**2*x**2 - 1)/(3*c) + 2*sqrt(c**2*x**2 - 1)/(3*c**3), Abs(c**2*x**2) > 1), (I*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 2*I*sqrt(-c**2*x**2 + 1)/(3*c**3), True))/(4*c)","A",0
57,1,228,0,6.599833," ","integrate((e*x+d)**2*(a+b*asec(c*x)),x)","a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} + b d^{2} x \operatorname{asec}{\left(c x \right)} + b d e x^{2} \operatorname{asec}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{asec}{\left(c x \right)}}{3} - \frac{b d^{2} \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c} - \frac{b d e \left(\begin{cases} \frac{\sqrt{c^{2} x^{2} - 1}}{c} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{- c^{2} x^{2} + 1}}{c} & \text{otherwise} \end{cases}\right)}{c} - \frac{b e^{2} \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"a*d**2*x + a*d*e*x**2 + a*e**2*x**3/3 + b*d**2*x*asec(c*x) + b*d*e*x**2*asec(c*x) + b*e**2*x**3*asec(c*x)/3 - b*d**2*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c - b*d*e*Piecewise((sqrt(c**2*x**2 - 1)/c, Abs(c**2*x**2) > 1), (I*sqrt(-c**2*x**2 + 1)/c, True))/c - b*e**2*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/(3*c)","A",0
58,1,104,0,4.422615," ","integrate((e*x+d)*(a+b*asec(c*x)),x)","a d x + \frac{a e x^{2}}{2} + b d x \operatorname{asec}{\left(c x \right)} + \frac{b e x^{2} \operatorname{asec}{\left(c x \right)}}{2} - \frac{b d \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c} - \frac{b e \left(\begin{cases} \frac{\sqrt{c^{2} x^{2} - 1}}{c} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{- c^{2} x^{2} + 1}}{c} & \text{otherwise} \end{cases}\right)}{2 c}"," ",0,"a*d*x + a*e*x**2/2 + b*d*x*asec(c*x) + b*e*x**2*asec(c*x)/2 - b*d*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c - b*e*Piecewise((sqrt(c**2*x**2 - 1)/c, Abs(c**2*x**2) > 1), (I*sqrt(-c**2*x**2 + 1)/c, True))/(2*c)","A",0
59,1,32,0,2.270403," ","integrate(a+b*asec(c*x),x)","a x + b \left(x \operatorname{asec}{\left(c x \right)} - \frac{\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}}{c}\right)"," ",0,"a*x + b*(x*asec(c*x) - Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c)","A",0
60,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*asec(c*x))/(d + e*x), x)","F",0
61,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x+d)**2,x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(d + e*x)**2, x)","F",0
62,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x+d)**3,x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(d + e*x)**3, x)","F",0
63,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(a+b*asec(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(a+b*asec(c*x)),x)","\int \left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x}\, dx"," ",0,"Integral((a + b*asec(c*x))*sqrt(d + e*x), x)","F",0
65,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x+d)**(1/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{\sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*asec(c*x))/sqrt(d + e*x), x)","F",0
66,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x+d)**(3/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(d + e*x)**(3/2), x)","F",0
67,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x+d)**(5/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(d + e*x)**(5/2), x)","F",0
68,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x+d)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,1,408,0,11.684485," ","integrate(x**4*(e*x**2+d)*(a+b*asec(c*x)),x)","\frac{a d x^{5}}{5} + \frac{a e x^{7}}{7} + \frac{b d x^{5} \operatorname{asec}{\left(c x \right)}}{5} + \frac{b e x^{7} \operatorname{asec}{\left(c x \right)}}{7} - \frac{b d \left(\begin{cases} \frac{c x^{5}}{4 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{3}}{8 c \sqrt{c^{2} x^{2} - 1}} - \frac{3 x}{8 c^{3} \sqrt{c^{2} x^{2} - 1}} + \frac{3 \operatorname{acosh}{\left(c x \right)}}{8 c^{4}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{5}}{4 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{3}}{8 c \sqrt{- c^{2} x^{2} + 1}} + \frac{3 i x}{8 c^{3} \sqrt{- c^{2} x^{2} + 1}} - \frac{3 i \operatorname{asin}{\left(c x \right)}}{8 c^{4}} & \text{otherwise} \end{cases}\right)}{5 c} - \frac{b e \left(\begin{cases} \frac{c x^{7}}{6 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{5}}{24 c \sqrt{c^{2} x^{2} - 1}} + \frac{5 x^{3}}{48 c^{3} \sqrt{c^{2} x^{2} - 1}} - \frac{5 x}{16 c^{5} \sqrt{c^{2} x^{2} - 1}} + \frac{5 \operatorname{acosh}{\left(c x \right)}}{16 c^{6}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{7}}{6 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{5}}{24 c \sqrt{- c^{2} x^{2} + 1}} - \frac{5 i x^{3}}{48 c^{3} \sqrt{- c^{2} x^{2} + 1}} + \frac{5 i x}{16 c^{5} \sqrt{- c^{2} x^{2} + 1}} - \frac{5 i \operatorname{asin}{\left(c x \right)}}{16 c^{6}} & \text{otherwise} \end{cases}\right)}{7 c}"," ",0,"a*d*x**5/5 + a*e*x**7/7 + b*d*x**5*asec(c*x)/5 + b*e*x**7*asec(c*x)/7 - b*d*Piecewise((c*x**5/(4*sqrt(c**2*x**2 - 1)) + x**3/(8*c*sqrt(c**2*x**2 - 1)) - 3*x/(8*c**3*sqrt(c**2*x**2 - 1)) + 3*acosh(c*x)/(8*c**4), Abs(c**2*x**2) > 1), (-I*c*x**5/(4*sqrt(-c**2*x**2 + 1)) - I*x**3/(8*c*sqrt(-c**2*x**2 + 1)) + 3*I*x/(8*c**3*sqrt(-c**2*x**2 + 1)) - 3*I*asin(c*x)/(8*c**4), True))/(5*c) - b*e*Piecewise((c*x**7/(6*sqrt(c**2*x**2 - 1)) + x**5/(24*c*sqrt(c**2*x**2 - 1)) + 5*x**3/(48*c**3*sqrt(c**2*x**2 - 1)) - 5*x/(16*c**5*sqrt(c**2*x**2 - 1)) + 5*acosh(c*x)/(16*c**6), Abs(c**2*x**2) > 1), (-I*c*x**7/(6*sqrt(-c**2*x**2 + 1)) - I*x**5/(24*c*sqrt(-c**2*x**2 + 1)) - 5*I*x**3/(48*c**3*sqrt(-c**2*x**2 + 1)) + 5*I*x/(16*c**5*sqrt(-c**2*x**2 + 1)) - 5*I*asin(c*x)/(16*c**6), True))/(7*c)","A",0
70,1,294,0,7.295861," ","integrate(x**2*(e*x**2+d)*(a+b*asec(c*x)),x)","\frac{a d x^{3}}{3} + \frac{a e x^{5}}{5} + \frac{b d x^{3} \operatorname{asec}{\left(c x \right)}}{3} + \frac{b e x^{5} \operatorname{asec}{\left(c x \right)}}{5} - \frac{b d \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{3 c} - \frac{b e \left(\begin{cases} \frac{c x^{5}}{4 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{3}}{8 c \sqrt{c^{2} x^{2} - 1}} - \frac{3 x}{8 c^{3} \sqrt{c^{2} x^{2} - 1}} + \frac{3 \operatorname{acosh}{\left(c x \right)}}{8 c^{4}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{5}}{4 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{3}}{8 c \sqrt{- c^{2} x^{2} + 1}} + \frac{3 i x}{8 c^{3} \sqrt{- c^{2} x^{2} + 1}} - \frac{3 i \operatorname{asin}{\left(c x \right)}}{8 c^{4}} & \text{otherwise} \end{cases}\right)}{5 c}"," ",0,"a*d*x**3/3 + a*e*x**5/5 + b*d*x**3*asec(c*x)/3 + b*e*x**5*asec(c*x)/5 - b*d*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/(3*c) - b*e*Piecewise((c*x**5/(4*sqrt(c**2*x**2 - 1)) + x**3/(8*c*sqrt(c**2*x**2 - 1)) - 3*x/(8*c**3*sqrt(c**2*x**2 - 1)) + 3*acosh(c*x)/(8*c**4), Abs(c**2*x**2) > 1), (-I*c*x**5/(4*sqrt(-c**2*x**2 + 1)) - I*x**3/(8*c*sqrt(-c**2*x**2 + 1)) + 3*I*x/(8*c**3*sqrt(-c**2*x**2 + 1)) - 3*I*asin(c*x)/(8*c**4), True))/(5*c)","A",0
71,1,153,0,5.719840," ","integrate((e*x**2+d)*(a+b*asec(c*x)),x)","a d x + \frac{a e x^{3}}{3} + b d x \operatorname{asec}{\left(c x \right)} + \frac{b e x^{3} \operatorname{asec}{\left(c x \right)}}{3} - \frac{b d \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c} - \frac{b e \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"a*d*x + a*e*x**3/3 + b*d*x*asec(c*x) + b*e*x**3*asec(c*x)/3 - b*d*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c - b*e*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/(3*c)","A",0
72,1,73,0,5.110075," ","integrate((e*x**2+d)*(a+b*asec(c*x))/x**2,x)","- \frac{a d}{x} + a e x + b c d \sqrt{1 - \frac{1}{c^{2} x^{2}}} - \frac{b d \operatorname{asec}{\left(c x \right)}}{x} + b e x \operatorname{asec}{\left(c x \right)} - \frac{b e \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c}"," ",0,"-a*d/x + a*e*x + b*c*d*sqrt(1 - 1/(c**2*x**2)) - b*d*asec(c*x)/x + b*e*x*asec(c*x) - b*e*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c","A",0
73,1,150,0,4.540781," ","integrate((e*x**2+d)*(a+b*asec(c*x))/x**4,x)","- \frac{a d}{3 x^{3}} - \frac{a e}{x} + b c e \sqrt{1 - \frac{1}{c^{2} x^{2}}} - \frac{b d \operatorname{asec}{\left(c x \right)}}{3 x^{3}} - \frac{b e \operatorname{asec}{\left(c x \right)}}{x} + \frac{b d \left(\begin{cases} \frac{2 c^{3} \sqrt{c^{2} x^{2} - 1}}{3 x} + \frac{c \sqrt{c^{2} x^{2} - 1}}{3 x^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{2 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{3 x} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{3 x^{3}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"-a*d/(3*x**3) - a*e/x + b*c*e*sqrt(1 - 1/(c**2*x**2)) - b*d*asec(c*x)/(3*x**3) - b*e*asec(c*x)/x + b*d*Piecewise((2*c**3*sqrt(c**2*x**2 - 1)/(3*x) + c*sqrt(c**2*x**2 - 1)/(3*x**3), Abs(c**2*x**2) > 1), (2*I*c**3*sqrt(-c**2*x**2 + 1)/(3*x) + I*c*sqrt(-c**2*x**2 + 1)/(3*x**3), True))/(3*c)","A",0
74,1,279,0,9.293448," ","integrate((e*x**2+d)*(a+b*asec(c*x))/x**6,x)","- \frac{a d}{5 x^{5}} - \frac{a e}{3 x^{3}} - \frac{b d \operatorname{asec}{\left(c x \right)}}{5 x^{5}} - \frac{b e \operatorname{asec}{\left(c x \right)}}{3 x^{3}} + \frac{b d \left(\begin{cases} \frac{8 c^{5} \sqrt{c^{2} x^{2} - 1}}{15 x} + \frac{4 c^{3} \sqrt{c^{2} x^{2} - 1}}{15 x^{3}} + \frac{c \sqrt{c^{2} x^{2} - 1}}{5 x^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{8 i c^{5} \sqrt{- c^{2} x^{2} + 1}}{15 x} + \frac{4 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{15 x^{3}} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{5 x^{5}} & \text{otherwise} \end{cases}\right)}{5 c} + \frac{b e \left(\begin{cases} \frac{2 c^{3} \sqrt{c^{2} x^{2} - 1}}{3 x} + \frac{c \sqrt{c^{2} x^{2} - 1}}{3 x^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{2 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{3 x} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{3 x^{3}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"-a*d/(5*x**5) - a*e/(3*x**3) - b*d*asec(c*x)/(5*x**5) - b*e*asec(c*x)/(3*x**3) + b*d*Piecewise((8*c**5*sqrt(c**2*x**2 - 1)/(15*x) + 4*c**3*sqrt(c**2*x**2 - 1)/(15*x**3) + c*sqrt(c**2*x**2 - 1)/(5*x**5), Abs(c**2*x**2) > 1), (8*I*c**5*sqrt(-c**2*x**2 + 1)/(15*x) + 4*I*c**3*sqrt(-c**2*x**2 + 1)/(15*x**3) + I*c*sqrt(-c**2*x**2 + 1)/(5*x**5), True))/(5*c) + b*e*Piecewise((2*c**3*sqrt(c**2*x**2 - 1)/(3*x) + c*sqrt(c**2*x**2 - 1)/(3*x**3), Abs(c**2*x**2) > 1), (2*I*c**3*sqrt(-c**2*x**2 + 1)/(3*x) + I*c*sqrt(-c**2*x**2 + 1)/(3*x**3), True))/(3*c)","A",0
75,1,371,0,55.095809," ","integrate((e*x**2+d)*(a+b*asec(c*x))/x**8,x)","- \frac{a d}{7 x^{7}} - \frac{a e}{5 x^{5}} - \frac{b d \operatorname{asec}{\left(c x \right)}}{7 x^{7}} - \frac{b e \operatorname{asec}{\left(c x \right)}}{5 x^{5}} + \frac{b d \left(\begin{cases} \frac{16 c^{7} \sqrt{c^{2} x^{2} - 1}}{35 x} + \frac{8 c^{5} \sqrt{c^{2} x^{2} - 1}}{35 x^{3}} + \frac{6 c^{3} \sqrt{c^{2} x^{2} - 1}}{35 x^{5}} + \frac{c \sqrt{c^{2} x^{2} - 1}}{7 x^{7}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{16 i c^{7} \sqrt{- c^{2} x^{2} + 1}}{35 x} + \frac{8 i c^{5} \sqrt{- c^{2} x^{2} + 1}}{35 x^{3}} + \frac{6 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{35 x^{5}} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{7 x^{7}} & \text{otherwise} \end{cases}\right)}{7 c} + \frac{b e \left(\begin{cases} \frac{8 c^{5} \sqrt{c^{2} x^{2} - 1}}{15 x} + \frac{4 c^{3} \sqrt{c^{2} x^{2} - 1}}{15 x^{3}} + \frac{c \sqrt{c^{2} x^{2} - 1}}{5 x^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{8 i c^{5} \sqrt{- c^{2} x^{2} + 1}}{15 x} + \frac{4 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{15 x^{3}} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{5 x^{5}} & \text{otherwise} \end{cases}\right)}{5 c}"," ",0,"-a*d/(7*x**7) - a*e/(5*x**5) - b*d*asec(c*x)/(7*x**7) - b*e*asec(c*x)/(5*x**5) + b*d*Piecewise((16*c**7*sqrt(c**2*x**2 - 1)/(35*x) + 8*c**5*sqrt(c**2*x**2 - 1)/(35*x**3) + 6*c**3*sqrt(c**2*x**2 - 1)/(35*x**5) + c*sqrt(c**2*x**2 - 1)/(7*x**7), Abs(c**2*x**2) > 1), (16*I*c**7*sqrt(-c**2*x**2 + 1)/(35*x) + 8*I*c**5*sqrt(-c**2*x**2 + 1)/(35*x**3) + 6*I*c**3*sqrt(-c**2*x**2 + 1)/(35*x**5) + I*c*sqrt(-c**2*x**2 + 1)/(7*x**7), True))/(7*c) + b*e*Piecewise((8*c**5*sqrt(c**2*x**2 - 1)/(15*x) + 4*c**3*sqrt(c**2*x**2 - 1)/(15*x**3) + c*sqrt(c**2*x**2 - 1)/(5*x**5), Abs(c**2*x**2) > 1), (8*I*c**5*sqrt(-c**2*x**2 + 1)/(15*x) + 4*I*c**3*sqrt(-c**2*x**2 + 1)/(15*x**3) + I*c*sqrt(-c**2*x**2 + 1)/(5*x**5), True))/(5*c)","A",0
76,1,364,0,7.924173," ","integrate(x**5*(e*x**2+d)*(a+b*asec(c*x)),x)","\frac{a d x^{6}}{6} + \frac{a e x^{8}}{8} + \frac{b d x^{6} \operatorname{asec}{\left(c x \right)}}{6} + \frac{b e x^{8} \operatorname{asec}{\left(c x \right)}}{8} - \frac{b d \left(\begin{cases} \frac{x^{4} \sqrt{c^{2} x^{2} - 1}}{5 c} + \frac{4 x^{2} \sqrt{c^{2} x^{2} - 1}}{15 c^{3}} + \frac{8 \sqrt{c^{2} x^{2} - 1}}{15 c^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{4} \sqrt{- c^{2} x^{2} + 1}}{5 c} + \frac{4 i x^{2} \sqrt{- c^{2} x^{2} + 1}}{15 c^{3}} + \frac{8 i \sqrt{- c^{2} x^{2} + 1}}{15 c^{5}} & \text{otherwise} \end{cases}\right)}{6 c} - \frac{b e \left(\begin{cases} \frac{x^{6} \sqrt{c^{2} x^{2} - 1}}{7 c} + \frac{6 x^{4} \sqrt{c^{2} x^{2} - 1}}{35 c^{3}} + \frac{8 x^{2} \sqrt{c^{2} x^{2} - 1}}{35 c^{5}} + \frac{16 \sqrt{c^{2} x^{2} - 1}}{35 c^{7}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{6} \sqrt{- c^{2} x^{2} + 1}}{7 c} + \frac{6 i x^{4} \sqrt{- c^{2} x^{2} + 1}}{35 c^{3}} + \frac{8 i x^{2} \sqrt{- c^{2} x^{2} + 1}}{35 c^{5}} + \frac{16 i \sqrt{- c^{2} x^{2} + 1}}{35 c^{7}} & \text{otherwise} \end{cases}\right)}{8 c}"," ",0,"a*d*x**6/6 + a*e*x**8/8 + b*d*x**6*asec(c*x)/6 + b*e*x**8*asec(c*x)/8 - b*d*Piecewise((x**4*sqrt(c**2*x**2 - 1)/(5*c) + 4*x**2*sqrt(c**2*x**2 - 1)/(15*c**3) + 8*sqrt(c**2*x**2 - 1)/(15*c**5), Abs(c**2*x**2) > 1), (I*x**4*sqrt(-c**2*x**2 + 1)/(5*c) + 4*I*x**2*sqrt(-c**2*x**2 + 1)/(15*c**3) + 8*I*sqrt(-c**2*x**2 + 1)/(15*c**5), True))/(6*c) - b*e*Piecewise((x**6*sqrt(c**2*x**2 - 1)/(7*c) + 6*x**4*sqrt(c**2*x**2 - 1)/(35*c**3) + 8*x**2*sqrt(c**2*x**2 - 1)/(35*c**5) + 16*sqrt(c**2*x**2 - 1)/(35*c**7), Abs(c**2*x**2) > 1), (I*x**6*sqrt(-c**2*x**2 + 1)/(7*c) + 6*I*x**4*sqrt(-c**2*x**2 + 1)/(35*c**3) + 8*I*x**2*sqrt(-c**2*x**2 + 1)/(35*c**5) + 16*I*sqrt(-c**2*x**2 + 1)/(35*c**7), True))/(8*c)","A",0
77,1,272,0,5.292642," ","integrate(x**3*(e*x**2+d)*(a+b*asec(c*x)),x)","\frac{a d x^{4}}{4} + \frac{a e x^{6}}{6} + \frac{b d x^{4} \operatorname{asec}{\left(c x \right)}}{4} + \frac{b e x^{6} \operatorname{asec}{\left(c x \right)}}{6} - \frac{b d \left(\begin{cases} \frac{x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} + \frac{2 \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{2 i \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} & \text{otherwise} \end{cases}\right)}{4 c} - \frac{b e \left(\begin{cases} \frac{x^{4} \sqrt{c^{2} x^{2} - 1}}{5 c} + \frac{4 x^{2} \sqrt{c^{2} x^{2} - 1}}{15 c^{3}} + \frac{8 \sqrt{c^{2} x^{2} - 1}}{15 c^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{4} \sqrt{- c^{2} x^{2} + 1}}{5 c} + \frac{4 i x^{2} \sqrt{- c^{2} x^{2} + 1}}{15 c^{3}} + \frac{8 i \sqrt{- c^{2} x^{2} + 1}}{15 c^{5}} & \text{otherwise} \end{cases}\right)}{6 c}"," ",0,"a*d*x**4/4 + a*e*x**6/6 + b*d*x**4*asec(c*x)/4 + b*e*x**6*asec(c*x)/6 - b*d*Piecewise((x**2*sqrt(c**2*x**2 - 1)/(3*c) + 2*sqrt(c**2*x**2 - 1)/(3*c**3), Abs(c**2*x**2) > 1), (I*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 2*I*sqrt(-c**2*x**2 + 1)/(3*c**3), True))/(4*c) - b*e*Piecewise((x**4*sqrt(c**2*x**2 - 1)/(5*c) + 4*x**2*sqrt(c**2*x**2 - 1)/(15*c**3) + 8*sqrt(c**2*x**2 - 1)/(15*c**5), Abs(c**2*x**2) > 1), (I*x**4*sqrt(-c**2*x**2 + 1)/(5*c) + 4*I*x**2*sqrt(-c**2*x**2 + 1)/(15*c**3) + 8*I*sqrt(-c**2*x**2 + 1)/(15*c**5), True))/(6*c)","A",0
78,1,177,0,3.657512," ","integrate(x*(e*x**2+d)*(a+b*asec(c*x)),x)","\frac{a d x^{2}}{2} + \frac{a e x^{4}}{4} + \frac{b d x^{2} \operatorname{asec}{\left(c x \right)}}{2} + \frac{b e x^{4} \operatorname{asec}{\left(c x \right)}}{4} - \frac{b d \left(\begin{cases} \frac{\sqrt{c^{2} x^{2} - 1}}{c} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{- c^{2} x^{2} + 1}}{c} & \text{otherwise} \end{cases}\right)}{2 c} - \frac{b e \left(\begin{cases} \frac{x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} + \frac{2 \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{2 i \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} & \text{otherwise} \end{cases}\right)}{4 c}"," ",0,"a*d*x**2/2 + a*e*x**4/4 + b*d*x**2*asec(c*x)/2 + b*e*x**4*asec(c*x)/4 - b*d*Piecewise((sqrt(c**2*x**2 - 1)/c, Abs(c**2*x**2) > 1), (I*sqrt(-c**2*x**2 + 1)/c, True))/(2*c) - b*e*Piecewise((x**2*sqrt(c**2*x**2 - 1)/(3*c) + 2*sqrt(c**2*x**2 - 1)/(3*c**3), Abs(c**2*x**2) > 1), (I*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 2*I*sqrt(-c**2*x**2 + 1)/(3*c**3), True))/(4*c)","A",0
79,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*asec(c*x))/x,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)}{x}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)/x, x)","F",0
80,0,0,0,0.000000," ","integrate((e*x**2+d)*(a+b*asec(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)}{x^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)/x**3, x)","F",0
81,1,542,0,13.680185," ","integrate(x**2*(e*x**2+d)**2*(a+b*asec(c*x)),x)","\frac{a d^{2} x^{3}}{3} + \frac{2 a d e x^{5}}{5} + \frac{a e^{2} x^{7}}{7} + \frac{b d^{2} x^{3} \operatorname{asec}{\left(c x \right)}}{3} + \frac{2 b d e x^{5} \operatorname{asec}{\left(c x \right)}}{5} + \frac{b e^{2} x^{7} \operatorname{asec}{\left(c x \right)}}{7} - \frac{b d^{2} \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{3 c} - \frac{2 b d e \left(\begin{cases} \frac{c x^{5}}{4 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{3}}{8 c \sqrt{c^{2} x^{2} - 1}} - \frac{3 x}{8 c^{3} \sqrt{c^{2} x^{2} - 1}} + \frac{3 \operatorname{acosh}{\left(c x \right)}}{8 c^{4}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{5}}{4 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{3}}{8 c \sqrt{- c^{2} x^{2} + 1}} + \frac{3 i x}{8 c^{3} \sqrt{- c^{2} x^{2} + 1}} - \frac{3 i \operatorname{asin}{\left(c x \right)}}{8 c^{4}} & \text{otherwise} \end{cases}\right)}{5 c} - \frac{b e^{2} \left(\begin{cases} \frac{c x^{7}}{6 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{5}}{24 c \sqrt{c^{2} x^{2} - 1}} + \frac{5 x^{3}}{48 c^{3} \sqrt{c^{2} x^{2} - 1}} - \frac{5 x}{16 c^{5} \sqrt{c^{2} x^{2} - 1}} + \frac{5 \operatorname{acosh}{\left(c x \right)}}{16 c^{6}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{7}}{6 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{5}}{24 c \sqrt{- c^{2} x^{2} + 1}} - \frac{5 i x^{3}}{48 c^{3} \sqrt{- c^{2} x^{2} + 1}} + \frac{5 i x}{16 c^{5} \sqrt{- c^{2} x^{2} + 1}} - \frac{5 i \operatorname{asin}{\left(c x \right)}}{16 c^{6}} & \text{otherwise} \end{cases}\right)}{7 c}"," ",0,"a*d**2*x**3/3 + 2*a*d*e*x**5/5 + a*e**2*x**7/7 + b*d**2*x**3*asec(c*x)/3 + 2*b*d*e*x**5*asec(c*x)/5 + b*e**2*x**7*asec(c*x)/7 - b*d**2*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/(3*c) - 2*b*d*e*Piecewise((c*x**5/(4*sqrt(c**2*x**2 - 1)) + x**3/(8*c*sqrt(c**2*x**2 - 1)) - 3*x/(8*c**3*sqrt(c**2*x**2 - 1)) + 3*acosh(c*x)/(8*c**4), Abs(c**2*x**2) > 1), (-I*c*x**5/(4*sqrt(-c**2*x**2 + 1)) - I*x**3/(8*c*sqrt(-c**2*x**2 + 1)) + 3*I*x/(8*c**3*sqrt(-c**2*x**2 + 1)) - 3*I*asin(c*x)/(8*c**4), True))/(5*c) - b*e**2*Piecewise((c*x**7/(6*sqrt(c**2*x**2 - 1)) + x**5/(24*c*sqrt(c**2*x**2 - 1)) + 5*x**3/(48*c**3*sqrt(c**2*x**2 - 1)) - 5*x/(16*c**5*sqrt(c**2*x**2 - 1)) + 5*acosh(c*x)/(16*c**6), Abs(c**2*x**2) > 1), (-I*c*x**7/(6*sqrt(-c**2*x**2 + 1)) - I*x**5/(24*c*sqrt(-c**2*x**2 + 1)) - 5*I*x**3/(48*c**3*sqrt(-c**2*x**2 + 1)) + 5*I*x/(16*c**5*sqrt(-c**2*x**2 + 1)) - 5*I*asin(c*x)/(16*c**6), True))/(7*c)","A",0
82,1,355,0,9.792437," ","integrate((e*x**2+d)**2*(a+b*asec(c*x)),x)","a d^{2} x + \frac{2 a d e x^{3}}{3} + \frac{a e^{2} x^{5}}{5} + b d^{2} x \operatorname{asec}{\left(c x \right)} + \frac{2 b d e x^{3} \operatorname{asec}{\left(c x \right)}}{3} + \frac{b e^{2} x^{5} \operatorname{asec}{\left(c x \right)}}{5} - \frac{b d^{2} \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c} - \frac{2 b d e \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{3 c} - \frac{b e^{2} \left(\begin{cases} \frac{c x^{5}}{4 \sqrt{c^{2} x^{2} - 1}} + \frac{x^{3}}{8 c \sqrt{c^{2} x^{2} - 1}} - \frac{3 x}{8 c^{3} \sqrt{c^{2} x^{2} - 1}} + \frac{3 \operatorname{acosh}{\left(c x \right)}}{8 c^{4}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{5}}{4 \sqrt{- c^{2} x^{2} + 1}} - \frac{i x^{3}}{8 c \sqrt{- c^{2} x^{2} + 1}} + \frac{3 i x}{8 c^{3} \sqrt{- c^{2} x^{2} + 1}} - \frac{3 i \operatorname{asin}{\left(c x \right)}}{8 c^{4}} & \text{otherwise} \end{cases}\right)}{5 c}"," ",0,"a*d**2*x + 2*a*d*e*x**3/3 + a*e**2*x**5/5 + b*d**2*x*asec(c*x) + 2*b*d*e*x**3*asec(c*x)/3 + b*e**2*x**5*asec(c*x)/5 - b*d**2*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c - 2*b*d*e*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/(3*c) - b*e**2*Piecewise((c*x**5/(4*sqrt(c**2*x**2 - 1)) + x**3/(8*c*sqrt(c**2*x**2 - 1)) - 3*x/(8*c**3*sqrt(c**2*x**2 - 1)) + 3*acosh(c*x)/(8*c**4), Abs(c**2*x**2) > 1), (-I*c*x**5/(4*sqrt(-c**2*x**2 + 1)) - I*x**3/(8*c*sqrt(-c**2*x**2 + 1)) + 3*I*x/(8*c**3*sqrt(-c**2*x**2 + 1)) - 3*I*asin(c*x)/(8*c**4), True))/(5*c)","A",0
83,1,207,0,8.564390," ","integrate((e*x**2+d)**2*(a+b*asec(c*x))/x**2,x)","- \frac{a d^{2}}{x} + 2 a d e x + \frac{a e^{2} x^{3}}{3} + b c d^{2} \sqrt{1 - \frac{1}{c^{2} x^{2}}} - \frac{b d^{2} \operatorname{asec}{\left(c x \right)}}{x} + 2 b d e x \operatorname{asec}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{asec}{\left(c x \right)}}{3} - \frac{2 b d e \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c} - \frac{b e^{2} \left(\begin{cases} \frac{x \sqrt{c^{2} x^{2} - 1}}{2 c} + \frac{\operatorname{acosh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- \frac{i c x^{3}}{2 \sqrt{- c^{2} x^{2} + 1}} + \frac{i x}{2 c \sqrt{- c^{2} x^{2} + 1}} - \frac{i \operatorname{asin}{\left(c x \right)}}{2 c^{2}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"-a*d**2/x + 2*a*d*e*x + a*e**2*x**3/3 + b*c*d**2*sqrt(1 - 1/(c**2*x**2)) - b*d**2*asec(c*x)/x + 2*b*d*e*x*asec(c*x) + b*e**2*x**3*asec(c*x)/3 - 2*b*d*e*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c - b*e**2*Piecewise((x*sqrt(c**2*x**2 - 1)/(2*c) + acosh(c*x)/(2*c**2), Abs(c**2*x**2) > 1), (-I*c*x**3/(2*sqrt(-c**2*x**2 + 1)) + I*x/(2*c*sqrt(-c**2*x**2 + 1)) - I*asin(c*x)/(2*c**2), True))/(3*c)","A",0
84,1,211,0,7.988075," ","integrate((e*x**2+d)**2*(a+b*asec(c*x))/x**4,x)","- \frac{a d^{2}}{3 x^{3}} - \frac{2 a d e}{x} + a e^{2} x + 2 b c d e \sqrt{1 - \frac{1}{c^{2} x^{2}}} - \frac{b d^{2} \operatorname{asec}{\left(c x \right)}}{3 x^{3}} - \frac{2 b d e \operatorname{asec}{\left(c x \right)}}{x} + b e^{2} x \operatorname{asec}{\left(c x \right)} + \frac{b d^{2} \left(\begin{cases} \frac{2 c^{3} \sqrt{c^{2} x^{2} - 1}}{3 x} + \frac{c \sqrt{c^{2} x^{2} - 1}}{3 x^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{2 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{3 x} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{3 x^{3}} & \text{otherwise} \end{cases}\right)}{3 c} - \frac{b e^{2} \left(\begin{cases} \operatorname{acosh}{\left(c x \right)} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\- i \operatorname{asin}{\left(c x \right)} & \text{otherwise} \end{cases}\right)}{c}"," ",0,"-a*d**2/(3*x**3) - 2*a*d*e/x + a*e**2*x + 2*b*c*d*e*sqrt(1 - 1/(c**2*x**2)) - b*d**2*asec(c*x)/(3*x**3) - 2*b*d*e*asec(c*x)/x + b*e**2*x*asec(c*x) + b*d**2*Piecewise((2*c**3*sqrt(c**2*x**2 - 1)/(3*x) + c*sqrt(c**2*x**2 - 1)/(3*x**3), Abs(c**2*x**2) > 1), (2*I*c**3*sqrt(-c**2*x**2 + 1)/(3*x) + I*c*sqrt(-c**2*x**2 + 1)/(3*x**3), True))/(3*c) - b*e**2*Piecewise((acosh(c*x), Abs(c**2*x**2) > 1), (-I*asin(c*x), True))/c","A",0
85,1,333,0,10.528644," ","integrate((e*x**2+d)**2*(a+b*asec(c*x))/x**6,x)","- \frac{a d^{2}}{5 x^{5}} - \frac{2 a d e}{3 x^{3}} - \frac{a e^{2}}{x} + b c e^{2} \sqrt{1 - \frac{1}{c^{2} x^{2}}} - \frac{b d^{2} \operatorname{asec}{\left(c x \right)}}{5 x^{5}} - \frac{2 b d e \operatorname{asec}{\left(c x \right)}}{3 x^{3}} - \frac{b e^{2} \operatorname{asec}{\left(c x \right)}}{x} + \frac{b d^{2} \left(\begin{cases} \frac{8 c^{5} \sqrt{c^{2} x^{2} - 1}}{15 x} + \frac{4 c^{3} \sqrt{c^{2} x^{2} - 1}}{15 x^{3}} + \frac{c \sqrt{c^{2} x^{2} - 1}}{5 x^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{8 i c^{5} \sqrt{- c^{2} x^{2} + 1}}{15 x} + \frac{4 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{15 x^{3}} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{5 x^{5}} & \text{otherwise} \end{cases}\right)}{5 c} + \frac{2 b d e \left(\begin{cases} \frac{2 c^{3} \sqrt{c^{2} x^{2} - 1}}{3 x} + \frac{c \sqrt{c^{2} x^{2} - 1}}{3 x^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{2 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{3 x} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{3 x^{3}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"-a*d**2/(5*x**5) - 2*a*d*e/(3*x**3) - a*e**2/x + b*c*e**2*sqrt(1 - 1/(c**2*x**2)) - b*d**2*asec(c*x)/(5*x**5) - 2*b*d*e*asec(c*x)/(3*x**3) - b*e**2*asec(c*x)/x + b*d**2*Piecewise((8*c**5*sqrt(c**2*x**2 - 1)/(15*x) + 4*c**3*sqrt(c**2*x**2 - 1)/(15*x**3) + c*sqrt(c**2*x**2 - 1)/(5*x**5), Abs(c**2*x**2) > 1), (8*I*c**5*sqrt(-c**2*x**2 + 1)/(15*x) + 4*I*c**3*sqrt(-c**2*x**2 + 1)/(15*x**3) + I*c*sqrt(-c**2*x**2 + 1)/(5*x**5), True))/(5*c) + 2*b*d*e*Piecewise((2*c**3*sqrt(c**2*x**2 - 1)/(3*x) + c*sqrt(c**2*x**2 - 1)/(3*x**3), Abs(c**2*x**2) > 1), (2*I*c**3*sqrt(-c**2*x**2 + 1)/(3*x) + I*c*sqrt(-c**2*x**2 + 1)/(3*x**3), True))/(3*c)","A",0
86,1,508,0,57.340422," ","integrate((e*x**2+d)**2*(a+b*asec(c*x))/x**8,x)","- \frac{a d^{2}}{7 x^{7}} - \frac{2 a d e}{5 x^{5}} - \frac{a e^{2}}{3 x^{3}} - \frac{b d^{2} \operatorname{asec}{\left(c x \right)}}{7 x^{7}} - \frac{2 b d e \operatorname{asec}{\left(c x \right)}}{5 x^{5}} - \frac{b e^{2} \operatorname{asec}{\left(c x \right)}}{3 x^{3}} + \frac{b d^{2} \left(\begin{cases} \frac{16 c^{7} \sqrt{c^{2} x^{2} - 1}}{35 x} + \frac{8 c^{5} \sqrt{c^{2} x^{2} - 1}}{35 x^{3}} + \frac{6 c^{3} \sqrt{c^{2} x^{2} - 1}}{35 x^{5}} + \frac{c \sqrt{c^{2} x^{2} - 1}}{7 x^{7}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{16 i c^{7} \sqrt{- c^{2} x^{2} + 1}}{35 x} + \frac{8 i c^{5} \sqrt{- c^{2} x^{2} + 1}}{35 x^{3}} + \frac{6 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{35 x^{5}} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{7 x^{7}} & \text{otherwise} \end{cases}\right)}{7 c} + \frac{2 b d e \left(\begin{cases} \frac{8 c^{5} \sqrt{c^{2} x^{2} - 1}}{15 x} + \frac{4 c^{3} \sqrt{c^{2} x^{2} - 1}}{15 x^{3}} + \frac{c \sqrt{c^{2} x^{2} - 1}}{5 x^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{8 i c^{5} \sqrt{- c^{2} x^{2} + 1}}{15 x} + \frac{4 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{15 x^{3}} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{5 x^{5}} & \text{otherwise} \end{cases}\right)}{5 c} + \frac{b e^{2} \left(\begin{cases} \frac{2 c^{3} \sqrt{c^{2} x^{2} - 1}}{3 x} + \frac{c \sqrt{c^{2} x^{2} - 1}}{3 x^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{2 i c^{3} \sqrt{- c^{2} x^{2} + 1}}{3 x} + \frac{i c \sqrt{- c^{2} x^{2} + 1}}{3 x^{3}} & \text{otherwise} \end{cases}\right)}{3 c}"," ",0,"-a*d**2/(7*x**7) - 2*a*d*e/(5*x**5) - a*e**2/(3*x**3) - b*d**2*asec(c*x)/(7*x**7) - 2*b*d*e*asec(c*x)/(5*x**5) - b*e**2*asec(c*x)/(3*x**3) + b*d**2*Piecewise((16*c**7*sqrt(c**2*x**2 - 1)/(35*x) + 8*c**5*sqrt(c**2*x**2 - 1)/(35*x**3) + 6*c**3*sqrt(c**2*x**2 - 1)/(35*x**5) + c*sqrt(c**2*x**2 - 1)/(7*x**7), Abs(c**2*x**2) > 1), (16*I*c**7*sqrt(-c**2*x**2 + 1)/(35*x) + 8*I*c**5*sqrt(-c**2*x**2 + 1)/(35*x**3) + 6*I*c**3*sqrt(-c**2*x**2 + 1)/(35*x**5) + I*c*sqrt(-c**2*x**2 + 1)/(7*x**7), True))/(7*c) + 2*b*d*e*Piecewise((8*c**5*sqrt(c**2*x**2 - 1)/(15*x) + 4*c**3*sqrt(c**2*x**2 - 1)/(15*x**3) + c*sqrt(c**2*x**2 - 1)/(5*x**5), Abs(c**2*x**2) > 1), (8*I*c**5*sqrt(-c**2*x**2 + 1)/(15*x) + 4*I*c**3*sqrt(-c**2*x**2 + 1)/(15*x**3) + I*c*sqrt(-c**2*x**2 + 1)/(5*x**5), True))/(5*c) + b*e**2*Piecewise((2*c**3*sqrt(c**2*x**2 - 1)/(3*x) + c*sqrt(c**2*x**2 - 1)/(3*x**3), Abs(c**2*x**2) > 1), (2*I*c**3*sqrt(-c**2*x**2 + 1)/(3*x) + I*c*sqrt(-c**2*x**2 + 1)/(3*x**3), True))/(3*c)","A",0
87,1,493,0,9.005825," ","integrate(x**3*(e*x**2+d)**2*(a+b*asec(c*x)),x)","\frac{a d^{2} x^{4}}{4} + \frac{a d e x^{6}}{3} + \frac{a e^{2} x^{8}}{8} + \frac{b d^{2} x^{4} \operatorname{asec}{\left(c x \right)}}{4} + \frac{b d e x^{6} \operatorname{asec}{\left(c x \right)}}{3} + \frac{b e^{2} x^{8} \operatorname{asec}{\left(c x \right)}}{8} - \frac{b d^{2} \left(\begin{cases} \frac{x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} + \frac{2 \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{2 i \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} & \text{otherwise} \end{cases}\right)}{4 c} - \frac{b d e \left(\begin{cases} \frac{x^{4} \sqrt{c^{2} x^{2} - 1}}{5 c} + \frac{4 x^{2} \sqrt{c^{2} x^{2} - 1}}{15 c^{3}} + \frac{8 \sqrt{c^{2} x^{2} - 1}}{15 c^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{4} \sqrt{- c^{2} x^{2} + 1}}{5 c} + \frac{4 i x^{2} \sqrt{- c^{2} x^{2} + 1}}{15 c^{3}} + \frac{8 i \sqrt{- c^{2} x^{2} + 1}}{15 c^{5}} & \text{otherwise} \end{cases}\right)}{3 c} - \frac{b e^{2} \left(\begin{cases} \frac{x^{6} \sqrt{c^{2} x^{2} - 1}}{7 c} + \frac{6 x^{4} \sqrt{c^{2} x^{2} - 1}}{35 c^{3}} + \frac{8 x^{2} \sqrt{c^{2} x^{2} - 1}}{35 c^{5}} + \frac{16 \sqrt{c^{2} x^{2} - 1}}{35 c^{7}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{6} \sqrt{- c^{2} x^{2} + 1}}{7 c} + \frac{6 i x^{4} \sqrt{- c^{2} x^{2} + 1}}{35 c^{3}} + \frac{8 i x^{2} \sqrt{- c^{2} x^{2} + 1}}{35 c^{5}} + \frac{16 i \sqrt{- c^{2} x^{2} + 1}}{35 c^{7}} & \text{otherwise} \end{cases}\right)}{8 c}"," ",0,"a*d**2*x**4/4 + a*d*e*x**6/3 + a*e**2*x**8/8 + b*d**2*x**4*asec(c*x)/4 + b*d*e*x**6*asec(c*x)/3 + b*e**2*x**8*asec(c*x)/8 - b*d**2*Piecewise((x**2*sqrt(c**2*x**2 - 1)/(3*c) + 2*sqrt(c**2*x**2 - 1)/(3*c**3), Abs(c**2*x**2) > 1), (I*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 2*I*sqrt(-c**2*x**2 + 1)/(3*c**3), True))/(4*c) - b*d*e*Piecewise((x**4*sqrt(c**2*x**2 - 1)/(5*c) + 4*x**2*sqrt(c**2*x**2 - 1)/(15*c**3) + 8*sqrt(c**2*x**2 - 1)/(15*c**5), Abs(c**2*x**2) > 1), (I*x**4*sqrt(-c**2*x**2 + 1)/(5*c) + 4*I*x**2*sqrt(-c**2*x**2 + 1)/(15*c**3) + 8*I*sqrt(-c**2*x**2 + 1)/(15*c**5), True))/(3*c) - b*e**2*Piecewise((x**6*sqrt(c**2*x**2 - 1)/(7*c) + 6*x**4*sqrt(c**2*x**2 - 1)/(35*c**3) + 8*x**2*sqrt(c**2*x**2 - 1)/(35*c**5) + 16*sqrt(c**2*x**2 - 1)/(35*c**7), Abs(c**2*x**2) > 1), (I*x**6*sqrt(-c**2*x**2 + 1)/(7*c) + 6*I*x**4*sqrt(-c**2*x**2 + 1)/(35*c**3) + 8*I*x**2*sqrt(-c**2*x**2 + 1)/(35*c**5) + 16*I*sqrt(-c**2*x**2 + 1)/(35*c**7), True))/(8*c)","A",0
88,1,352,0,6.163062," ","integrate(x*(e*x**2+d)**2*(a+b*asec(c*x)),x)","\frac{a d^{2} x^{2}}{2} + \frac{a d e x^{4}}{2} + \frac{a e^{2} x^{6}}{6} + \frac{b d^{2} x^{2} \operatorname{asec}{\left(c x \right)}}{2} + \frac{b d e x^{4} \operatorname{asec}{\left(c x \right)}}{2} + \frac{b e^{2} x^{6} \operatorname{asec}{\left(c x \right)}}{6} - \frac{b d^{2} \left(\begin{cases} \frac{\sqrt{c^{2} x^{2} - 1}}{c} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i \sqrt{- c^{2} x^{2} + 1}}{c} & \text{otherwise} \end{cases}\right)}{2 c} - \frac{b d e \left(\begin{cases} \frac{x^{2} \sqrt{c^{2} x^{2} - 1}}{3 c} + \frac{2 \sqrt{c^{2} x^{2} - 1}}{3 c^{3}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{2 i \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} & \text{otherwise} \end{cases}\right)}{2 c} - \frac{b e^{2} \left(\begin{cases} \frac{x^{4} \sqrt{c^{2} x^{2} - 1}}{5 c} + \frac{4 x^{2} \sqrt{c^{2} x^{2} - 1}}{15 c^{3}} + \frac{8 \sqrt{c^{2} x^{2} - 1}}{15 c^{5}} & \text{for}\: \left|{c^{2} x^{2}}\right| > 1 \\\frac{i x^{4} \sqrt{- c^{2} x^{2} + 1}}{5 c} + \frac{4 i x^{2} \sqrt{- c^{2} x^{2} + 1}}{15 c^{3}} + \frac{8 i \sqrt{- c^{2} x^{2} + 1}}{15 c^{5}} & \text{otherwise} \end{cases}\right)}{6 c}"," ",0,"a*d**2*x**2/2 + a*d*e*x**4/2 + a*e**2*x**6/6 + b*d**2*x**2*asec(c*x)/2 + b*d*e*x**4*asec(c*x)/2 + b*e**2*x**6*asec(c*x)/6 - b*d**2*Piecewise((sqrt(c**2*x**2 - 1)/c, Abs(c**2*x**2) > 1), (I*sqrt(-c**2*x**2 + 1)/c, True))/(2*c) - b*d*e*Piecewise((x**2*sqrt(c**2*x**2 - 1)/(3*c) + 2*sqrt(c**2*x**2 - 1)/(3*c**3), Abs(c**2*x**2) > 1), (I*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 2*I*sqrt(-c**2*x**2 + 1)/(3*c**3), True))/(2*c) - b*e**2*Piecewise((x**4*sqrt(c**2*x**2 - 1)/(5*c) + 4*x**2*sqrt(c**2*x**2 - 1)/(15*c**3) + 8*sqrt(c**2*x**2 - 1)/(15*c**5), Abs(c**2*x**2) > 1), (I*x**4*sqrt(-c**2*x**2 + 1)/(5*c) + 4*I*x**2*sqrt(-c**2*x**2 + 1)/(15*c**3) + 8*I*sqrt(-c**2*x**2 + 1)/(15*c**5), True))/(6*c)","A",0
89,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*asec(c*x))/x,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)**2/x, x)","F",0
90,0,0,0,0.000000," ","integrate((e*x**2+d)**2*(a+b*asec(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)**2/x**3, x)","F",0
91,0,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))/(e*x**2+d),x)","\int \frac{x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral(x**2*(a + b*asec(c*x))/(d + e*x**2), x)","F",0
92,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))/(e*x**2+d),x)","\int \frac{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))/(d + e*x**2), x)","F",0
93,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x**2+d),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{d + e x^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(d + e*x**2), x)","F",0
94,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x/(e*x**2+d),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x*(d + e*x**2)), x)","F",0
95,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**2/(e*x**2+d),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x^{2} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x**2*(d + e*x**2)), x)","F",0
96,-1,0,0,0.000000," ","integrate(x**5*(a+b*asec(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))/(e*x**2+d)**2,x)","\int \frac{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))/(d + e*x**2)**2, x)","F",0
99,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(x**4*(a+b*asec(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**2/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(x**5*(a+b*asec(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(x**4*(a+b*asec(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(x**5*(a+b*asec(c*x))*(e*x**2+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,0,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))*(e*x**2+d)**(1/2),x)","\int x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**3*(a + b*asec(c*x))*sqrt(d + e*x**2), x)","F",0
113,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))*(e*x**2+d)**(1/2),x)","\int x \left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))*sqrt(d + e*x**2), x)","F",0
114,0,0,0,0.000000," ","integrate((a+b*asec(c*x))*(e*x**2+d)**(1/2)/x,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x}\, dx"," ",0,"Integral((a + b*asec(c*x))*sqrt(d + e*x**2)/x, x)","F",0
115,0,0,0,0.000000," ","integrate((a+b*asec(c*x))*(e*x**2+d)**(1/2)/x**3,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))*sqrt(d + e*x**2)/x**3, x)","F",0
116,0,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))*(e*x**2+d)**(1/2),x)","\int x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**2*(a + b*asec(c*x))*sqrt(d + e*x**2), x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*asec(c*x))*(e*x**2+d)**(1/2),x)","\int \left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))*sqrt(d + e*x**2), x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*asec(c*x))*(e*x**2+d)**(1/2)/x**2,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))*sqrt(d + e*x**2)/x**2, x)","F",0
119,0,0,0,0.000000," ","integrate((a+b*asec(c*x))*(e*x**2+d)**(1/2)/x**4,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*asec(c*x))*sqrt(d + e*x**2)/x**4, x)","F",0
120,0,0,0,0.000000," ","integrate((a+b*asec(c*x))*(e*x**2+d)**(1/2)/x**6,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}}{x^{6}}\, dx"," ",0,"Integral((a + b*asec(c*x))*sqrt(d + e*x**2)/x**6, x)","F",0
121,-1,0,0,0.000000," ","integrate(x**3*(e*x**2+d)**(3/2)*(a+b*asec(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate(x*(e*x**2+d)**(3/2)*(a+b*asec(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*asec(c*x))/x,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)**(3/2)/x, x)","F",0
124,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*asec(c*x))/x**3,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)**(3/2)/x**3, x)","F",0
125,-1,0,0,0.000000," ","integrate(x**2*(e*x**2+d)**(3/2)*(a+b*asec(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*asec(c*x)),x)","\int \left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)**(3/2), x)","F",0
127,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*asec(c*x))/x**2,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)**(3/2)/x**2, x)","F",0
128,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*asec(c*x))/x**4,x)","\int \frac{\left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*asec(c*x))*(d + e*x**2)**(3/2)/x**4, x)","F",0
129,-1,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*asec(c*x))/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*asec(c*x))/x**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,0,0,0,0.000000," ","integrate(x**5*(a+b*asec(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x^{5} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**5*(a + b*asec(c*x))/sqrt(d + e*x**2), x)","F",0
132,0,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**3*(a + b*asec(c*x))/sqrt(d + e*x**2), x)","F",0
133,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))/sqrt(d + e*x**2), x)","F",0
134,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x*sqrt(d + e*x**2)), x)","F",0
135,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**3/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x^{3} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x**3*sqrt(d + e*x**2)), x)","F",0
136,0,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**2*(a + b*asec(c*x))/sqrt(d + e*x**2), x)","F",0
137,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x**2+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**2/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x^{2} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x**2*sqrt(d + e*x**2)), x)","F",0
139,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**4/(e*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x^{4} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x**4*sqrt(d + e*x**2)), x)","F",0
140,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**6/(e*x**2+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(x**5*(a+b*asec(c*x))/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,0,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*asec(c*x))/(d + e*x**2)**(3/2), x)","F",0
143,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))/(d + e*x**2)**(3/2), x)","F",0
144,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**3/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate(x**4*(a+b*asec(c*x))/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,0,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{x^{2} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*asec(c*x))/(d + e*x**2)**(3/2), x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(d + e*x**2)**(3/2), x)","F",0
149,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**2/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**4/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate(x**5*(a+b*asec(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,0,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))/(e*x**2+d)**(5/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*asec(c*x))/(d + e*x**2)**(5/2), x)","F",0
153,0,0,0,0.000000," ","integrate(x*(a+b*asec(c*x))/(e*x**2+d)**(5/2),x)","\int \frac{x \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\left(d + e x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*(a + b*asec(c*x))/(d + e*x**2)**(5/2), x)","F",0
154,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**3/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate(x**6*(a+b*asec(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate(x**4*(a+b*asec(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(x**2*(a+b*asec(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**2/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate((f*x)**m*(e*x**2+d)**3*(a+b*asec(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,0,0,0,0.000000," ","integrate((f*x)**m*(e*x**2+d)**2*(a+b*asec(c*x)),x)","\int \left(f x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)^{2}\, dx"," ",0,"Integral((f*x)**m*(a + b*asec(c*x))*(d + e*x**2)**2, x)","F",0
163,0,0,0,0.000000," ","integrate((f*x)**m*(e*x**2+d)*(a+b*asec(c*x)),x)","\int \left(f x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right) \left(d + e x^{2}\right)\, dx"," ",0,"Integral((f*x)**m*(a + b*asec(c*x))*(d + e*x**2), x)","F",0
164,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*asec(c*x))/(e*x**2+d),x)","\int \frac{\left(f x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral((f*x)**m*(a + b*asec(c*x))/(d + e*x**2), x)","F",0
165,-1,0,0,0.000000," ","integrate((f*x)**m*(a+b*asec(c*x))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((f*x)**m*(e*x**2+d)**(3/2)*(a+b*asec(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,0,0,0,0.000000," ","integrate((f*x)**m*(e*x**2+d)**(1/2)*(a+b*asec(c*x)),x)","\int \left(f x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral((f*x)**m*(a + b*asec(c*x))*sqrt(d + e*x**2), x)","F",0
168,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*asec(c*x))/(e*x**2+d)**(1/2),x)","\int \frac{\left(f x\right)^{m} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((f*x)**m*(a + b*asec(c*x))/sqrt(d + e*x**2), x)","F",0
169,-1,0,0,0.000000," ","integrate((f*x)**m*(a+b*asec(c*x))/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(x**11*(a+b*asec(c*x))/(-c**4*x**4+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(x**7*(a+b*asec(c*x))/(-c**4*x**4+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,0,0,0,0.000000," ","integrate(x**3*(a+b*asec(c*x))/(-c**4*x**4+1)**(1/2),x)","\int \frac{x^{3} \left(a + b \operatorname{asec}{\left(c x \right)}\right)}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right) \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(x**3*(a + b*asec(c*x))/sqrt(-(c*x - 1)*(c*x + 1)*(c**2*x**2 + 1)), x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x/(-c**4*x**4+1)**(1/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x \sqrt{- \left(c x - 1\right) \left(c x + 1\right) \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x*sqrt(-(c*x - 1)*(c*x + 1)*(c**2*x**2 + 1))), x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*asec(c*x))/x**5/(-c**4*x**4+1)**(1/2),x)","\int \frac{a + b \operatorname{asec}{\left(c x \right)}}{x^{5} \sqrt{- \left(c x - 1\right) \left(c x + 1\right) \left(c^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*asec(c*x))/(x**5*sqrt(-(c*x - 1)*(c*x + 1)*(c**2*x**2 + 1))), x)","F",0
