1,1,29,0,0.103431," ","integrate(x**2*(b*x**2+a)*(B*x**2+A),x)","\frac{A a x^{3}}{3} + \frac{B b x^{7}}{7} + x^{5} \left(\frac{A b}{5} + \frac{B a}{5}\right)"," ",0,"A*a*x**3/3 + B*b*x**7/7 + x**5*(A*b/5 + B*a/5)","A",0
2,1,29,0,0.065107," ","integrate(x*(b*x**2+a)*(B*x**2+A),x)","\frac{A a x^{2}}{2} + \frac{B b x^{6}}{6} + x^{4} \left(\frac{A b}{4} + \frac{B a}{4}\right)"," ",0,"A*a*x**2/2 + B*b*x**6/6 + x**4*(A*b/4 + B*a/4)","A",0
3,1,26,0,0.062583," ","integrate((b*x**2+a)*(B*x**2+A),x)","A a x + \frac{B b x^{5}}{5} + x^{3} \left(\frac{A b}{3} + \frac{B a}{3}\right)"," ",0,"A*a*x + B*b*x**5/5 + x**3*(A*b/3 + B*a/3)","A",0
4,1,27,0,0.112907," ","integrate((b*x**2+a)*(B*x**2+A)/x,x)","A a \log{\left(x \right)} + \frac{B b x^{4}}{4} + x^{2} \left(\frac{A b}{2} + \frac{B a}{2}\right)"," ",0,"A*a*log(x) + B*b*x**4/4 + x**2*(A*b/2 + B*a/2)","A",0
5,1,20,0,0.105374," ","integrate((b*x**2+a)*(B*x**2+A)/x**2,x)","- \frac{A a}{x} + \frac{B b x^{3}}{3} + x \left(A b + B a\right)"," ",0,"-A*a/x + B*b*x**3/3 + x*(A*b + B*a)","A",0
6,1,26,0,0.183687," ","integrate((b*x**2+a)*(B*x**2+A)/x**3,x)","- \frac{A a}{2 x^{2}} + \frac{B b x^{2}}{2} + \left(A b + B a\right) \log{\left(x \right)}"," ",0,"-A*a/(2*x**2) + B*b*x**2/2 + (A*b + B*a)*log(x)","A",0
7,1,27,0,0.205416," ","integrate((b*x**2+a)*(B*x**2+A)/x**4,x)","B b x + \frac{- A a + x^{2} \left(- 3 A b - 3 B a\right)}{3 x^{3}}"," ",0,"B*b*x + (-A*a + x**2*(-3*A*b - 3*B*a))/(3*x**3)","A",0
8,1,29,0,0.358750," ","integrate((b*x**2+a)*(B*x**2+A)/x**5,x)","B b \log{\left(x \right)} + \frac{- A a + x^{2} \left(- 2 A b - 2 B a\right)}{4 x^{4}}"," ",0,"B*b*log(x) + (-A*a + x**2*(-2*A*b - 2*B*a))/(4*x**4)","A",0
9,1,32,0,0.365917," ","integrate((b*x**2+a)*(B*x**2+A)/x**6,x)","\frac{- 3 A a - 15 B b x^{4} + x^{2} \left(- 5 A b - 5 B a\right)}{15 x^{5}}"," ",0,"(-3*A*a - 15*B*b*x**4 + x**2*(-5*A*b - 5*B*a))/(15*x**5)","A",0
10,1,32,0,0.490063," ","integrate((b*x**2+a)*(B*x**2+A)/x**7,x)","\frac{- 2 A a - 6 B b x^{4} + x^{2} \left(- 3 A b - 3 B a\right)}{12 x^{6}}"," ",0,"(-2*A*a - 6*B*b*x**4 + x**2*(-3*A*b - 3*B*a))/(12*x**6)","A",0
11,1,56,0,0.074636," ","integrate(x**2*(b*x**2+a)**2*(B*x**2+A),x)","\frac{A a^{2} x^{3}}{3} + \frac{B b^{2} x^{9}}{9} + x^{7} \left(\frac{A b^{2}}{7} + \frac{2 B a b}{7}\right) + x^{5} \left(\frac{2 A a b}{5} + \frac{B a^{2}}{5}\right)"," ",0,"A*a**2*x**3/3 + B*b**2*x**9/9 + x**7*(A*b**2/7 + 2*B*a*b/7) + x**5*(2*A*a*b/5 + B*a**2/5)","A",0
12,1,53,0,0.076404," ","integrate(x*(b*x**2+a)**2*(B*x**2+A),x)","\frac{A a^{2} x^{2}}{2} + \frac{B b^{2} x^{8}}{8} + x^{6} \left(\frac{A b^{2}}{6} + \frac{B a b}{3}\right) + x^{4} \left(\frac{A a b}{2} + \frac{B a^{2}}{4}\right)"," ",0,"A*a**2*x**2/2 + B*b**2*x**8/8 + x**6*(A*b**2/6 + B*a*b/3) + x**4*(A*a*b/2 + B*a**2/4)","A",0
13,1,53,0,0.074278," ","integrate((b*x**2+a)**2*(B*x**2+A),x)","A a^{2} x + \frac{B b^{2} x^{7}}{7} + x^{5} \left(\frac{A b^{2}}{5} + \frac{2 B a b}{5}\right) + x^{3} \left(\frac{2 A a b}{3} + \frac{B a^{2}}{3}\right)"," ",0,"A*a**2*x + B*b**2*x**7/7 + x**5*(A*b**2/5 + 2*B*a*b/5) + x**3*(2*A*a*b/3 + B*a**2/3)","A",0
14,1,49,0,0.143760," ","integrate((b*x**2+a)**2*(B*x**2+A)/x,x)","A a^{2} \log{\left(x \right)} + \frac{B b^{2} x^{6}}{6} + x^{4} \left(\frac{A b^{2}}{4} + \frac{B a b}{2}\right) + x^{2} \left(A a b + \frac{B a^{2}}{2}\right)"," ",0,"A*a**2*log(x) + B*b**2*x**6/6 + x**4*(A*b**2/4 + B*a*b/2) + x**2*(A*a*b + B*a**2/2)","A",0
15,1,48,0,0.138467," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**2,x)","- \frac{A a^{2}}{x} + \frac{B b^{2} x^{5}}{5} + x^{3} \left(\frac{A b^{2}}{3} + \frac{2 B a b}{3}\right) + x \left(2 A a b + B a^{2}\right)"," ",0,"-A*a**2/x + B*b**2*x**5/5 + x**3*(A*b**2/3 + 2*B*a*b/3) + x*(2*A*a*b + B*a**2)","A",0
16,1,48,0,0.235763," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**3,x)","- \frac{A a^{2}}{2 x^{2}} + \frac{B b^{2} x^{4}}{4} + a \left(2 A b + B a\right) \log{\left(x \right)} + x^{2} \left(\frac{A b^{2}}{2} + B a b\right)"," ",0,"-A*a**2/(2*x**2) + B*b**2*x**4/4 + a*(2*A*b + B*a)*log(x) + x**2*(A*b**2/2 + B*a*b)","A",0
17,1,51,0,0.253403," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**4,x)","\frac{B b^{2} x^{3}}{3} + x \left(A b^{2} + 2 B a b\right) + \frac{- A a^{2} + x^{2} \left(- 6 A a b - 3 B a^{2}\right)}{3 x^{3}}"," ",0,"B*b**2*x**3/3 + x*(A*b**2 + 2*B*a*b) + (-A*a**2 + x**2*(-6*A*a*b - 3*B*a**2))/(3*x**3)","A",0
18,1,51,0,0.522157," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**5,x)","\frac{B b^{2} x^{2}}{2} + b \left(A b + 2 B a\right) \log{\left(x \right)} + \frac{- A a^{2} + x^{2} \left(- 4 A a b - 2 B a^{2}\right)}{4 x^{4}}"," ",0,"B*b**2*x**2/2 + b*(A*b + 2*B*a)*log(x) + (-A*a**2 + x**2*(-4*A*a*b - 2*B*a**2))/(4*x**4)","A",0
19,1,54,0,0.602934," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**6,x)","B b^{2} x + \frac{- 3 A a^{2} + x^{4} \left(- 15 A b^{2} - 30 B a b\right) + x^{2} \left(- 10 A a b - 5 B a^{2}\right)}{15 x^{5}}"," ",0,"B*b**2*x + (-3*A*a**2 + x**4*(-15*A*b**2 - 30*B*a*b) + x**2*(-10*A*a*b - 5*B*a**2))/(15*x**5)","A",0
20,1,56,0,0.997393," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**7,x)","B b^{2} \log{\left(x \right)} + \frac{- 2 A a^{2} + x^{4} \left(- 6 A b^{2} - 12 B a b\right) + x^{2} \left(- 6 A a b - 3 B a^{2}\right)}{12 x^{6}}"," ",0,"B*b**2*log(x) + (-2*A*a**2 + x**4*(-6*A*b**2 - 12*B*a*b) + x**2*(-6*A*a*b - 3*B*a**2))/(12*x**6)","A",0
21,1,58,0,1.061438," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**8,x)","\frac{- 15 A a^{2} - 105 B b^{2} x^{6} + x^{4} \left(- 35 A b^{2} - 70 B a b\right) + x^{2} \left(- 42 A a b - 21 B a^{2}\right)}{105 x^{7}}"," ",0,"(-15*A*a**2 - 105*B*b**2*x**6 + x**4*(-35*A*b**2 - 70*B*a*b) + x**2*(-42*A*a*b - 21*B*a**2))/(105*x**7)","A",0
22,1,58,0,1.480219," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**9,x)","\frac{- 3 A a^{2} - 12 B b^{2} x^{6} + x^{4} \left(- 6 A b^{2} - 12 B a b\right) + x^{2} \left(- 8 A a b - 4 B a^{2}\right)}{24 x^{8}}"," ",0,"(-3*A*a**2 - 12*B*b**2*x**6 + x**4*(-6*A*b**2 - 12*B*a*b) + x**2*(-8*A*a*b - 4*B*a**2))/(24*x**8)","A",0
23,1,136,0,0.094599," ","integrate(x**9*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{10}}{10} + \frac{B b^{5} x^{22}}{22} + x^{20} \left(\frac{A b^{5}}{20} + \frac{B a b^{4}}{4}\right) + x^{18} \left(\frac{5 A a b^{4}}{18} + \frac{5 B a^{2} b^{3}}{9}\right) + x^{16} \left(\frac{5 A a^{2} b^{3}}{8} + \frac{5 B a^{3} b^{2}}{8}\right) + x^{14} \left(\frac{5 A a^{3} b^{2}}{7} + \frac{5 B a^{4} b}{14}\right) + x^{12} \left(\frac{5 A a^{4} b}{12} + \frac{B a^{5}}{12}\right)"," ",0,"A*a**5*x**10/10 + B*b**5*x**22/22 + x**20*(A*b**5/20 + B*a*b**4/4) + x**18*(5*A*a*b**4/18 + 5*B*a**2*b**3/9) + x**16*(5*A*a**2*b**3/8 + 5*B*a**3*b**2/8) + x**14*(5*A*a**3*b**2/7 + 5*B*a**4*b/14) + x**12*(5*A*a**4*b/12 + B*a**5/12)","A",0
24,1,138,0,0.092458," ","integrate(x**8*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{9}}{9} + \frac{B b^{5} x^{21}}{21} + x^{19} \left(\frac{A b^{5}}{19} + \frac{5 B a b^{4}}{19}\right) + x^{17} \left(\frac{5 A a b^{4}}{17} + \frac{10 B a^{2} b^{3}}{17}\right) + x^{15} \left(\frac{2 A a^{2} b^{3}}{3} + \frac{2 B a^{3} b^{2}}{3}\right) + x^{13} \left(\frac{10 A a^{3} b^{2}}{13} + \frac{5 B a^{4} b}{13}\right) + x^{11} \left(\frac{5 A a^{4} b}{11} + \frac{B a^{5}}{11}\right)"," ",0,"A*a**5*x**9/9 + B*b**5*x**21/21 + x**19*(A*b**5/19 + 5*B*a*b**4/19) + x**17*(5*A*a*b**4/17 + 10*B*a**2*b**3/17) + x**15*(2*A*a**2*b**3/3 + 2*B*a**3*b**2/3) + x**13*(10*A*a**3*b**2/13 + 5*B*a**4*b/13) + x**11*(5*A*a**4*b/11 + B*a**5/11)","A",0
25,1,136,0,0.093040," ","integrate(x**7*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{8}}{8} + \frac{B b^{5} x^{20}}{20} + x^{18} \left(\frac{A b^{5}}{18} + \frac{5 B a b^{4}}{18}\right) + x^{16} \left(\frac{5 A a b^{4}}{16} + \frac{5 B a^{2} b^{3}}{8}\right) + x^{14} \left(\frac{5 A a^{2} b^{3}}{7} + \frac{5 B a^{3} b^{2}}{7}\right) + x^{12} \left(\frac{5 A a^{3} b^{2}}{6} + \frac{5 B a^{4} b}{12}\right) + x^{10} \left(\frac{A a^{4} b}{2} + \frac{B a^{5}}{10}\right)"," ",0,"A*a**5*x**8/8 + B*b**5*x**20/20 + x**18*(A*b**5/18 + 5*B*a*b**4/18) + x**16*(5*A*a*b**4/16 + 5*B*a**2*b**3/8) + x**14*(5*A*a**2*b**3/7 + 5*B*a**3*b**2/7) + x**12*(5*A*a**3*b**2/6 + 5*B*a**4*b/12) + x**10*(A*a**4*b/2 + B*a**5/10)","A",0
26,1,136,0,0.092546," ","integrate(x**6*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{7}}{7} + \frac{B b^{5} x^{19}}{19} + x^{17} \left(\frac{A b^{5}}{17} + \frac{5 B a b^{4}}{17}\right) + x^{15} \left(\frac{A a b^{4}}{3} + \frac{2 B a^{2} b^{3}}{3}\right) + x^{13} \left(\frac{10 A a^{2} b^{3}}{13} + \frac{10 B a^{3} b^{2}}{13}\right) + x^{11} \left(\frac{10 A a^{3} b^{2}}{11} + \frac{5 B a^{4} b}{11}\right) + x^{9} \left(\frac{5 A a^{4} b}{9} + \frac{B a^{5}}{9}\right)"," ",0,"A*a**5*x**7/7 + B*b**5*x**19/19 + x**17*(A*b**5/17 + 5*B*a*b**4/17) + x**15*(A*a*b**4/3 + 2*B*a**2*b**3/3) + x**13*(10*A*a**2*b**3/13 + 10*B*a**3*b**2/13) + x**11*(10*A*a**3*b**2/11 + 5*B*a**4*b/11) + x**9*(5*A*a**4*b/9 + B*a**5/9)","A",0
27,1,133,0,0.092232," ","integrate(x**5*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{6}}{6} + \frac{B b^{5} x^{18}}{18} + x^{16} \left(\frac{A b^{5}}{16} + \frac{5 B a b^{4}}{16}\right) + x^{14} \left(\frac{5 A a b^{4}}{14} + \frac{5 B a^{2} b^{3}}{7}\right) + x^{12} \left(\frac{5 A a^{2} b^{3}}{6} + \frac{5 B a^{3} b^{2}}{6}\right) + x^{10} \left(A a^{3} b^{2} + \frac{B a^{4} b}{2}\right) + x^{8} \left(\frac{5 A a^{4} b}{8} + \frac{B a^{5}}{8}\right)"," ",0,"A*a**5*x**6/6 + B*b**5*x**18/18 + x**16*(A*b**5/16 + 5*B*a*b**4/16) + x**14*(5*A*a*b**4/14 + 5*B*a**2*b**3/7) + x**12*(5*A*a**2*b**3/6 + 5*B*a**3*b**2/6) + x**10*(A*a**3*b**2 + B*a**4*b/2) + x**8*(5*A*a**4*b/8 + B*a**5/8)","A",0
28,1,136,0,0.093821," ","integrate(x**4*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{5}}{5} + \frac{B b^{5} x^{17}}{17} + x^{15} \left(\frac{A b^{5}}{15} + \frac{B a b^{4}}{3}\right) + x^{13} \left(\frac{5 A a b^{4}}{13} + \frac{10 B a^{2} b^{3}}{13}\right) + x^{11} \left(\frac{10 A a^{2} b^{3}}{11} + \frac{10 B a^{3} b^{2}}{11}\right) + x^{9} \left(\frac{10 A a^{3} b^{2}}{9} + \frac{5 B a^{4} b}{9}\right) + x^{7} \left(\frac{5 A a^{4} b}{7} + \frac{B a^{5}}{7}\right)"," ",0,"A*a**5*x**5/5 + B*b**5*x**17/17 + x**15*(A*b**5/15 + B*a*b**4/3) + x**13*(5*A*a*b**4/13 + 10*B*a**2*b**3/13) + x**11*(10*A*a**2*b**3/11 + 10*B*a**3*b**2/11) + x**9*(10*A*a**3*b**2/9 + 5*B*a**4*b/9) + x**7*(5*A*a**4*b/7 + B*a**5/7)","A",0
29,1,131,0,0.093358," ","integrate(x**3*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{4}}{4} + \frac{B b^{5} x^{16}}{16} + x^{14} \left(\frac{A b^{5}}{14} + \frac{5 B a b^{4}}{14}\right) + x^{12} \left(\frac{5 A a b^{4}}{12} + \frac{5 B a^{2} b^{3}}{6}\right) + x^{10} \left(A a^{2} b^{3} + B a^{3} b^{2}\right) + x^{8} \left(\frac{5 A a^{3} b^{2}}{4} + \frac{5 B a^{4} b}{8}\right) + x^{6} \left(\frac{5 A a^{4} b}{6} + \frac{B a^{5}}{6}\right)"," ",0,"A*a**5*x**4/4 + B*b**5*x**16/16 + x**14*(A*b**5/14 + 5*B*a*b**4/14) + x**12*(5*A*a*b**4/12 + 5*B*a**2*b**3/6) + x**10*(A*a**2*b**3 + B*a**3*b**2) + x**8*(5*A*a**3*b**2/4 + 5*B*a**4*b/8) + x**6*(5*A*a**4*b/6 + B*a**5/6)","B",0
30,1,134,0,0.094069," ","integrate(x**2*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{3}}{3} + \frac{B b^{5} x^{15}}{15} + x^{13} \left(\frac{A b^{5}}{13} + \frac{5 B a b^{4}}{13}\right) + x^{11} \left(\frac{5 A a b^{4}}{11} + \frac{10 B a^{2} b^{3}}{11}\right) + x^{9} \left(\frac{10 A a^{2} b^{3}}{9} + \frac{10 B a^{3} b^{2}}{9}\right) + x^{7} \left(\frac{10 A a^{3} b^{2}}{7} + \frac{5 B a^{4} b}{7}\right) + x^{5} \left(A a^{4} b + \frac{B a^{5}}{5}\right)"," ",0,"A*a**5*x**3/3 + B*b**5*x**15/15 + x**13*(A*b**5/13 + 5*B*a*b**4/13) + x**11*(5*A*a*b**4/11 + 10*B*a**2*b**3/11) + x**9*(10*A*a**2*b**3/9 + 10*B*a**3*b**2/9) + x**7*(10*A*a**3*b**2/7 + 5*B*a**4*b/7) + x**5*(A*a**4*b + B*a**5/5)","A",0
31,1,133,0,0.092084," ","integrate(x*(b*x**2+a)**5*(B*x**2+A),x)","\frac{A a^{5} x^{2}}{2} + \frac{B b^{5} x^{14}}{14} + x^{12} \left(\frac{A b^{5}}{12} + \frac{5 B a b^{4}}{12}\right) + x^{10} \left(\frac{A a b^{4}}{2} + B a^{2} b^{3}\right) + x^{8} \left(\frac{5 A a^{2} b^{3}}{4} + \frac{5 B a^{3} b^{2}}{4}\right) + x^{6} \left(\frac{5 A a^{3} b^{2}}{3} + \frac{5 B a^{4} b}{6}\right) + x^{4} \left(\frac{5 A a^{4} b}{4} + \frac{B a^{5}}{4}\right)"," ",0,"A*a**5*x**2/2 + B*b**5*x**14/14 + x**12*(A*b**5/12 + 5*B*a*b**4/12) + x**10*(A*a*b**4/2 + B*a**2*b**3) + x**8*(5*A*a**2*b**3/4 + 5*B*a**3*b**2/4) + x**6*(5*A*a**3*b**2/3 + 5*B*a**4*b/6) + x**4*(5*A*a**4*b/4 + B*a**5/4)","B",0
32,1,129,0,0.094993," ","integrate((b*x**2+a)**5*(B*x**2+A),x)","A a^{5} x + \frac{B b^{5} x^{13}}{13} + x^{11} \left(\frac{A b^{5}}{11} + \frac{5 B a b^{4}}{11}\right) + x^{9} \left(\frac{5 A a b^{4}}{9} + \frac{10 B a^{2} b^{3}}{9}\right) + x^{7} \left(\frac{10 A a^{2} b^{3}}{7} + \frac{10 B a^{3} b^{2}}{7}\right) + x^{5} \left(2 A a^{3} b^{2} + B a^{4} b\right) + x^{3} \left(\frac{5 A a^{4} b}{3} + \frac{B a^{5}}{3}\right)"," ",0,"A*a**5*x + B*b**5*x**13/13 + x**11*(A*b**5/11 + 5*B*a*b**4/11) + x**9*(5*A*a*b**4/9 + 10*B*a**2*b**3/9) + x**7*(10*A*a**2*b**3/7 + 10*B*a**3*b**2/7) + x**5*(2*A*a**3*b**2 + B*a**4*b) + x**3*(5*A*a**4*b/3 + B*a**5/3)","A",0
33,1,134,0,0.241004," ","integrate((b*x**2+a)**5*(B*x**2+A)/x,x)","A a^{5} \log{\left(x \right)} + \frac{B b^{5} x^{12}}{12} + x^{10} \left(\frac{A b^{5}}{10} + \frac{B a b^{4}}{2}\right) + x^{8} \left(\frac{5 A a b^{4}}{8} + \frac{5 B a^{2} b^{3}}{4}\right) + x^{6} \left(\frac{5 A a^{2} b^{3}}{3} + \frac{5 B a^{3} b^{2}}{3}\right) + x^{4} \left(\frac{5 A a^{3} b^{2}}{2} + \frac{5 B a^{4} b}{4}\right) + x^{2} \left(\frac{5 A a^{4} b}{2} + \frac{B a^{5}}{2}\right)"," ",0,"A*a**5*log(x) + B*b**5*x**12/12 + x**10*(A*b**5/10 + B*a*b**4/2) + x**8*(5*A*a*b**4/8 + 5*B*a**2*b**3/4) + x**6*(5*A*a**2*b**3/3 + 5*B*a**3*b**2/3) + x**4*(5*A*a**3*b**2/2 + 5*B*a**4*b/4) + x**2*(5*A*a**4*b/2 + B*a**5/2)","A",0
34,1,126,0,0.239170," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**2,x)","- \frac{A a^{5}}{x} + \frac{B b^{5} x^{11}}{11} + x^{9} \left(\frac{A b^{5}}{9} + \frac{5 B a b^{4}}{9}\right) + x^{7} \left(\frac{5 A a b^{4}}{7} + \frac{10 B a^{2} b^{3}}{7}\right) + x^{5} \left(2 A a^{2} b^{3} + 2 B a^{3} b^{2}\right) + x^{3} \left(\frac{10 A a^{3} b^{2}}{3} + \frac{5 B a^{4} b}{3}\right) + x \left(5 A a^{4} b + B a^{5}\right)"," ",0,"-A*a**5/x + B*b**5*x**11/11 + x**9*(A*b**5/9 + 5*B*a*b**4/9) + x**7*(5*A*a*b**4/7 + 10*B*a**2*b**3/7) + x**5*(2*A*a**2*b**3 + 2*B*a**3*b**2) + x**3*(10*A*a**3*b**2/3 + 5*B*a**4*b/3) + x*(5*A*a**4*b + B*a**5)","A",0
35,1,131,0,0.345197," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**3,x)","- \frac{A a^{5}}{2 x^{2}} + \frac{B b^{5} x^{10}}{10} + a^{4} \left(5 A b + B a\right) \log{\left(x \right)} + x^{8} \left(\frac{A b^{5}}{8} + \frac{5 B a b^{4}}{8}\right) + x^{6} \left(\frac{5 A a b^{4}}{6} + \frac{5 B a^{2} b^{3}}{3}\right) + x^{4} \left(\frac{5 A a^{2} b^{3}}{2} + \frac{5 B a^{3} b^{2}}{2}\right) + x^{2} \left(5 A a^{3} b^{2} + \frac{5 B a^{4} b}{2}\right)"," ",0,"-A*a**5/(2*x**2) + B*b**5*x**10/10 + a**4*(5*A*b + B*a)*log(x) + x**8*(A*b**5/8 + 5*B*a*b**4/8) + x**6*(5*A*a*b**4/6 + 5*B*a**2*b**3/3) + x**4*(5*A*a**2*b**3/2 + 5*B*a**3*b**2/2) + x**2*(5*A*a**3*b**2 + 5*B*a**4*b/2)","A",0
36,1,128,0,0.356084," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**4,x)","\frac{B b^{5} x^{9}}{9} + x^{7} \left(\frac{A b^{5}}{7} + \frac{5 B a b^{4}}{7}\right) + x^{5} \left(A a b^{4} + 2 B a^{2} b^{3}\right) + x^{3} \left(\frac{10 A a^{2} b^{3}}{3} + \frac{10 B a^{3} b^{2}}{3}\right) + x \left(10 A a^{3} b^{2} + 5 B a^{4} b\right) + \frac{- A a^{5} + x^{2} \left(- 15 A a^{4} b - 3 B a^{5}\right)}{3 x^{3}}"," ",0,"B*b**5*x**9/9 + x**7*(A*b**5/7 + 5*B*a*b**4/7) + x**5*(A*a*b**4 + 2*B*a**2*b**3) + x**3*(10*A*a**2*b**3/3 + 10*B*a**3*b**2/3) + x*(10*A*a**3*b**2 + 5*B*a**4*b) + (-A*a**5 + x**2*(-15*A*a**4*b - 3*B*a**5))/(3*x**3)","A",0
37,1,128,0,0.697317," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**5,x)","\frac{B b^{5} x^{8}}{8} + 5 a^{3} b \left(2 A b + B a\right) \log{\left(x \right)} + x^{6} \left(\frac{A b^{5}}{6} + \frac{5 B a b^{4}}{6}\right) + x^{4} \left(\frac{5 A a b^{4}}{4} + \frac{5 B a^{2} b^{3}}{2}\right) + x^{2} \left(5 A a^{2} b^{3} + 5 B a^{3} b^{2}\right) + \frac{- A a^{5} + x^{2} \left(- 10 A a^{4} b - 2 B a^{5}\right)}{4 x^{4}}"," ",0,"B*b**5*x**8/8 + 5*a**3*b*(2*A*b + B*a)*log(x) + x**6*(A*b**5/6 + 5*B*a*b**4/6) + x**4*(5*A*a*b**4/4 + 5*B*a**2*b**3/2) + x**2*(5*A*a**2*b**3 + 5*B*a**3*b**2) + (-A*a**5 + x**2*(-10*A*a**4*b - 2*B*a**5))/(4*x**4)","A",0
38,1,129,0,0.771276," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**6,x)","\frac{B b^{5} x^{7}}{7} + x^{5} \left(\frac{A b^{5}}{5} + B a b^{4}\right) + x^{3} \left(\frac{5 A a b^{4}}{3} + \frac{10 B a^{2} b^{3}}{3}\right) + x \left(10 A a^{2} b^{3} + 10 B a^{3} b^{2}\right) + \frac{- 3 A a^{5} + x^{4} \left(- 150 A a^{3} b^{2} - 75 B a^{4} b\right) + x^{2} \left(- 25 A a^{4} b - 5 B a^{5}\right)}{15 x^{5}}"," ",0,"B*b**5*x**7/7 + x**5*(A*b**5/5 + B*a*b**4) + x**3*(5*A*a*b**4/3 + 10*B*a**2*b**3/3) + x*(10*A*a**2*b**3 + 10*B*a**3*b**2) + (-3*A*a**5 + x**4*(-150*A*a**3*b**2 - 75*B*a**4*b) + x**2*(-25*A*a**4*b - 5*B*a**5))/(15*x**5)","A",0
39,1,128,0,1.413507," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**7,x)","\frac{B b^{5} x^{6}}{6} + 10 a^{2} b^{2} \left(A b + B a\right) \log{\left(x \right)} + x^{4} \left(\frac{A b^{5}}{4} + \frac{5 B a b^{4}}{4}\right) + x^{2} \left(\frac{5 A a b^{4}}{2} + 5 B a^{2} b^{3}\right) + \frac{- 2 A a^{5} + x^{4} \left(- 60 A a^{3} b^{2} - 30 B a^{4} b\right) + x^{2} \left(- 15 A a^{4} b - 3 B a^{5}\right)}{12 x^{6}}"," ",0,"B*b**5*x**6/6 + 10*a**2*b**2*(A*b + B*a)*log(x) + x**4*(A*b**5/4 + 5*B*a*b**4/4) + x**2*(5*A*a*b**4/2 + 5*B*a**2*b**3) + (-2*A*a**5 + x**4*(-60*A*a**3*b**2 - 30*B*a**4*b) + x**2*(-15*A*a**4*b - 3*B*a**5))/(12*x**6)","A",0
40,1,131,0,1.615756," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**8,x)","\frac{B b^{5} x^{5}}{5} + x^{3} \left(\frac{A b^{5}}{3} + \frac{5 B a b^{4}}{3}\right) + x \left(5 A a b^{4} + 10 B a^{2} b^{3}\right) + \frac{- 15 A a^{5} + x^{6} \left(- 1050 A a^{2} b^{3} - 1050 B a^{3} b^{2}\right) + x^{4} \left(- 350 A a^{3} b^{2} - 175 B a^{4} b\right) + x^{2} \left(- 105 A a^{4} b - 21 B a^{5}\right)}{105 x^{7}}"," ",0,"B*b**5*x**5/5 + x**3*(A*b**5/3 + 5*B*a*b**4/3) + x*(5*A*a*b**4 + 10*B*a**2*b**3) + (-15*A*a**5 + x**6*(-1050*A*a**2*b**3 - 1050*B*a**3*b**2) + x**4*(-350*A*a**3*b**2 - 175*B*a**4*b) + x**2*(-105*A*a**4*b - 21*B*a**5))/(105*x**7)","A",0
41,1,129,0,2.731080," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**9,x)","\frac{B b^{5} x^{4}}{4} + 5 a b^{3} \left(A b + 2 B a\right) \log{\left(x \right)} + x^{2} \left(\frac{A b^{5}}{2} + \frac{5 B a b^{4}}{2}\right) + \frac{- 3 A a^{5} + x^{6} \left(- 120 A a^{2} b^{3} - 120 B a^{3} b^{2}\right) + x^{4} \left(- 60 A a^{3} b^{2} - 30 B a^{4} b\right) + x^{2} \left(- 20 A a^{4} b - 4 B a^{5}\right)}{24 x^{8}}"," ",0,"B*b**5*x**4/4 + 5*a*b**3*(A*b + 2*B*a)*log(x) + x**2*(A*b**5/2 + 5*B*a*b**4/2) + (-3*A*a**5 + x**6*(-120*A*a**2*b**3 - 120*B*a**3*b**2) + x**4*(-60*A*a**3*b**2 - 30*B*a**4*b) + x**2*(-20*A*a**4*b - 4*B*a**5))/(24*x**8)","A",0
42,1,129,0,3.089564," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**10,x)","\frac{B b^{5} x^{3}}{3} + x \left(A b^{5} + 5 B a b^{4}\right) + \frac{- 7 A a^{5} + x^{8} \left(- 315 A a b^{4} - 630 B a^{2} b^{3}\right) + x^{6} \left(- 210 A a^{2} b^{3} - 210 B a^{3} b^{2}\right) + x^{4} \left(- 126 A a^{3} b^{2} - 63 B a^{4} b\right) + x^{2} \left(- 45 A a^{4} b - 9 B a^{5}\right)}{63 x^{9}}"," ",0,"B*b**5*x**3/3 + x*(A*b**5 + 5*B*a*b**4) + (-7*A*a**5 + x**8*(-315*A*a*b**4 - 630*B*a**2*b**3) + x**6*(-210*A*a**2*b**3 - 210*B*a**3*b**2) + x**4*(-126*A*a**3*b**2 - 63*B*a**4*b) + x**2*(-45*A*a**4*b - 9*B*a**5))/(63*x**9)","A",0
43,1,129,0,5.004373," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**11,x)","\frac{B b^{5} x^{2}}{2} + b^{4} \left(A b + 5 B a\right) \log{\left(x \right)} + \frac{- 12 A a^{5} + x^{8} \left(- 300 A a b^{4} - 600 B a^{2} b^{3}\right) + x^{6} \left(- 300 A a^{2} b^{3} - 300 B a^{3} b^{2}\right) + x^{4} \left(- 200 A a^{3} b^{2} - 100 B a^{4} b\right) + x^{2} \left(- 75 A a^{4} b - 15 B a^{5}\right)}{120 x^{10}}"," ",0,"B*b**5*x**2/2 + b**4*(A*b + 5*B*a)*log(x) + (-12*A*a**5 + x**8*(-300*A*a*b**4 - 600*B*a**2*b**3) + x**6*(-300*A*a**2*b**3 - 300*B*a**3*b**2) + x**4*(-200*A*a**3*b**2 - 100*B*a**4*b) + x**2*(-75*A*a**4*b - 15*B*a**5))/(120*x**10)","A",0
44,1,131,0,6.684540," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**12,x)","B b^{5} x + \frac{- 63 A a^{5} + x^{10} \left(- 693 A b^{5} - 3465 B a b^{4}\right) + x^{8} \left(- 1155 A a b^{4} - 2310 B a^{2} b^{3}\right) + x^{6} \left(- 1386 A a^{2} b^{3} - 1386 B a^{3} b^{2}\right) + x^{4} \left(- 990 A a^{3} b^{2} - 495 B a^{4} b\right) + x^{2} \left(- 385 A a^{4} b - 77 B a^{5}\right)}{693 x^{11}}"," ",0,"B*b**5*x + (-63*A*a**5 + x**10*(-693*A*b**5 - 3465*B*a*b**4) + x**8*(-1155*A*a*b**4 - 2310*B*a**2*b**3) + x**6*(-1386*A*a**2*b**3 - 1386*B*a**3*b**2) + x**4*(-990*A*a**3*b**2 - 495*B*a**4*b) + x**2*(-385*A*a**4*b - 77*B*a**5))/(693*x**11)","A",0
45,1,133,0,8.684180," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**13,x)","B b^{5} \log{\left(x \right)} + \frac{- 10 A a^{5} + x^{10} \left(- 60 A b^{5} - 300 B a b^{4}\right) + x^{8} \left(- 150 A a b^{4} - 300 B a^{2} b^{3}\right) + x^{6} \left(- 200 A a^{2} b^{3} - 200 B a^{3} b^{2}\right) + x^{4} \left(- 150 A a^{3} b^{2} - 75 B a^{4} b\right) + x^{2} \left(- 60 A a^{4} b - 12 B a^{5}\right)}{120 x^{12}}"," ",0,"B*b**5*log(x) + (-10*A*a**5 + x**10*(-60*A*b**5 - 300*B*a*b**4) + x**8*(-150*A*a*b**4 - 300*B*a**2*b**3) + x**6*(-200*A*a**2*b**3 - 200*B*a**3*b**2) + x**4*(-150*A*a**3*b**2 - 75*B*a**4*b) + x**2*(-60*A*a**4*b - 12*B*a**5))/(120*x**12)","A",0
46,1,134,0,14.039934," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**14,x)","\frac{- 693 A a^{5} - 9009 B b^{5} x^{12} + x^{10} \left(- 3003 A b^{5} - 15015 B a b^{4}\right) + x^{8} \left(- 9009 A a b^{4} - 18018 B a^{2} b^{3}\right) + x^{6} \left(- 12870 A a^{2} b^{3} - 12870 B a^{3} b^{2}\right) + x^{4} \left(- 10010 A a^{3} b^{2} - 5005 B a^{4} b\right) + x^{2} \left(- 4095 A a^{4} b - 819 B a^{5}\right)}{9009 x^{13}}"," ",0,"(-693*A*a**5 - 9009*B*b**5*x**12 + x**10*(-3003*A*b**5 - 15015*B*a*b**4) + x**8*(-9009*A*a*b**4 - 18018*B*a**2*b**3) + x**6*(-12870*A*a**2*b**3 - 12870*B*a**3*b**2) + x**4*(-10010*A*a**3*b**2 - 5005*B*a**4*b) + x**2*(-4095*A*a**4*b - 819*B*a**5))/(9009*x**13)","A",0
47,1,134,0,15.800967," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**15,x)","\frac{- 6 A a^{5} - 42 B b^{5} x^{12} + x^{10} \left(- 21 A b^{5} - 105 B a b^{4}\right) + x^{8} \left(- 70 A a b^{4} - 140 B a^{2} b^{3}\right) + x^{6} \left(- 105 A a^{2} b^{3} - 105 B a^{3} b^{2}\right) + x^{4} \left(- 84 A a^{3} b^{2} - 42 B a^{4} b\right) + x^{2} \left(- 35 A a^{4} b - 7 B a^{5}\right)}{84 x^{14}}"," ",0,"(-6*A*a**5 - 42*B*b**5*x**12 + x**10*(-21*A*b**5 - 105*B*a*b**4) + x**8*(-70*A*a*b**4 - 140*B*a**2*b**3) + x**6*(-105*A*a**2*b**3 - 105*B*a**3*b**2) + x**4*(-84*A*a**3*b**2 - 42*B*a**4*b) + x**2*(-35*A*a**4*b - 7*B*a**5))/(84*x**14)","B",0
48,1,134,0,36.444356," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**16,x)","\frac{- 3003 A a^{5} - 15015 B b^{5} x^{12} + x^{10} \left(- 9009 A b^{5} - 45045 B a b^{4}\right) + x^{8} \left(- 32175 A a b^{4} - 64350 B a^{2} b^{3}\right) + x^{6} \left(- 50050 A a^{2} b^{3} - 50050 B a^{3} b^{2}\right) + x^{4} \left(- 40950 A a^{3} b^{2} - 20475 B a^{4} b\right) + x^{2} \left(- 17325 A a^{4} b - 3465 B a^{5}\right)}{45045 x^{15}}"," ",0,"(-3003*A*a**5 - 15015*B*b**5*x**12 + x**10*(-9009*A*b**5 - 45045*B*a*b**4) + x**8*(-32175*A*a*b**4 - 64350*B*a**2*b**3) + x**6*(-50050*A*a**2*b**3 - 50050*B*a**3*b**2) + x**4*(-40950*A*a**3*b**2 - 20475*B*a**4*b) + x**2*(-17325*A*a**4*b - 3465*B*a**5))/(45045*x**15)","A",0
49,1,134,0,32.114962," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**17,x)","\frac{- 21 A a^{5} - 84 B b^{5} x^{12} + x^{10} \left(- 56 A b^{5} - 280 B a b^{4}\right) + x^{8} \left(- 210 A a b^{4} - 420 B a^{2} b^{3}\right) + x^{6} \left(- 336 A a^{2} b^{3} - 336 B a^{3} b^{2}\right) + x^{4} \left(- 280 A a^{3} b^{2} - 140 B a^{4} b\right) + x^{2} \left(- 120 A a^{4} b - 24 B a^{5}\right)}{336 x^{16}}"," ",0,"(-21*A*a**5 - 84*B*b**5*x**12 + x**10*(-56*A*b**5 - 280*B*a*b**4) + x**8*(-210*A*a*b**4 - 420*B*a**2*b**3) + x**6*(-336*A*a**2*b**3 - 336*B*a**3*b**2) + x**4*(-280*A*a**3*b**2 - 140*B*a**4*b) + x**2*(-120*A*a**4*b - 24*B*a**5))/(336*x**16)","A",0
50,1,134,0,94.111999," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**18,x)","\frac{- 45045 A a^{5} - 153153 B b^{5} x^{12} + x^{10} \left(- 109395 A b^{5} - 546975 B a b^{4}\right) + x^{8} \left(- 425425 A a b^{4} - 850850 B a^{2} b^{3}\right) + x^{6} \left(- 696150 A a^{2} b^{3} - 696150 B a^{3} b^{2}\right) + x^{4} \left(- 589050 A a^{3} b^{2} - 294525 B a^{4} b\right) + x^{2} \left(- 255255 A a^{4} b - 51051 B a^{5}\right)}{765765 x^{17}}"," ",0,"(-45045*A*a**5 - 153153*B*b**5*x**12 + x**10*(-109395*A*b**5 - 546975*B*a*b**4) + x**8*(-425425*A*a*b**4 - 850850*B*a**2*b**3) + x**6*(-696150*A*a**2*b**3 - 696150*B*a**3*b**2) + x**4*(-589050*A*a**3*b**2 - 294525*B*a**4*b) + x**2*(-255255*A*a**4*b - 51051*B*a**5))/(765765*x**17)","A",0
51,1,134,0,65.259925," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**19,x)","\frac{- 56 A a^{5} - 168 B b^{5} x^{12} + x^{10} \left(- 126 A b^{5} - 630 B a b^{4}\right) + x^{8} \left(- 504 A a b^{4} - 1008 B a^{2} b^{3}\right) + x^{6} \left(- 840 A a^{2} b^{3} - 840 B a^{3} b^{2}\right) + x^{4} \left(- 720 A a^{3} b^{2} - 360 B a^{4} b\right) + x^{2} \left(- 315 A a^{4} b - 63 B a^{5}\right)}{1008 x^{18}}"," ",0,"(-56*A*a**5 - 168*B*b**5*x**12 + x**10*(-126*A*b**5 - 630*B*a*b**4) + x**8*(-504*A*a*b**4 - 1008*B*a**2*b**3) + x**6*(-840*A*a**2*b**3 - 840*B*a**3*b**2) + x**4*(-720*A*a**3*b**2 - 360*B*a**4*b) + x**2*(-315*A*a**4*b - 63*B*a**5))/(1008*x**18)","A",0
52,-1,0,0,0.000000," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**20,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,1,134,0,127.672111," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**21,x)","\frac{- 252 A a^{5} - 630 B b^{5} x^{12} + x^{10} \left(- 504 A b^{5} - 2520 B a b^{4}\right) + x^{8} \left(- 2100 A a b^{4} - 4200 B a^{2} b^{3}\right) + x^{6} \left(- 3600 A a^{2} b^{3} - 3600 B a^{3} b^{2}\right) + x^{4} \left(- 3150 A a^{3} b^{2} - 1575 B a^{4} b\right) + x^{2} \left(- 1400 A a^{4} b - 280 B a^{5}\right)}{5040 x^{20}}"," ",0,"(-252*A*a**5 - 630*B*b**5*x**12 + x**10*(-504*A*b**5 - 2520*B*a*b**4) + x**8*(-2100*A*a*b**4 - 4200*B*a**2*b**3) + x**6*(-3600*A*a**2*b**3 - 3600*B*a**3*b**2) + x**4*(-3150*A*a**3*b**2 - 1575*B*a**4*b) + x**2*(-1400*A*a**4*b - 280*B*a**5))/(5040*x**20)","A",0
54,-1,0,0,0.000000," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**22,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate((b*x**2+a)**5*(B*x**2+A)/x**23,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,1,180,0,0.413777," ","integrate(x**6*(B*x**2+A)/(b*x**2+a),x)","\frac{B x^{7}}{7 b} + x^{5} \left(\frac{A}{5 b} - \frac{B a}{5 b^{2}}\right) + x^{3} \left(- \frac{A a}{3 b^{2}} + \frac{B a^{2}}{3 b^{3}}\right) + x \left(\frac{A a^{2}}{b^{3}} - \frac{B a^{3}}{b^{4}}\right) - \frac{\sqrt{- \frac{a^{5}}{b^{9}}} \left(- A b + B a\right) \log{\left(- \frac{b^{4} \sqrt{- \frac{a^{5}}{b^{9}}} \left(- A b + B a\right)}{- A a^{2} b + B a^{3}} + x \right)}}{2} + \frac{\sqrt{- \frac{a^{5}}{b^{9}}} \left(- A b + B a\right) \log{\left(\frac{b^{4} \sqrt{- \frac{a^{5}}{b^{9}}} \left(- A b + B a\right)}{- A a^{2} b + B a^{3}} + x \right)}}{2}"," ",0,"B*x**7/(7*b) + x**5*(A/(5*b) - B*a/(5*b**2)) + x**3*(-A*a/(3*b**2) + B*a**2/(3*b**3)) + x*(A*a**2/b**3 - B*a**3/b**4) - sqrt(-a**5/b**9)*(-A*b + B*a)*log(-b**4*sqrt(-a**5/b**9)*(-A*b + B*a)/(-A*a**2*b + B*a**3) + x)/2 + sqrt(-a**5/b**9)*(-A*b + B*a)*log(b**4*sqrt(-a**5/b**9)*(-A*b + B*a)/(-A*a**2*b + B*a**3) + x)/2","B",0
57,1,70,0,0.323440," ","integrate(x**5*(B*x**2+A)/(b*x**2+a),x)","\frac{B x^{6}}{6 b} - \frac{a^{2} \left(- A b + B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{4}} + x^{4} \left(\frac{A}{4 b} - \frac{B a}{4 b^{2}}\right) + x^{2} \left(- \frac{A a}{2 b^{2}} + \frac{B a^{2}}{2 b^{3}}\right)"," ",0,"B*x**6/(6*b) - a**2*(-A*b + B*a)*log(a + b*x**2)/(2*b**4) + x**4*(A/(4*b) - B*a/(4*b**2)) + x**2*(-A*a/(2*b**2) + B*a**2/(2*b**3))","A",0
58,1,153,0,0.374676," ","integrate(x**4*(B*x**2+A)/(b*x**2+a),x)","\frac{B x^{5}}{5 b} + x^{3} \left(\frac{A}{3 b} - \frac{B a}{3 b^{2}}\right) + x \left(- \frac{A a}{b^{2}} + \frac{B a^{2}}{b^{3}}\right) + \frac{\sqrt{- \frac{a^{3}}{b^{7}}} \left(- A b + B a\right) \log{\left(- \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}} \left(- A b + B a\right)}{- A a b + B a^{2}} + x \right)}}{2} - \frac{\sqrt{- \frac{a^{3}}{b^{7}}} \left(- A b + B a\right) \log{\left(\frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}} \left(- A b + B a\right)}{- A a b + B a^{2}} + x \right)}}{2}"," ",0,"B*x**5/(5*b) + x**3*(A/(3*b) - B*a/(3*b**2)) + x*(-A*a/b**2 + B*a**2/b**3) + sqrt(-a**3/b**7)*(-A*b + B*a)*log(-b**3*sqrt(-a**3/b**7)*(-A*b + B*a)/(-A*a*b + B*a**2) + x)/2 - sqrt(-a**3/b**7)*(-A*b + B*a)*log(b**3*sqrt(-a**3/b**7)*(-A*b + B*a)/(-A*a*b + B*a**2) + x)/2","B",0
59,1,46,0,0.287874," ","integrate(x**3*(B*x**2+A)/(b*x**2+a),x)","\frac{B x^{4}}{4 b} + \frac{a \left(- A b + B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{3}} + x^{2} \left(\frac{A}{2 b} - \frac{B a}{2 b^{2}}\right)"," ",0,"B*x**4/(4*b) + a*(-A*b + B*a)*log(a + b*x**2)/(2*b**3) + x**2*(A/(2*b) - B*a/(2*b**2))","A",0
60,1,90,0,0.331959," ","integrate(x**2*(B*x**2+A)/(b*x**2+a),x)","\frac{B x^{3}}{3 b} + x \left(\frac{A}{b} - \frac{B a}{b^{2}}\right) - \frac{\sqrt{- \frac{a}{b^{5}}} \left(- A b + B a\right) \log{\left(- b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{2} + \frac{\sqrt{- \frac{a}{b^{5}}} \left(- A b + B a\right) \log{\left(b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{2}"," ",0,"B*x**3/(3*b) + x*(A/b - B*a/b**2) - sqrt(-a/b**5)*(-A*b + B*a)*log(-b**2*sqrt(-a/b**5) + x)/2 + sqrt(-a/b**5)*(-A*b + B*a)*log(b**2*sqrt(-a/b**5) + x)/2","A",0
61,1,27,0,0.246343," ","integrate(x*(B*x**2+A)/(b*x**2+a),x)","\frac{B x^{2}}{2 b} - \frac{\left(- A b + B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{2}}"," ",0,"B*x**2/(2*b) - (-A*b + B*a)*log(a + b*x**2)/(2*b**2)","A",0
62,1,82,0,0.282290," ","integrate((B*x**2+A)/(b*x**2+a),x)","\frac{B x}{b} + \frac{\sqrt{- \frac{1}{a b^{3}}} \left(- A b + B a\right) \log{\left(- a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a b^{3}}} \left(- A b + B a\right) \log{\left(a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{2}"," ",0,"B*x/b + sqrt(-1/(a*b**3))*(-A*b + B*a)*log(-a*b*sqrt(-1/(a*b**3)) + x)/2 - sqrt(-1/(a*b**3))*(-A*b + B*a)*log(a*b*sqrt(-1/(a*b**3)) + x)/2","B",0
63,1,26,0,0.695232," ","integrate((B*x**2+A)/x/(b*x**2+a),x)","\frac{A \log{\left(x \right)}}{a} + \frac{\left(- A b + B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a b}"," ",0,"A*log(x)/a + (-A*b + B*a)*log(a/b + x**2)/(2*a*b)","A",0
64,1,82,0,0.341001," ","integrate((B*x**2+A)/x**2/(b*x**2+a),x)","- \frac{A}{a x} - \frac{\sqrt{- \frac{1}{a^{3} b}} \left(- A b + B a\right) \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a^{3} b}} \left(- A b + B a\right) \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{2}"," ",0,"-A/(a*x) - sqrt(-1/(a**3*b))*(-A*b + B*a)*log(-a**2*sqrt(-1/(a**3*b)) + x)/2 + sqrt(-1/(a**3*b))*(-A*b + B*a)*log(a**2*sqrt(-1/(a**3*b)) + x)/2","B",0
65,1,41,0,0.712408," ","integrate((B*x**2+A)/x**3/(b*x**2+a),x)","- \frac{A}{2 a x^{2}} + \frac{\left(- A b + B a\right) \log{\left(x \right)}}{a^{2}} - \frac{\left(- A b + B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"-A/(2*a*x**2) + (-A*b + B*a)*log(x)/a**2 - (-A*b + B*a)*log(a/b + x**2)/(2*a**2)","A",0
66,1,129,0,0.417253," ","integrate((B*x**2+A)/x**4/(b*x**2+a),x)","\frac{\sqrt{- \frac{b}{a^{5}}} \left(- A b + B a\right) \log{\left(- \frac{a^{3} \sqrt{- \frac{b}{a^{5}}} \left(- A b + B a\right)}{- A b^{2} + B a b} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{a^{5}}} \left(- A b + B a\right) \log{\left(\frac{a^{3} \sqrt{- \frac{b}{a^{5}}} \left(- A b + B a\right)}{- A b^{2} + B a b} + x \right)}}{2} + \frac{- A a + x^{2} \left(3 A b - 3 B a\right)}{3 a^{2} x^{3}}"," ",0,"sqrt(-b/a**5)*(-A*b + B*a)*log(-a**3*sqrt(-b/a**5)*(-A*b + B*a)/(-A*b**2 + B*a*b) + x)/2 - sqrt(-b/a**5)*(-A*b + B*a)*log(a**3*sqrt(-b/a**5)*(-A*b + B*a)/(-A*b**2 + B*a*b) + x)/2 + (-A*a + x**2*(3*A*b - 3*B*a))/(3*a**2*x**3)","B",0
67,1,61,0,0.826562," ","integrate((B*x**2+A)/x**5/(b*x**2+a),x)","\frac{- A a + x^{2} \left(2 A b - 2 B a\right)}{4 a^{2} x^{4}} - \frac{b \left(- A b + B a\right) \log{\left(x \right)}}{a^{3}} + \frac{b \left(- A b + B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{3}}"," ",0,"(-A*a + x**2*(2*A*b - 2*B*a))/(4*a**2*x**4) - b*(-A*b + B*a)*log(x)/a**3 + b*(-A*b + B*a)*log(a/b + x**2)/(2*a**3)","A",0
68,1,163,0,0.486809," ","integrate((B*x**2+A)/x**6/(b*x**2+a),x)","- \frac{\sqrt{- \frac{b^{3}}{a^{7}}} \left(- A b + B a\right) \log{\left(- \frac{a^{4} \sqrt{- \frac{b^{3}}{a^{7}}} \left(- A b + B a\right)}{- A b^{3} + B a b^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{b^{3}}{a^{7}}} \left(- A b + B a\right) \log{\left(\frac{a^{4} \sqrt{- \frac{b^{3}}{a^{7}}} \left(- A b + B a\right)}{- A b^{3} + B a b^{2}} + x \right)}}{2} + \frac{- 3 A a^{2} + x^{4} \left(- 15 A b^{2} + 15 B a b\right) + x^{2} \left(5 A a b - 5 B a^{2}\right)}{15 a^{3} x^{5}}"," ",0,"-sqrt(-b**3/a**7)*(-A*b + B*a)*log(-a**4*sqrt(-b**3/a**7)*(-A*b + B*a)/(-A*b**3 + B*a*b**2) + x)/2 + sqrt(-b**3/a**7)*(-A*b + B*a)*log(a**4*sqrt(-b**3/a**7)*(-A*b + B*a)/(-A*b**3 + B*a*b**2) + x)/2 + (-3*A*a**2 + x**4*(-15*A*b**2 + 15*B*a*b) + x**2*(5*A*a*b - 5*B*a**2))/(15*a**3*x**5)","B",0
69,1,88,0,0.895985," ","integrate((B*x**2+A)/x**7/(b*x**2+a),x)","\frac{- 2 A a^{2} + x^{4} \left(- 6 A b^{2} + 6 B a b\right) + x^{2} \left(3 A a b - 3 B a^{2}\right)}{12 a^{3} x^{6}} + \frac{b^{2} \left(- A b + B a\right) \log{\left(x \right)}}{a^{4}} - \frac{b^{2} \left(- A b + B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(-2*A*a**2 + x**4*(-6*A*b**2 + 6*B*a*b) + x**2*(3*A*a*b - 3*B*a**2))/(12*a**3*x**6) + b**2*(-A*b + B*a)*log(x)/a**4 - b**2*(-A*b + B*a)*log(a/b + x**2)/(2*a**4)","A",0
70,1,187,0,0.547874," ","integrate((B*x**2+A)/x**8/(b*x**2+a),x)","\frac{\sqrt{- \frac{b^{5}}{a^{9}}} \left(- A b + B a\right) \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{5}}{a^{9}}} \left(- A b + B a\right)}{- A b^{4} + B a b^{3}} + x \right)}}{2} - \frac{\sqrt{- \frac{b^{5}}{a^{9}}} \left(- A b + B a\right) \log{\left(\frac{a^{5} \sqrt{- \frac{b^{5}}{a^{9}}} \left(- A b + B a\right)}{- A b^{4} + B a b^{3}} + x \right)}}{2} + \frac{- 15 A a^{3} + x^{6} \left(105 A b^{3} - 105 B a b^{2}\right) + x^{4} \left(- 35 A a b^{2} + 35 B a^{2} b\right) + x^{2} \left(21 A a^{2} b - 21 B a^{3}\right)}{105 a^{4} x^{7}}"," ",0,"sqrt(-b**5/a**9)*(-A*b + B*a)*log(-a**5*sqrt(-b**5/a**9)*(-A*b + B*a)/(-A*b**4 + B*a*b**3) + x)/2 - sqrt(-b**5/a**9)*(-A*b + B*a)*log(a**5*sqrt(-b**5/a**9)*(-A*b + B*a)/(-A*b**4 + B*a*b**3) + x)/2 + (-15*A*a**3 + x**6*(105*A*b**3 - 105*B*a*b**2) + x**4*(-35*A*a*b**2 + 35*B*a**2*b) + x**2*(21*A*a**2*b - 21*B*a**3))/(105*a**4*x**7)","B",0
71,1,131,0,0.787618," ","integrate(x**9*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x^{8}}{8 b^{2}} + \frac{a^{3} \left(- 4 A b + 5 B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{6}} + x^{6} \left(\frac{A}{6 b^{2}} - \frac{B a}{3 b^{3}}\right) + x^{4} \left(- \frac{A a}{2 b^{3}} + \frac{3 B a^{2}}{4 b^{4}}\right) + x^{2} \left(\frac{3 A a^{2}}{2 b^{4}} - \frac{2 B a^{3}}{b^{5}}\right) + \frac{- A a^{4} b + B a^{5}}{2 a b^{6} + 2 b^{7} x^{2}}"," ",0,"B*x**8/(8*b**2) + a**3*(-4*A*b + 5*B*a)*log(a + b*x**2)/(2*b**6) + x**6*(A/(6*b**2) - B*a/(3*b**3)) + x**4*(-A*a/(2*b**3) + 3*B*a**2/(4*b**4)) + x**2*(3*A*a**2/(2*b**4) - 2*B*a**3/b**5) + (-A*a**4*b + B*a**5)/(2*a*b**6 + 2*b**7*x**2)","A",0
72,1,238,0,0.790203," ","integrate(x**8*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x^{7}}{7 b^{2}} + x^{5} \left(\frac{A}{5 b^{2}} - \frac{2 B a}{5 b^{3}}\right) + x^{3} \left(- \frac{2 A a}{3 b^{3}} + \frac{B a^{2}}{b^{4}}\right) + x \left(\frac{3 A a^{2}}{b^{4}} - \frac{4 B a^{3}}{b^{5}}\right) + \frac{x \left(A a^{3} b - B a^{4}\right)}{2 a b^{5} + 2 b^{6} x^{2}} - \frac{\sqrt{- \frac{a^{5}}{b^{11}}} \left(- 7 A b + 9 B a\right) \log{\left(- \frac{b^{5} \sqrt{- \frac{a^{5}}{b^{11}}} \left(- 7 A b + 9 B a\right)}{- 7 A a^{2} b + 9 B a^{3}} + x \right)}}{4} + \frac{\sqrt{- \frac{a^{5}}{b^{11}}} \left(- 7 A b + 9 B a\right) \log{\left(\frac{b^{5} \sqrt{- \frac{a^{5}}{b^{11}}} \left(- 7 A b + 9 B a\right)}{- 7 A a^{2} b + 9 B a^{3}} + x \right)}}{4}"," ",0,"B*x**7/(7*b**2) + x**5*(A/(5*b**2) - 2*B*a/(5*b**3)) + x**3*(-2*A*a/(3*b**3) + B*a**2/b**4) + x*(3*A*a**2/b**4 - 4*B*a**3/b**5) + x*(A*a**3*b - B*a**4)/(2*a*b**5 + 2*b**6*x**2) - sqrt(-a**5/b**11)*(-7*A*b + 9*B*a)*log(-b**5*sqrt(-a**5/b**11)*(-7*A*b + 9*B*a)/(-7*A*a**2*b + 9*B*a**3) + x)/4 + sqrt(-a**5/b**11)*(-7*A*b + 9*B*a)*log(b**5*sqrt(-a**5/b**11)*(-7*A*b + 9*B*a)/(-7*A*a**2*b + 9*B*a**3) + x)/4","A",0
73,1,104,0,0.722835," ","integrate(x**7*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x^{6}}{6 b^{2}} - \frac{a^{2} \left(- 3 A b + 4 B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{5}} + x^{4} \left(\frac{A}{4 b^{2}} - \frac{B a}{2 b^{3}}\right) + x^{2} \left(- \frac{A a}{b^{3}} + \frac{3 B a^{2}}{2 b^{4}}\right) + \frac{A a^{3} b - B a^{4}}{2 a b^{5} + 2 b^{6} x^{2}}"," ",0,"B*x**6/(6*b**2) - a**2*(-3*A*b + 4*B*a)*log(a + b*x**2)/(2*b**5) + x**4*(A/(4*b**2) - B*a/(2*b**3)) + x**2*(-A*a/b**3 + 3*B*a**2/(2*b**4)) + (A*a**3*b - B*a**4)/(2*a*b**5 + 2*b**6*x**2)","A",0
74,1,211,0,0.717713," ","integrate(x**6*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x^{5}}{5 b^{2}} + x^{3} \left(\frac{A}{3 b^{2}} - \frac{2 B a}{3 b^{3}}\right) + x \left(- \frac{2 A a}{b^{3}} + \frac{3 B a^{2}}{b^{4}}\right) + \frac{x \left(- A a^{2} b + B a^{3}\right)}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{\sqrt{- \frac{a^{3}}{b^{9}}} \left(- 5 A b + 7 B a\right) \log{\left(- \frac{b^{4} \sqrt{- \frac{a^{3}}{b^{9}}} \left(- 5 A b + 7 B a\right)}{- 5 A a b + 7 B a^{2}} + x \right)}}{4} - \frac{\sqrt{- \frac{a^{3}}{b^{9}}} \left(- 5 A b + 7 B a\right) \log{\left(\frac{b^{4} \sqrt{- \frac{a^{3}}{b^{9}}} \left(- 5 A b + 7 B a\right)}{- 5 A a b + 7 B a^{2}} + x \right)}}{4}"," ",0,"B*x**5/(5*b**2) + x**3*(A/(3*b**2) - 2*B*a/(3*b**3)) + x*(-2*A*a/b**3 + 3*B*a**2/b**4) + x*(-A*a**2*b + B*a**3)/(2*a*b**4 + 2*b**5*x**2) + sqrt(-a**3/b**9)*(-5*A*b + 7*B*a)*log(-b**4*sqrt(-a**3/b**9)*(-5*A*b + 7*B*a)/(-5*A*a*b + 7*B*a**2) + x)/4 - sqrt(-a**3/b**9)*(-5*A*b + 7*B*a)*log(b**4*sqrt(-a**3/b**9)*(-5*A*b + 7*B*a)/(-5*A*a*b + 7*B*a**2) + x)/4","B",0
75,1,78,0,0.660772," ","integrate(x**5*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x^{4}}{4 b^{2}} + \frac{a \left(- 2 A b + 3 B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{4}} + x^{2} \left(\frac{A}{2 b^{2}} - \frac{B a}{b^{3}}\right) + \frac{- A a^{2} b + B a^{3}}{2 a b^{4} + 2 b^{5} x^{2}}"," ",0,"B*x**4/(4*b**2) + a*(-2*A*b + 3*B*a)*log(a + b*x**2)/(2*b**4) + x**2*(A/(2*b**2) - B*a/b**3) + (-A*a**2*b + B*a**3)/(2*a*b**4 + 2*b**5*x**2)","A",0
76,1,129,0,0.640590," ","integrate(x**4*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x^{3}}{3 b^{2}} + x \left(\frac{A}{b^{2}} - \frac{2 B a}{b^{3}}\right) + \frac{x \left(A a b - B a^{2}\right)}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{\sqrt{- \frac{a}{b^{7}}} \left(- 3 A b + 5 B a\right) \log{\left(- b^{3} \sqrt{- \frac{a}{b^{7}}} + x \right)}}{4} + \frac{\sqrt{- \frac{a}{b^{7}}} \left(- 3 A b + 5 B a\right) \log{\left(b^{3} \sqrt{- \frac{a}{b^{7}}} + x \right)}}{4}"," ",0,"B*x**3/(3*b**2) + x*(A/b**2 - 2*B*a/b**3) + x*(A*a*b - B*a**2)/(2*a*b**3 + 2*b**4*x**2) - sqrt(-a/b**7)*(-3*A*b + 5*B*a)*log(-b**3*sqrt(-a/b**7) + x)/4 + sqrt(-a/b**7)*(-3*A*b + 5*B*a)*log(b**3*sqrt(-a/b**7) + x)/4","A",0
77,1,56,0,0.573669," ","integrate(x**3*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x^{2}}{2 b^{2}} + \frac{A a b - B a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{\left(- A b + 2 B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{3}}"," ",0,"B*x**2/(2*b**2) + (A*a*b - B*a**2)/(2*a*b**3 + 2*b**4*x**2) - (-A*b + 2*B*a)*log(a + b*x**2)/(2*b**3)","A",0
78,1,114,0,0.532975," ","integrate(x**2*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B x}{b^{2}} + \frac{x \left(- A b + B a\right)}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{\sqrt{- \frac{1}{a b^{5}}} \left(- A b + 3 B a\right) \log{\left(- a b^{2} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a b^{5}}} \left(- A b + 3 B a\right) \log{\left(a b^{2} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{4}"," ",0,"B*x/b**2 + x*(-A*b + B*a)/(2*a*b**2 + 2*b**3*x**2) + sqrt(-1/(a*b**5))*(-A*b + 3*B*a)*log(-a*b**2*sqrt(-1/(a*b**5)) + x)/4 - sqrt(-1/(a*b**5))*(-A*b + 3*B*a)*log(a*b**2*sqrt(-1/(a*b**5)) + x)/4","A",0
79,1,36,0,0.365745," ","integrate(x*(B*x**2+A)/(b*x**2+a)**2,x)","\frac{B \log{\left(a + b x^{2} \right)}}{2 b^{2}} + \frac{- A b + B a}{2 a b^{2} + 2 b^{3} x^{2}}"," ",0,"B*log(a + b*x**2)/(2*b**2) + (-A*b + B*a)/(2*a*b**2 + 2*b**3*x**2)","A",0
80,1,112,0,0.398108," ","integrate((B*x**2+A)/(b*x**2+a)**2,x)","\frac{x \left(A b - B a\right)}{2 a^{2} b + 2 a b^{2} x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(A b + B a\right) \log{\left(- a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(A b + B a\right) \log{\left(a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{4}"," ",0,"x*(A*b - B*a)/(2*a**2*b + 2*a*b**2*x**2) - sqrt(-1/(a**3*b**3))*(A*b + B*a)*log(-a**2*b*sqrt(-1/(a**3*b**3)) + x)/4 + sqrt(-1/(a**3*b**3))*(A*b + B*a)*log(a**2*b*sqrt(-1/(a**3*b**3)) + x)/4","B",0
81,1,46,0,0.415071," ","integrate((B*x**2+A)/x/(b*x**2+a)**2,x)","\frac{A \log{\left(x \right)}}{a^{2}} - \frac{A \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}} + \frac{A b - B a}{2 a^{2} b + 2 a b^{2} x^{2}}"," ",0,"A*log(x)/a**2 - A*log(a/b + x**2)/(2*a**2) + (A*b - B*a)/(2*a**2*b + 2*a*b**2*x**2)","A",0
82,1,114,0,0.491645," ","integrate((B*x**2+A)/x**2/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{5} b}} \left(- 3 A b + B a\right) \log{\left(- a^{3} \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{5} b}} \left(- 3 A b + B a\right) \log{\left(a^{3} \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{4} + \frac{- 2 A a + x^{2} \left(- 3 A b + B a\right)}{2 a^{3} x + 2 a^{2} b x^{3}}"," ",0,"-sqrt(-1/(a**5*b))*(-3*A*b + B*a)*log(-a**3*sqrt(-1/(a**5*b)) + x)/4 + sqrt(-1/(a**5*b))*(-3*A*b + B*a)*log(a**3*sqrt(-1/(a**5*b)) + x)/4 + (-2*A*a + x**2*(-3*A*b + B*a))/(2*a**3*x + 2*a**2*b*x**3)","A",0
83,1,70,0,0.883868," ","integrate((B*x**2+A)/x**3/(b*x**2+a)**2,x)","\frac{- A a + x^{2} \left(- 2 A b + B a\right)}{2 a^{3} x^{2} + 2 a^{2} b x^{4}} + \frac{\left(- 2 A b + B a\right) \log{\left(x \right)}}{a^{3}} - \frac{\left(- 2 A b + B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{3}}"," ",0,"(-A*a + x**2*(-2*A*b + B*a))/(2*a**3*x**2 + 2*a**2*b*x**4) + (-2*A*b + B*a)*log(x)/a**3 - (-2*A*b + B*a)*log(a/b + x**2)/(2*a**3)","A",0
84,1,184,0,0.593305," ","integrate((B*x**2+A)/x**4/(b*x**2+a)**2,x)","\frac{\sqrt{- \frac{b}{a^{7}}} \left(- 5 A b + 3 B a\right) \log{\left(- \frac{a^{4} \sqrt{- \frac{b}{a^{7}}} \left(- 5 A b + 3 B a\right)}{- 5 A b^{2} + 3 B a b} + x \right)}}{4} - \frac{\sqrt{- \frac{b}{a^{7}}} \left(- 5 A b + 3 B a\right) \log{\left(\frac{a^{4} \sqrt{- \frac{b}{a^{7}}} \left(- 5 A b + 3 B a\right)}{- 5 A b^{2} + 3 B a b} + x \right)}}{4} + \frac{- 2 A a^{2} + x^{4} \left(15 A b^{2} - 9 B a b\right) + x^{2} \left(10 A a b - 6 B a^{2}\right)}{6 a^{4} x^{3} + 6 a^{3} b x^{5}}"," ",0,"sqrt(-b/a**7)*(-5*A*b + 3*B*a)*log(-a**4*sqrt(-b/a**7)*(-5*A*b + 3*B*a)/(-5*A*b**2 + 3*B*a*b) + x)/4 - sqrt(-b/a**7)*(-5*A*b + 3*B*a)*log(a**4*sqrt(-b/a**7)*(-5*A*b + 3*B*a)/(-5*A*b**2 + 3*B*a*b) + x)/4 + (-2*A*a**2 + x**4*(15*A*b**2 - 9*B*a*b) + x**2*(10*A*a*b - 6*B*a**2))/(6*a**4*x**3 + 6*a**3*b*x**5)","B",0
85,1,100,0,1.020721," ","integrate((B*x**2+A)/x**5/(b*x**2+a)**2,x)","\frac{- A a^{2} + x^{4} \left(6 A b^{2} - 4 B a b\right) + x^{2} \left(3 A a b - 2 B a^{2}\right)}{4 a^{4} x^{4} + 4 a^{3} b x^{6}} - \frac{b \left(- 3 A b + 2 B a\right) \log{\left(x \right)}}{a^{4}} + \frac{b \left(- 3 A b + 2 B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(-A*a**2 + x**4*(6*A*b**2 - 4*B*a*b) + x**2*(3*A*a*b - 2*B*a**2))/(4*a**4*x**4 + 4*a**3*b*x**6) - b*(-3*A*b + 2*B*a)*log(x)/a**4 + b*(-3*A*b + 2*B*a)*log(a/b + x**2)/(2*a**4)","A",0
86,1,218,0,0.676298," ","integrate((B*x**2+A)/x**6/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{b^{3}}{a^{9}}} \left(- 7 A b + 5 B a\right) \log{\left(- \frac{a^{5} \sqrt{- \frac{b^{3}}{a^{9}}} \left(- 7 A b + 5 B a\right)}{- 7 A b^{3} + 5 B a b^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{b^{3}}{a^{9}}} \left(- 7 A b + 5 B a\right) \log{\left(\frac{a^{5} \sqrt{- \frac{b^{3}}{a^{9}}} \left(- 7 A b + 5 B a\right)}{- 7 A b^{3} + 5 B a b^{2}} + x \right)}}{4} + \frac{- 6 A a^{3} + x^{6} \left(- 105 A b^{3} + 75 B a b^{2}\right) + x^{4} \left(- 70 A a b^{2} + 50 B a^{2} b\right) + x^{2} \left(14 A a^{2} b - 10 B a^{3}\right)}{30 a^{5} x^{5} + 30 a^{4} b x^{7}}"," ",0,"-sqrt(-b**3/a**9)*(-7*A*b + 5*B*a)*log(-a**5*sqrt(-b**3/a**9)*(-7*A*b + 5*B*a)/(-7*A*b**3 + 5*B*a*b**2) + x)/4 + sqrt(-b**3/a**9)*(-7*A*b + 5*B*a)*log(a**5*sqrt(-b**3/a**9)*(-7*A*b + 5*B*a)/(-7*A*b**3 + 5*B*a*b**2) + x)/4 + (-6*A*a**3 + x**6*(-105*A*b**3 + 75*B*a*b**2) + x**4*(-70*A*a*b**2 + 50*B*a**2*b) + x**2*(14*A*a**2*b - 10*B*a**3))/(30*a**5*x**5 + 30*a**4*b*x**7)","B",0
87,1,129,0,1.098449," ","integrate((B*x**2+A)/x**7/(b*x**2+a)**2,x)","\frac{- 2 A a^{3} + x^{6} \left(- 24 A b^{3} + 18 B a b^{2}\right) + x^{4} \left(- 12 A a b^{2} + 9 B a^{2} b\right) + x^{2} \left(4 A a^{2} b - 3 B a^{3}\right)}{12 a^{5} x^{6} + 12 a^{4} b x^{8}} + \frac{b^{2} \left(- 4 A b + 3 B a\right) \log{\left(x \right)}}{a^{5}} - \frac{b^{2} \left(- 4 A b + 3 B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{5}}"," ",0,"(-2*A*a**3 + x**6*(-24*A*b**3 + 18*B*a*b**2) + x**4*(-12*A*a*b**2 + 9*B*a**2*b) + x**2*(4*A*a**2*b - 3*B*a**3))/(12*a**5*x**6 + 12*a**4*b*x**8) + b**2*(-4*A*b + 3*B*a)*log(x)/a**5 - b**2*(-4*A*b + 3*B*a)*log(a/b + x**2)/(2*a**5)","A",0
88,1,170,0,1.605045," ","integrate(x**11*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x^{8}}{8 b^{3}} + \frac{5 a^{3} \left(- 2 A b + 3 B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{7}} + x^{6} \left(\frac{A}{6 b^{3}} - \frac{B a}{2 b^{4}}\right) + x^{4} \left(- \frac{3 A a}{4 b^{4}} + \frac{3 B a^{2}}{2 b^{5}}\right) + x^{2} \left(\frac{3 A a^{2}}{b^{5}} - \frac{5 B a^{3}}{b^{6}}\right) + \frac{- 9 A a^{5} b + 11 B a^{6} + x^{2} \left(- 10 A a^{4} b^{2} + 12 B a^{5} b\right)}{4 a^{2} b^{7} + 8 a b^{8} x^{2} + 4 b^{9} x^{4}}"," ",0,"B*x**8/(8*b**3) + 5*a**3*(-2*A*b + 3*B*a)*log(a + b*x**2)/(2*b**7) + x**6*(A/(6*b**3) - B*a/(2*b**4)) + x**4*(-3*A*a/(4*b**4) + 3*B*a**2/(2*b**5)) + x**2*(3*A*a**2/b**5 - 5*B*a**3/b**6) + (-9*A*a**5*b + 11*B*a**6 + x**2*(-10*A*a**4*b**2 + 12*B*a**5*b))/(4*a**2*b**7 + 8*a*b**8*x**2 + 4*b**9*x**4)","A",0
89,1,143,0,1.511470," ","integrate(x**9*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x^{6}}{6 b^{3}} - \frac{a^{2} \left(- 3 A b + 5 B a\right) \log{\left(a + b x^{2} \right)}}{b^{6}} + x^{4} \left(\frac{A}{4 b^{3}} - \frac{3 B a}{4 b^{4}}\right) + x^{2} \left(- \frac{3 A a}{2 b^{4}} + \frac{3 B a^{2}}{b^{5}}\right) + \frac{7 A a^{4} b - 9 B a^{5} + x^{2} \left(8 A a^{3} b^{2} - 10 B a^{4} b\right)}{4 a^{2} b^{6} + 8 a b^{7} x^{2} + 4 b^{8} x^{4}}"," ",0,"B*x**6/(6*b**3) - a**2*(-3*A*b + 5*B*a)*log(a + b*x**2)/b**6 + x**4*(A/(4*b**3) - 3*B*a/(4*b**4)) + x**2*(-3*A*a/(2*b**4) + 3*B*a**2/b**5) + (7*A*a**4*b - 9*B*a**5 + x**2*(8*A*a**3*b**2 - 10*B*a**4*b))/(4*a**2*b**6 + 8*a*b**7*x**2 + 4*b**8*x**4)","A",0
90,1,119,0,1.413895," ","integrate(x**7*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x^{4}}{4 b^{3}} + \frac{3 a \left(- A b + 2 B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{5}} + x^{2} \left(\frac{A}{2 b^{3}} - \frac{3 B a}{2 b^{4}}\right) + \frac{- 5 A a^{3} b + 7 B a^{4} + x^{2} \left(- 6 A a^{2} b^{2} + 8 B a^{3} b\right)}{4 a^{2} b^{5} + 8 a b^{6} x^{2} + 4 b^{7} x^{4}}"," ",0,"B*x**4/(4*b**3) + 3*a*(-A*b + 2*B*a)*log(a + b*x**2)/(2*b**5) + x**2*(A/(2*b**3) - 3*B*a/(2*b**4)) + (-5*A*a**3*b + 7*B*a**4 + x**2*(-6*A*a**2*b**2 + 8*B*a**3*b))/(4*a**2*b**5 + 8*a*b**6*x**2 + 4*b**7*x**4)","A",0
91,1,94,0,1.249738," ","integrate(x**5*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x^{2}}{2 b^{3}} + \frac{3 A a^{2} b - 5 B a^{3} + x^{2} \left(4 A a b^{2} - 6 B a^{2} b\right)}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{\left(- A b + 3 B a\right) \log{\left(a + b x^{2} \right)}}{2 b^{4}}"," ",0,"B*x**2/(2*b**3) + (3*A*a**2*b - 5*B*a**3 + x**2*(4*A*a*b**2 - 6*B*a**2*b))/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - (-A*b + 3*B*a)*log(a + b*x**2)/(2*b**4)","A",0
92,1,70,0,0.906852," ","integrate(x**3*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B \log{\left(a + b x^{2} \right)}}{2 b^{3}} + \frac{- A a b + 3 B a^{2} + x^{2} \left(- 2 A b^{2} + 4 B a b\right)}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}}"," ",0,"B*log(a + b*x**2)/(2*b**3) + (-A*a*b + 3*B*a**2 + x**2*(-2*A*b**2 + 4*B*a*b))/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4)","A",0
93,1,42,0,0.520612," ","integrate(x*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{- A b - B a - 2 B b x^{2}}{4 a^{2} b^{2} + 8 a b^{3} x^{2} + 4 b^{4} x^{4}}"," ",0,"(-A*b - B*a - 2*B*b*x**2)/(4*a**2*b**2 + 8*a*b**3*x**2 + 4*b**4*x**4)","A",0
94,1,75,0,0.579799," ","integrate((B*x**2+A)/x/(b*x**2+a)**3,x)","\frac{A \log{\left(x \right)}}{a^{3}} - \frac{A \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{3}} + \frac{3 A a b + 2 A b^{2} x^{2} - B a^{2}}{4 a^{4} b + 8 a^{3} b^{2} x^{2} + 4 a^{2} b^{3} x^{4}}"," ",0,"A*log(x)/a**3 - A*log(a/b + x**2)/(2*a**3) + (3*A*a*b + 2*A*b**2*x**2 - B*a**2)/(4*a**4*b + 8*a**3*b**2*x**2 + 4*a**2*b**3*x**4)","A",0
95,1,107,0,1.051930," ","integrate((B*x**2+A)/x**3/(b*x**2+a)**3,x)","\frac{- 2 A a^{2} + x^{4} \left(- 6 A b^{2} + 2 B a b\right) + x^{2} \left(- 9 A a b + 3 B a^{2}\right)}{4 a^{5} x^{2} + 8 a^{4} b x^{4} + 4 a^{3} b^{2} x^{6}} + \frac{\left(- 3 A b + B a\right) \log{\left(x \right)}}{a^{4}} - \frac{\left(- 3 A b + B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{4}}"," ",0,"(-2*A*a**2 + x**4*(-6*A*b**2 + 2*B*a*b) + x**2*(-9*A*a*b + 3*B*a**2))/(4*a**5*x**2 + 8*a**4*b*x**4 + 4*a**3*b**2*x**6) + (-3*A*b + B*a)*log(x)/a**4 - (-3*A*b + B*a)*log(a/b + x**2)/(2*a**4)","A",0
96,1,136,0,1.217435," ","integrate((B*x**2+A)/x**5/(b*x**2+a)**3,x)","\frac{- A a^{3} + x^{6} \left(12 A b^{3} - 6 B a b^{2}\right) + x^{4} \left(18 A a b^{2} - 9 B a^{2} b\right) + x^{2} \left(4 A a^{2} b - 2 B a^{3}\right)}{4 a^{6} x^{4} + 8 a^{5} b x^{6} + 4 a^{4} b^{2} x^{8}} - \frac{3 b \left(- 2 A b + B a\right) \log{\left(x \right)}}{a^{5}} + \frac{3 b \left(- 2 A b + B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{5}}"," ",0,"(-A*a**3 + x**6*(12*A*b**3 - 6*B*a*b**2) + x**4*(18*A*a*b**2 - 9*B*a**2*b) + x**2*(4*A*a**2*b - 2*B*a**3))/(4*a**6*x**4 + 8*a**5*b*x**6 + 4*a**4*b**2*x**8) - 3*b*(-2*A*b + B*a)*log(x)/a**5 + 3*b*(-2*A*b + B*a)*log(a/b + x**2)/(2*a**5)","A",0
97,1,165,0,1.264076," ","integrate((B*x**2+A)/x**7/(b*x**2+a)**3,x)","\frac{- 2 A a^{4} + x^{8} \left(- 60 A b^{4} + 36 B a b^{3}\right) + x^{6} \left(- 90 A a b^{3} + 54 B a^{2} b^{2}\right) + x^{4} \left(- 20 A a^{2} b^{2} + 12 B a^{3} b\right) + x^{2} \left(5 A a^{3} b - 3 B a^{4}\right)}{12 a^{7} x^{6} + 24 a^{6} b x^{8} + 12 a^{5} b^{2} x^{10}} + \frac{2 b^{2} \left(- 5 A b + 3 B a\right) \log{\left(x \right)}}{a^{6}} - \frac{b^{2} \left(- 5 A b + 3 B a\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{6}}"," ",0,"(-2*A*a**4 + x**8*(-60*A*b**4 + 36*B*a*b**3) + x**6*(-90*A*a*b**3 + 54*B*a**2*b**2) + x**4*(-20*A*a**2*b**2 + 12*B*a**3*b) + x**2*(5*A*a**3*b - 3*B*a**4))/(12*a**7*x**6 + 24*a**6*b*x**8 + 12*a**5*b**2*x**10) + 2*b**2*(-5*A*b + 3*B*a)*log(x)/a**6 - b**2*(-5*A*b + 3*B*a)*log(a/b + x**2)/a**6","A",0
98,1,280,0,1.441047," ","integrate(x**10*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x^{7}}{7 b^{3}} + x^{5} \left(\frac{A}{5 b^{3}} - \frac{3 B a}{5 b^{4}}\right) + x^{3} \left(- \frac{A a}{b^{4}} + \frac{2 B a^{2}}{b^{5}}\right) + x \left(\frac{6 A a^{2}}{b^{5}} - \frac{10 B a^{3}}{b^{6}}\right) - \frac{9 \sqrt{- \frac{a^{5}}{b^{13}}} \left(- 7 A b + 11 B a\right) \log{\left(- \frac{9 b^{6} \sqrt{- \frac{a^{5}}{b^{13}}} \left(- 7 A b + 11 B a\right)}{- 63 A a^{2} b + 99 B a^{3}} + x \right)}}{16} + \frac{9 \sqrt{- \frac{a^{5}}{b^{13}}} \left(- 7 A b + 11 B a\right) \log{\left(\frac{9 b^{6} \sqrt{- \frac{a^{5}}{b^{13}}} \left(- 7 A b + 11 B a\right)}{- 63 A a^{2} b + 99 B a^{3}} + x \right)}}{16} + \frac{x^{3} \left(17 A a^{3} b^{2} - 21 B a^{4} b\right) + x \left(15 A a^{4} b - 19 B a^{5}\right)}{8 a^{2} b^{6} + 16 a b^{7} x^{2} + 8 b^{8} x^{4}}"," ",0,"B*x**7/(7*b**3) + x**5*(A/(5*b**3) - 3*B*a/(5*b**4)) + x**3*(-A*a/b**4 + 2*B*a**2/b**5) + x*(6*A*a**2/b**5 - 10*B*a**3/b**6) - 9*sqrt(-a**5/b**13)*(-7*A*b + 11*B*a)*log(-9*b**6*sqrt(-a**5/b**13)*(-7*A*b + 11*B*a)/(-63*A*a**2*b + 99*B*a**3) + x)/16 + 9*sqrt(-a**5/b**13)*(-7*A*b + 11*B*a)*log(9*b**6*sqrt(-a**5/b**13)*(-7*A*b + 11*B*a)/(-63*A*a**2*b + 99*B*a**3) + x)/16 + (x**3*(17*A*a**3*b**2 - 21*B*a**4*b) + x*(15*A*a**4*b - 19*B*a**5))/(8*a**2*b**6 + 16*a*b**7*x**2 + 8*b**8*x**4)","A",0
99,1,252,0,1.363567," ","integrate(x**8*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x^{5}}{5 b^{3}} + x^{3} \left(\frac{A}{3 b^{3}} - \frac{B a}{b^{4}}\right) + x \left(- \frac{3 A a}{b^{4}} + \frac{6 B a^{2}}{b^{5}}\right) + \frac{7 \sqrt{- \frac{a^{3}}{b^{11}}} \left(- 5 A b + 9 B a\right) \log{\left(- \frac{7 b^{5} \sqrt{- \frac{a^{3}}{b^{11}}} \left(- 5 A b + 9 B a\right)}{- 35 A a b + 63 B a^{2}} + x \right)}}{16} - \frac{7 \sqrt{- \frac{a^{3}}{b^{11}}} \left(- 5 A b + 9 B a\right) \log{\left(\frac{7 b^{5} \sqrt{- \frac{a^{3}}{b^{11}}} \left(- 5 A b + 9 B a\right)}{- 35 A a b + 63 B a^{2}} + x \right)}}{16} + \frac{x^{3} \left(- 13 A a^{2} b^{2} + 17 B a^{3} b\right) + x \left(- 11 A a^{3} b + 15 B a^{4}\right)}{8 a^{2} b^{5} + 16 a b^{6} x^{2} + 8 b^{7} x^{4}}"," ",0,"B*x**5/(5*b**3) + x**3*(A/(3*b**3) - B*a/b**4) + x*(-3*A*a/b**4 + 6*B*a**2/b**5) + 7*sqrt(-a**3/b**11)*(-5*A*b + 9*B*a)*log(-7*b**5*sqrt(-a**3/b**11)*(-5*A*b + 9*B*a)/(-35*A*a*b + 63*B*a**2) + x)/16 - 7*sqrt(-a**3/b**11)*(-5*A*b + 9*B*a)*log(7*b**5*sqrt(-a**3/b**11)*(-5*A*b + 9*B*a)/(-35*A*a*b + 63*B*a**2) + x)/16 + (x**3*(-13*A*a**2*b**2 + 17*B*a**3*b) + x*(-11*A*a**3*b + 15*B*a**4))/(8*a**2*b**5 + 16*a*b**6*x**2 + 8*b**7*x**4)","A",0
100,1,214,0,1.252121," ","integrate(x**6*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x^{3}}{3 b^{3}} + x \left(\frac{A}{b^{3}} - \frac{3 B a}{b^{4}}\right) - \frac{5 \sqrt{- \frac{a}{b^{9}}} \left(- 3 A b + 7 B a\right) \log{\left(- \frac{5 b^{4} \sqrt{- \frac{a}{b^{9}}} \left(- 3 A b + 7 B a\right)}{- 15 A b + 35 B a} + x \right)}}{16} + \frac{5 \sqrt{- \frac{a}{b^{9}}} \left(- 3 A b + 7 B a\right) \log{\left(\frac{5 b^{4} \sqrt{- \frac{a}{b^{9}}} \left(- 3 A b + 7 B a\right)}{- 15 A b + 35 B a} + x \right)}}{16} + \frac{x^{3} \left(9 A a b^{2} - 13 B a^{2} b\right) + x \left(7 A a^{2} b - 11 B a^{3}\right)}{8 a^{2} b^{4} + 16 a b^{5} x^{2} + 8 b^{6} x^{4}}"," ",0,"B*x**3/(3*b**3) + x*(A/b**3 - 3*B*a/b**4) - 5*sqrt(-a/b**9)*(-3*A*b + 7*B*a)*log(-5*b**4*sqrt(-a/b**9)*(-3*A*b + 7*B*a)/(-15*A*b + 35*B*a) + x)/16 + 5*sqrt(-a/b**9)*(-3*A*b + 7*B*a)*log(5*b**4*sqrt(-a/b**9)*(-3*A*b + 7*B*a)/(-15*A*b + 35*B*a) + x)/16 + (x**3*(9*A*a*b**2 - 13*B*a**2*b) + x*(7*A*a**2*b - 11*B*a**3))/(8*a**2*b**4 + 16*a*b**5*x**2 + 8*b**6*x**4)","A",0
101,1,194,0,1.064606," ","integrate(x**4*(B*x**2+A)/(b*x**2+a)**3,x)","\frac{B x}{b^{3}} + \frac{3 \sqrt{- \frac{1}{a b^{7}}} \left(- A b + 5 B a\right) \log{\left(- \frac{3 a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(- A b + 5 B a\right)}{- 3 A b + 15 B a} + x \right)}}{16} - \frac{3 \sqrt{- \frac{1}{a b^{7}}} \left(- A b + 5 B a\right) \log{\left(\frac{3 a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(- A b + 5 B a\right)}{- 3 A b + 15 B a} + x \right)}}{16} + \frac{x^{3} \left(- 5 A b^{2} + 9 B a b\right) + x \left(- 3 A a b + 7 B a^{2}\right)}{8 a^{2} b^{3} + 16 a b^{4} x^{2} + 8 b^{5} x^{4}}"," ",0,"B*x/b**3 + 3*sqrt(-1/(a*b**7))*(-A*b + 5*B*a)*log(-3*a*b**3*sqrt(-1/(a*b**7))*(-A*b + 5*B*a)/(-3*A*b + 15*B*a) + x)/16 - 3*sqrt(-1/(a*b**7))*(-A*b + 5*B*a)*log(3*a*b**3*sqrt(-1/(a*b**7))*(-A*b + 5*B*a)/(-3*A*b + 15*B*a) + x)/16 + (x**3*(-5*A*b**2 + 9*B*a*b) + x*(-3*A*a*b + 7*B*a**2))/(8*a**2*b**3 + 16*a*b**4*x**2 + 8*b**5*x**4)","B",0
102,1,155,0,0.732630," ","integrate(x**2*(B*x**2+A)/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(A b + 3 B a\right) \log{\left(- a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(A b + 3 B a\right) \log{\left(a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} + x \right)}}{16} + \frac{x^{3} \left(A b^{2} - 5 B a b\right) + x \left(- A a b - 3 B a^{2}\right)}{8 a^{3} b^{2} + 16 a^{2} b^{3} x^{2} + 8 a b^{4} x^{4}}"," ",0,"-sqrt(-1/(a**3*b**5))*(A*b + 3*B*a)*log(-a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/16 + sqrt(-1/(a**3*b**5))*(A*b + 3*B*a)*log(a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/16 + (x**3*(A*b**2 - 5*B*a*b) + x*(-A*a*b - 3*B*a**2))/(8*a**3*b**2 + 16*a**2*b**3*x**2 + 8*a*b**4*x**4)","A",0
103,1,150,0,0.545006," ","integrate((B*x**2+A)/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(3 A b + B a\right) \log{\left(- a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(3 A b + B a\right) \log{\left(a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{16} + \frac{x^{3} \left(3 A b^{2} + B a b\right) + x \left(5 A a b - B a^{2}\right)}{8 a^{4} b + 16 a^{3} b^{2} x^{2} + 8 a^{2} b^{3} x^{4}}"," ",0,"-sqrt(-1/(a**5*b**3))*(3*A*b + B*a)*log(-a**3*b*sqrt(-1/(a**5*b**3)) + x)/16 + sqrt(-1/(a**5*b**3))*(3*A*b + B*a)*log(a**3*b*sqrt(-1/(a**5*b**3)) + x)/16 + (x**3*(3*A*b**2 + B*a*b) + x*(5*A*a*b - B*a**2))/(8*a**4*b + 16*a**3*b**2*x**2 + 8*a**2*b**3*x**4)","A",0
104,1,194,0,0.673013," ","integrate((B*x**2+A)/x**2/(b*x**2+a)**3,x)","- \frac{3 \sqrt{- \frac{1}{a^{7} b}} \left(- 5 A b + B a\right) \log{\left(- \frac{3 a^{4} \sqrt{- \frac{1}{a^{7} b}} \left(- 5 A b + B a\right)}{- 15 A b + 3 B a} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{a^{7} b}} \left(- 5 A b + B a\right) \log{\left(\frac{3 a^{4} \sqrt{- \frac{1}{a^{7} b}} \left(- 5 A b + B a\right)}{- 15 A b + 3 B a} + x \right)}}{16} + \frac{- 8 A a^{2} + x^{4} \left(- 15 A b^{2} + 3 B a b\right) + x^{2} \left(- 25 A a b + 5 B a^{2}\right)}{8 a^{5} x + 16 a^{4} b x^{3} + 8 a^{3} b^{2} x^{5}}"," ",0,"-3*sqrt(-1/(a**7*b))*(-5*A*b + B*a)*log(-3*a**4*sqrt(-1/(a**7*b))*(-5*A*b + B*a)/(-15*A*b + 3*B*a) + x)/16 + 3*sqrt(-1/(a**7*b))*(-5*A*b + B*a)*log(3*a**4*sqrt(-1/(a**7*b))*(-5*A*b + B*a)/(-15*A*b + 3*B*a) + x)/16 + (-8*A*a**2 + x**4*(-15*A*b**2 + 3*B*a*b) + x**2*(-25*A*a*b + 5*B*a**2))/(8*a**5*x + 16*a**4*b*x**3 + 8*a**3*b**2*x**5)","B",0
105,1,226,0,0.774247," ","integrate((B*x**2+A)/x**4/(b*x**2+a)**3,x)","\frac{5 \sqrt{- \frac{b}{a^{9}}} \left(- 7 A b + 3 B a\right) \log{\left(- \frac{5 a^{5} \sqrt{- \frac{b}{a^{9}}} \left(- 7 A b + 3 B a\right)}{- 35 A b^{2} + 15 B a b} + x \right)}}{16} - \frac{5 \sqrt{- \frac{b}{a^{9}}} \left(- 7 A b + 3 B a\right) \log{\left(\frac{5 a^{5} \sqrt{- \frac{b}{a^{9}}} \left(- 7 A b + 3 B a\right)}{- 35 A b^{2} + 15 B a b} + x \right)}}{16} + \frac{- 8 A a^{3} + x^{6} \left(105 A b^{3} - 45 B a b^{2}\right) + x^{4} \left(175 A a b^{2} - 75 B a^{2} b\right) + x^{2} \left(56 A a^{2} b - 24 B a^{3}\right)}{24 a^{6} x^{3} + 48 a^{5} b x^{5} + 24 a^{4} b^{2} x^{7}}"," ",0,"5*sqrt(-b/a**9)*(-7*A*b + 3*B*a)*log(-5*a**5*sqrt(-b/a**9)*(-7*A*b + 3*B*a)/(-35*A*b**2 + 15*B*a*b) + x)/16 - 5*sqrt(-b/a**9)*(-7*A*b + 3*B*a)*log(5*a**5*sqrt(-b/a**9)*(-7*A*b + 3*B*a)/(-35*A*b**2 + 15*B*a*b) + x)/16 + (-8*A*a**3 + x**6*(105*A*b**3 - 45*B*a*b**2) + x**4*(175*A*a*b**2 - 75*B*a**2*b) + x**2*(56*A*a**2*b - 24*B*a**3))/(24*a**6*x**3 + 48*a**5*b*x**5 + 24*a**4*b**2*x**7)","B",0
106,1,260,0,0.868153," ","integrate((B*x**2+A)/x**6/(b*x**2+a)**3,x)","- \frac{7 \sqrt{- \frac{b^{3}}{a^{11}}} \left(- 9 A b + 5 B a\right) \log{\left(- \frac{7 a^{6} \sqrt{- \frac{b^{3}}{a^{11}}} \left(- 9 A b + 5 B a\right)}{- 63 A b^{3} + 35 B a b^{2}} + x \right)}}{16} + \frac{7 \sqrt{- \frac{b^{3}}{a^{11}}} \left(- 9 A b + 5 B a\right) \log{\left(\frac{7 a^{6} \sqrt{- \frac{b^{3}}{a^{11}}} \left(- 9 A b + 5 B a\right)}{- 63 A b^{3} + 35 B a b^{2}} + x \right)}}{16} + \frac{- 24 A a^{4} + x^{8} \left(- 945 A b^{4} + 525 B a b^{3}\right) + x^{6} \left(- 1575 A a b^{3} + 875 B a^{2} b^{2}\right) + x^{4} \left(- 504 A a^{2} b^{2} + 280 B a^{3} b\right) + x^{2} \left(72 A a^{3} b - 40 B a^{4}\right)}{120 a^{7} x^{5} + 240 a^{6} b x^{7} + 120 a^{5} b^{2} x^{9}}"," ",0,"-7*sqrt(-b**3/a**11)*(-9*A*b + 5*B*a)*log(-7*a**6*sqrt(-b**3/a**11)*(-9*A*b + 5*B*a)/(-63*A*b**3 + 35*B*a*b**2) + x)/16 + 7*sqrt(-b**3/a**11)*(-9*A*b + 5*B*a)*log(7*a**6*sqrt(-b**3/a**11)*(-9*A*b + 5*B*a)/(-63*A*b**3 + 35*B*a*b**2) + x)/16 + (-24*A*a**4 + x**8*(-945*A*b**4 + 525*B*a*b**3) + x**6*(-1575*A*a*b**3 + 875*B*a**2*b**2) + x**4*(-504*A*a**2*b**2 + 280*B*a**3*b) + x**2*(72*A*a**3*b - 40*B*a**4))/(120*a**7*x**5 + 240*a**6*b*x**7 + 120*a**5*b**2*x**9)","A",0
107,1,26,0,0.156756," ","integrate((b*x**2+a)/(x**2+1),x)","b x - \frac{i \left(a - b\right) \log{\left(x - i \right)}}{2} + \frac{i \left(a - b\right) \log{\left(x + i \right)}}{2}"," ",0,"b*x - I*(a - b)*log(x - I)/2 + I*(a - b)*log(x + I)/2","C",0
108,1,22,0,0.165765," ","integrate((b*x**2+a)/(-x**2+1),x)","- b x - \frac{\left(a + b\right) \log{\left(x - 1 \right)}}{2} + \frac{\left(a + b\right) \log{\left(x + 1 \right)}}{2}"," ",0,"-b*x - (a + b)*log(x - 1)/2 + (a + b)*log(x + 1)/2","B",0
109,1,7,0,0.085684," ","integrate((x**2+1)/(x**2-1)**2,x)","- \frac{x}{x^{2} - 1}"," ",0,"-x/(x**2 - 1)","A",0
110,1,5,0,0.087208," ","integrate((-x**2+1)/(x**2+1)**2,x)","\frac{x}{x^{2} + 1}"," ",0,"x/(x**2 + 1)","A",0
111,1,14,0,0.108418," ","integrate((2*x**2+3)/(x**2+1)**2,x)","\frac{x}{2 x^{2} + 2} + \frac{5 \operatorname{atan}{\left(x \right)}}{2}"," ",0,"x/(2*x**2 + 2) + 5*atan(x)/2","A",0
112,1,15,0,0.105054," ","integrate((x**2-2)/(x**2+1)**2,x)","- \frac{3 x}{2 x^{2} + 2} - \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"-3*x/(2*x**2 + 2) - atan(x)/2","A",0
113,1,10,0,0.102252," ","integrate((x**2+3)/(x**2+1)**2,x)","\frac{x}{x^{2} + 1} + 2 \operatorname{atan}{\left(x \right)}"," ",0,"x/(x**2 + 1) + 2*atan(x)","A",0
114,1,8,0,0.183573," ","integrate((b*x**2+a)/(b*x**2-a)**2,x)","- \frac{x}{- a + b x^{2}}"," ",0,"-x/(-a + b*x**2)","A",0
115,1,8,0,0.181030," ","integrate((b*x**2+a)/(-b*x**2+a)**2,x)","- \frac{x}{- a + b x^{2}}"," ",0,"-x/(-a + b*x**2)","A",0
116,1,75,0,0.291240," ","integrate((B*x**2+A)/(-b*x**2+a),x)","- \frac{B x}{b} - \frac{\sqrt{\frac{1}{a b^{3}}} \left(A b + B a\right) \log{\left(- a b \sqrt{\frac{1}{a b^{3}}} + x \right)}}{2} + \frac{\sqrt{\frac{1}{a b^{3}}} \left(A b + B a\right) \log{\left(a b \sqrt{\frac{1}{a b^{3}}} + x \right)}}{2}"," ",0,"-B*x/b - sqrt(1/(a*b**3))*(A*b + B*a)*log(-a*b*sqrt(1/(a*b**3)) + x)/2 + sqrt(1/(a*b**3))*(A*b + B*a)*log(a*b*sqrt(1/(a*b**3)) + x)/2","B",0
117,1,27,0,0.132910," ","integrate((x**2+1)/(x**2+16)**3,x)","\frac{19 x^{3} - 176 x}{2048 x^{4} + 65536 x^{2} + 524288} + \frac{19 \operatorname{atan}{\left(\frac{x}{4} \right)}}{8192}"," ",0,"(19*x**3 - 176*x)/(2048*x**4 + 65536*x**2 + 524288) + 19*atan(x/4)/8192","A",0
118,1,17,0,0.127810," ","integrate((2*x**2+1)/x**5/(x**2+1)**3,x)","- \frac{1}{4 x^{8} + 8 x^{6} + 4 x^{4}}"," ",0,"-1/(4*x**8 + 8*x**6 + 4*x**4)","A",0
119,1,0,0,0.060086," ","integrate((-x**2+1)**2/(x**2-1)**2,x)","x"," ",0,"x","A",0
120,1,5,0,0.072927," ","integrate(x**3*(b*c*x**2+a*c)/(b*x**2+a),x)","\frac{c x^{4}}{4}"," ",0,"c*x**4/4","A",0
121,1,5,0,0.071490," ","integrate(x**2*(b*c*x**2+a*c)/(b*x**2+a),x)","\frac{c x^{3}}{3}"," ",0,"c*x**3/3","A",0
122,1,5,0,0.071101," ","integrate(x*(b*c*x**2+a*c)/(b*x**2+a),x)","\frac{c x^{2}}{2}"," ",0,"c*x**2/2","A",0
123,1,2,0,0.066142," ","integrate((b*c*x**2+a*c)/(b*x**2+a),x)","c x"," ",0,"c*x","A",0
124,1,3,0,0.073213," ","integrate((b*c*x**2+a*c)/x/(b*x**2+a),x)","c \log{\left(x \right)}"," ",0,"c*log(x)","A",0
125,1,3,0,0.072397," ","integrate((b*c*x**2+a*c)/x**2/(b*x**2+a),x)","- \frac{c}{x}"," ",0,"-c/x","A",0
126,1,7,0,0.074564," ","integrate((b*c*x**2+a*c)/x**3/(b*x**2+a),x)","- \frac{c}{2 x^{2}}"," ",0,"-c/(2*x**2)","A",0
127,1,22,0,0.150417," ","integrate(x**3*(b*c*x**2+a*c)/(b*x**2+a)**2,x)","c \left(- \frac{a \log{\left(a + b x^{2} \right)}}{2 b^{2}} + \frac{x^{2}}{2 b}\right)"," ",0,"c*(-a*log(a + b*x**2)/(2*b**2) + x**2/(2*b))","A",0
128,1,58,0,0.162344," ","integrate(x**2*(b*c*x**2+a*c)/(b*x**2+a)**2,x)","c \left(\frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(- b \sqrt{- \frac{a}{b^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{a}{b^{3}}} \log{\left(b \sqrt{- \frac{a}{b^{3}}} + x \right)}}{2} + \frac{x}{b}\right)"," ",0,"c*(sqrt(-a/b**3)*log(-b*sqrt(-a/b**3) + x)/2 - sqrt(-a/b**3)*log(b*sqrt(-a/b**3) + x)/2 + x/b)","A",0
129,1,12,0,0.123563," ","integrate(x*(b*c*x**2+a*c)/(b*x**2+a)**2,x)","\frac{c \log{\left(a + b x^{2} \right)}}{2 b}"," ",0,"c*log(a + b*x**2)/(2*b)","A",0
130,1,54,0,0.147884," ","integrate((b*c*x**2+a*c)/(b*x**2+a)**2,x)","c \left(- \frac{\sqrt{- \frac{1}{a b}} \log{\left(- a \sqrt{- \frac{1}{a b}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a b}} \log{\left(a \sqrt{- \frac{1}{a b}} + x \right)}}{2}\right)"," ",0,"c*(-sqrt(-1/(a*b))*log(-a*sqrt(-1/(a*b)) + x)/2 + sqrt(-1/(a*b))*log(a*sqrt(-1/(a*b)) + x)/2)","B",0
131,1,17,0,0.216743," ","integrate((b*c*x**2+a*c)/x/(b*x**2+a)**2,x)","c \left(\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a}\right)"," ",0,"c*(log(x)/a - log(a/b + x**2)/(2*a))","A",0
132,1,66,0,0.192595," ","integrate((b*c*x**2+a*c)/x**2/(b*x**2+a)**2,x)","c \left(\frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(- \frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{a^{3}}} \log{\left(\frac{a^{2} \sqrt{- \frac{b}{a^{3}}}}{b} + x \right)}}{2} - \frac{1}{a x}\right)"," ",0,"c*(sqrt(-b/a**3)*log(-a**2*sqrt(-b/a**3)/b + x)/2 - sqrt(-b/a**3)*log(a**2*sqrt(-b/a**3)/b + x)/2 - 1/(a*x))","B",0
133,1,32,0,0.280091," ","integrate((b*c*x**2+a*c)/x**3/(b*x**2+a)**2,x)","c \left(- \frac{1}{2 a x^{2}} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}\right)"," ",0,"c*(-1/(2*a*x**2) - b*log(x)/a**2 + b*log(a/b + x**2)/(2*a**2))","A",0
134,1,31,0,0.205461," ","integrate(x**3*(b*c*x**2+a*c)/(b*x**2+a)**3,x)","c \left(\frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{\log{\left(a + b x^{2} \right)}}{2 b^{2}}\right)"," ",0,"c*(a/(2*a*b**2 + 2*b**3*x**2) + log(a + b*x**2)/(2*b**2))","A",0
135,1,80,0,0.221871," ","integrate(x**2*(b*c*x**2+a*c)/(b*x**2+a)**3,x)","c \left(- \frac{x}{2 a b + 2 b^{2} x^{2}} - \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(- a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a b^{3}}} \log{\left(a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{4}\right)"," ",0,"c*(-x/(2*a*b + 2*b**2*x**2) - sqrt(-1/(a*b**3))*log(-a*b*sqrt(-1/(a*b**3)) + x)/4 + sqrt(-1/(a*b**3))*log(a*b*sqrt(-1/(a*b**3)) + x)/4)","B",0
136,1,15,0,0.174985," ","integrate(x*(b*c*x**2+a*c)/(b*x**2+a)**3,x)","- \frac{c}{2 a b + 2 b^{2} x^{2}}"," ",0,"-c/(2*a*b + 2*b**2*x**2)","A",0
137,1,80,0,0.228431," ","integrate((b*c*x**2+a*c)/(b*x**2+a)**3,x)","c \left(\frac{x}{2 a^{2} + 2 a b x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b}} \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{4}\right)"," ",0,"c*(x/(2*a**2 + 2*a*b*x**2) - sqrt(-1/(a**3*b))*log(-a**2*sqrt(-1/(a**3*b)) + x)/4 + sqrt(-1/(a**3*b))*log(a**2*sqrt(-1/(a**3*b)) + x)/4)","B",0
138,1,36,0,0.306278," ","integrate((b*c*x**2+a*c)/x/(b*x**2+a)**3,x)","c \left(\frac{1}{2 a^{2} + 2 a b x^{2}} + \frac{\log{\left(x \right)}}{a^{2}} - \frac{\log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}\right)"," ",0,"c*(1/(2*a**2 + 2*a*b*x**2) + log(x)/a**2 - log(a/b + x**2)/(2*a**2))","A",0
139,1,94,0,0.309593," ","integrate((b*c*x**2+a*c)/x**2/(b*x**2+a)**3,x)","c \left(\frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(- \frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x \right)}}{4} - \frac{3 \sqrt{- \frac{b}{a^{5}}} \log{\left(\frac{a^{3} \sqrt{- \frac{b}{a^{5}}}}{b} + x \right)}}{4} + \frac{- 2 a - 3 b x^{2}}{2 a^{3} x + 2 a^{2} b x^{3}}\right)"," ",0,"c*(3*sqrt(-b/a**5)*log(-a**3*sqrt(-b/a**5)/b + x)/4 - 3*sqrt(-b/a**5)*log(a**3*sqrt(-b/a**5)/b + x)/4 + (-2*a - 3*b*x**2)/(2*a**3*x + 2*a**2*b*x**3))","A",0
140,1,53,0,0.378396," ","integrate((b*c*x**2+a*c)/x**3/(b*x**2+a)**3,x)","c \left(\frac{- a - 2 b x^{2}}{2 a^{3} x^{2} + 2 a^{2} b x^{4}} - \frac{2 b \log{\left(x \right)}}{a^{3}} + \frac{b \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{3}}\right)"," ",0,"c*((-a - 2*b*x**2)/(2*a**3*x**2 + 2*a**2*b*x**4) - 2*b*log(x)/a**3 + b*log(a/b + x**2)/a**3)","A",0
141,1,56,0,0.074387," ","integrate(x**4*(b*x**2+a)**2*(d*x**2+c),x)","\frac{a^{2} c x^{5}}{5} + \frac{b^{2} d x^{11}}{11} + x^{9} \left(\frac{2 a b d}{9} + \frac{b^{2} c}{9}\right) + x^{7} \left(\frac{a^{2} d}{7} + \frac{2 a b c}{7}\right)"," ",0,"a**2*c*x**5/5 + b**2*d*x**11/11 + x**9*(2*a*b*d/9 + b**2*c/9) + x**7*(a**2*d/7 + 2*a*b*c/7)","A",0
142,1,53,0,0.074556," ","integrate(x**3*(b*x**2+a)**2*(d*x**2+c),x)","\frac{a^{2} c x^{4}}{4} + \frac{b^{2} d x^{10}}{10} + x^{8} \left(\frac{a b d}{4} + \frac{b^{2} c}{8}\right) + x^{6} \left(\frac{a^{2} d}{6} + \frac{a b c}{3}\right)"," ",0,"a**2*c*x**4/4 + b**2*d*x**10/10 + x**8*(a*b*d/4 + b**2*c/8) + x**6*(a**2*d/6 + a*b*c/3)","A",0
143,1,56,0,0.073429," ","integrate(x**2*(b*x**2+a)**2*(d*x**2+c),x)","\frac{a^{2} c x^{3}}{3} + \frac{b^{2} d x^{9}}{9} + x^{7} \left(\frac{2 a b d}{7} + \frac{b^{2} c}{7}\right) + x^{5} \left(\frac{a^{2} d}{5} + \frac{2 a b c}{5}\right)"," ",0,"a**2*c*x**3/3 + b**2*d*x**9/9 + x**7*(2*a*b*d/7 + b**2*c/7) + x**5*(a**2*d/5 + 2*a*b*c/5)","A",0
144,1,53,0,0.073177," ","integrate(x*(b*x**2+a)**2*(d*x**2+c),x)","\frac{a^{2} c x^{2}}{2} + \frac{b^{2} d x^{8}}{8} + x^{6} \left(\frac{a b d}{3} + \frac{b^{2} c}{6}\right) + x^{4} \left(\frac{a^{2} d}{4} + \frac{a b c}{2}\right)"," ",0,"a**2*c*x**2/2 + b**2*d*x**8/8 + x**6*(a*b*d/3 + b**2*c/6) + x**4*(a**2*d/4 + a*b*c/2)","A",0
145,1,53,0,0.073472," ","integrate((b*x**2+a)**2*(d*x**2+c),x)","a^{2} c x + \frac{b^{2} d x^{7}}{7} + x^{5} \left(\frac{2 a b d}{5} + \frac{b^{2} c}{5}\right) + x^{3} \left(\frac{a^{2} d}{3} + \frac{2 a b c}{3}\right)"," ",0,"a**2*c*x + b**2*d*x**7/7 + x**5*(2*a*b*d/5 + b**2*c/5) + x**3*(a**2*d/3 + 2*a*b*c/3)","A",0
146,1,49,0,0.141633," ","integrate((b*x**2+a)**2*(d*x**2+c)/x,x)","a^{2} c \log{\left(x \right)} + \frac{b^{2} d x^{6}}{6} + x^{4} \left(\frac{a b d}{2} + \frac{b^{2} c}{4}\right) + x^{2} \left(\frac{a^{2} d}{2} + a b c\right)"," ",0,"a**2*c*log(x) + b**2*d*x**6/6 + x**4*(a*b*d/2 + b**2*c/4) + x**2*(a**2*d/2 + a*b*c)","A",0
147,1,48,0,0.136534," ","integrate((b*x**2+a)**2*(d*x**2+c)/x**2,x)","- \frac{a^{2} c}{x} + \frac{b^{2} d x^{5}}{5} + x^{3} \left(\frac{2 a b d}{3} + \frac{b^{2} c}{3}\right) + x \left(a^{2} d + 2 a b c\right)"," ",0,"-a**2*c/x + b**2*d*x**5/5 + x**3*(2*a*b*d/3 + b**2*c/3) + x*(a**2*d + 2*a*b*c)","A",0
148,1,48,0,0.233345," ","integrate((b*x**2+a)**2*(d*x**2+c)/x**3,x)","- \frac{a^{2} c}{2 x^{2}} + a \left(a d + 2 b c\right) \log{\left(x \right)} + \frac{b^{2} d x^{4}}{4} + x^{2} \left(a b d + \frac{b^{2} c}{2}\right)"," ",0,"-a**2*c/(2*x**2) + a*(a*d + 2*b*c)*log(x) + b**2*d*x**4/4 + x**2*(a*b*d + b**2*c/2)","A",0
149,1,51,0,0.245103," ","integrate((b*x**2+a)**2*(d*x**2+c)/x**4,x)","\frac{b^{2} d x^{3}}{3} + x \left(2 a b d + b^{2} c\right) + \frac{- a^{2} c + x^{2} \left(- 3 a^{2} d - 6 a b c\right)}{3 x^{3}}"," ",0,"b**2*d*x**3/3 + x*(2*a*b*d + b**2*c) + (-a**2*c + x**2*(-3*a**2*d - 6*a*b*c))/(3*x**3)","A",0
150,1,100,0,0.085021," ","integrate(x**4*(b*x**2+a)**2*(d*x**2+c)**2,x)","\frac{a^{2} c^{2} x^{5}}{5} + \frac{b^{2} d^{2} x^{13}}{13} + x^{11} \left(\frac{2 a b d^{2}}{11} + \frac{2 b^{2} c d}{11}\right) + x^{9} \left(\frac{a^{2} d^{2}}{9} + \frac{4 a b c d}{9} + \frac{b^{2} c^{2}}{9}\right) + x^{7} \left(\frac{2 a^{2} c d}{7} + \frac{2 a b c^{2}}{7}\right)"," ",0,"a**2*c**2*x**5/5 + b**2*d**2*x**13/13 + x**11*(2*a*b*d**2/11 + 2*b**2*c*d/11) + x**9*(a**2*d**2/9 + 4*a*b*c*d/9 + b**2*c**2/9) + x**7*(2*a**2*c*d/7 + 2*a*b*c**2/7)","A",0
151,1,92,0,0.086590," ","integrate(x**3*(b*x**2+a)**2*(d*x**2+c)**2,x)","\frac{a^{2} c^{2} x^{4}}{4} + \frac{b^{2} d^{2} x^{12}}{12} + x^{10} \left(\frac{a b d^{2}}{5} + \frac{b^{2} c d}{5}\right) + x^{8} \left(\frac{a^{2} d^{2}}{8} + \frac{a b c d}{2} + \frac{b^{2} c^{2}}{8}\right) + x^{6} \left(\frac{a^{2} c d}{3} + \frac{a b c^{2}}{3}\right)"," ",0,"a**2*c**2*x**4/4 + b**2*d**2*x**12/12 + x**10*(a*b*d**2/5 + b**2*c*d/5) + x**8*(a**2*d**2/8 + a*b*c*d/2 + b**2*c**2/8) + x**6*(a**2*c*d/3 + a*b*c**2/3)","A",0
152,1,100,0,0.084546," ","integrate(x**2*(b*x**2+a)**2*(d*x**2+c)**2,x)","\frac{a^{2} c^{2} x^{3}}{3} + \frac{b^{2} d^{2} x^{11}}{11} + x^{9} \left(\frac{2 a b d^{2}}{9} + \frac{2 b^{2} c d}{9}\right) + x^{7} \left(\frac{a^{2} d^{2}}{7} + \frac{4 a b c d}{7} + \frac{b^{2} c^{2}}{7}\right) + x^{5} \left(\frac{2 a^{2} c d}{5} + \frac{2 a b c^{2}}{5}\right)"," ",0,"a**2*c**2*x**3/3 + b**2*d**2*x**11/11 + x**9*(2*a*b*d**2/9 + 2*b**2*c*d/9) + x**7*(a**2*d**2/7 + 4*a*b*c*d/7 + b**2*c**2/7) + x**5*(2*a**2*c*d/5 + 2*a*b*c**2/5)","A",0
153,1,94,0,0.083996," ","integrate(x*(b*x**2+a)**2*(d*x**2+c)**2,x)","\frac{a^{2} c^{2} x^{2}}{2} + \frac{b^{2} d^{2} x^{10}}{10} + x^{8} \left(\frac{a b d^{2}}{4} + \frac{b^{2} c d}{4}\right) + x^{6} \left(\frac{a^{2} d^{2}}{6} + \frac{2 a b c d}{3} + \frac{b^{2} c^{2}}{6}\right) + x^{4} \left(\frac{a^{2} c d}{2} + \frac{a b c^{2}}{2}\right)"," ",0,"a**2*c**2*x**2/2 + b**2*d**2*x**10/10 + x**8*(a*b*d**2/4 + b**2*c*d/4) + x**6*(a**2*d**2/6 + 2*a*b*c*d/3 + b**2*c**2/6) + x**4*(a**2*c*d/2 + a*b*c**2/2)","A",0
154,1,97,0,0.082680," ","integrate((b*x**2+a)**2*(d*x**2+c)**2,x)","a^{2} c^{2} x + \frac{b^{2} d^{2} x^{9}}{9} + x^{7} \left(\frac{2 a b d^{2}}{7} + \frac{2 b^{2} c d}{7}\right) + x^{5} \left(\frac{a^{2} d^{2}}{5} + \frac{4 a b c d}{5} + \frac{b^{2} c^{2}}{5}\right) + x^{3} \left(\frac{2 a^{2} c d}{3} + \frac{2 a b c^{2}}{3}\right)"," ",0,"a**2*c**2*x + b**2*d**2*x**9/9 + x**7*(2*a*b*d**2/7 + 2*b**2*c*d/7) + x**5*(a**2*d**2/5 + 4*a*b*c*d/5 + b**2*c**2/5) + x**3*(2*a**2*c*d/3 + 2*a*b*c**2/3)","A",0
155,1,85,0,0.183982," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x,x)","a^{2} c^{2} \log{\left(x \right)} + \frac{b^{2} d^{2} x^{8}}{8} + x^{6} \left(\frac{a b d^{2}}{3} + \frac{b^{2} c d}{3}\right) + x^{4} \left(\frac{a^{2} d^{2}}{4} + a b c d + \frac{b^{2} c^{2}}{4}\right) + x^{2} \left(a^{2} c d + a b c^{2}\right)"," ",0,"a**2*c**2*log(x) + b**2*d**2*x**8/8 + x**6*(a*b*d**2/3 + b**2*c*d/3) + x**4*(a**2*d**2/4 + a*b*c*d + b**2*c**2/4) + x**2*(a**2*c*d + a*b*c**2)","A",0
156,1,92,0,0.178206," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x**2,x)","- \frac{a^{2} c^{2}}{x} + \frac{b^{2} d^{2} x^{7}}{7} + x^{5} \left(\frac{2 a b d^{2}}{5} + \frac{2 b^{2} c d}{5}\right) + x^{3} \left(\frac{a^{2} d^{2}}{3} + \frac{4 a b c d}{3} + \frac{b^{2} c^{2}}{3}\right) + x \left(2 a^{2} c d + 2 a b c^{2}\right)"," ",0,"-a**2*c**2/x + b**2*d**2*x**7/7 + x**5*(2*a*b*d**2/5 + 2*b**2*c*d/5) + x**3*(a**2*d**2/3 + 4*a*b*c*d/3 + b**2*c**2/3) + x*(2*a**2*c*d + 2*a*b*c**2)","A",0
157,1,87,0,0.279456," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x**3,x)","- \frac{a^{2} c^{2}}{2 x^{2}} + 2 a c \left(a d + b c\right) \log{\left(x \right)} + \frac{b^{2} d^{2} x^{6}}{6} + x^{4} \left(\frac{a b d^{2}}{2} + \frac{b^{2} c d}{2}\right) + x^{2} \left(\frac{a^{2} d^{2}}{2} + 2 a b c d + \frac{b^{2} c^{2}}{2}\right)"," ",0,"-a**2*c**2/(2*x**2) + 2*a*c*(a*d + b*c)*log(x) + b**2*d**2*x**6/6 + x**4*(a*b*d**2/2 + b**2*c*d/2) + x**2*(a**2*d**2/2 + 2*a*b*c*d + b**2*c**2/2)","A",0
158,1,92,0,0.295105," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x**4,x)","\frac{b^{2} d^{2} x^{5}}{5} + x^{3} \left(\frac{2 a b d^{2}}{3} + \frac{2 b^{2} c d}{3}\right) + x \left(a^{2} d^{2} + 4 a b c d + b^{2} c^{2}\right) + \frac{- a^{2} c^{2} + x^{2} \left(- 6 a^{2} c d - 6 a b c^{2}\right)}{3 x^{3}}"," ",0,"b**2*d**2*x**5/5 + x**3*(2*a*b*d**2/3 + 2*b**2*c*d/3) + x*(a**2*d**2 + 4*a*b*c*d + b**2*c**2) + (-a**2*c**2 + x**2*(-6*a**2*c*d - 6*a*b*c**2))/(3*x**3)","A",0
159,1,143,0,0.092919," ","integrate(x**4*(b*x**2+a)**2*(d*x**2+c)**3,x)","\frac{a^{2} c^{3} x^{5}}{5} + \frac{b^{2} d^{3} x^{15}}{15} + x^{13} \left(\frac{2 a b d^{3}}{13} + \frac{3 b^{2} c d^{2}}{13}\right) + x^{11} \left(\frac{a^{2} d^{3}}{11} + \frac{6 a b c d^{2}}{11} + \frac{3 b^{2} c^{2} d}{11}\right) + x^{9} \left(\frac{a^{2} c d^{2}}{3} + \frac{2 a b c^{2} d}{3} + \frac{b^{2} c^{3}}{9}\right) + x^{7} \left(\frac{3 a^{2} c^{2} d}{7} + \frac{2 a b c^{3}}{7}\right)"," ",0,"a**2*c**3*x**5/5 + b**2*d**3*x**15/15 + x**13*(2*a*b*d**3/13 + 3*b**2*c*d**2/13) + x**11*(a**2*d**3/11 + 6*a*b*c*d**2/11 + 3*b**2*c**2*d/11) + x**9*(a**2*c*d**2/3 + 2*a*b*c**2*d/3 + b**2*c**3/9) + x**7*(3*a**2*c**2*d/7 + 2*a*b*c**3/7)","A",0
160,1,138,0,0.092281," ","integrate(x**3*(b*x**2+a)**2*(d*x**2+c)**3,x)","\frac{a^{2} c^{3} x^{4}}{4} + \frac{b^{2} d^{3} x^{14}}{14} + x^{12} \left(\frac{a b d^{3}}{6} + \frac{b^{2} c d^{2}}{4}\right) + x^{10} \left(\frac{a^{2} d^{3}}{10} + \frac{3 a b c d^{2}}{5} + \frac{3 b^{2} c^{2} d}{10}\right) + x^{8} \left(\frac{3 a^{2} c d^{2}}{8} + \frac{3 a b c^{2} d}{4} + \frac{b^{2} c^{3}}{8}\right) + x^{6} \left(\frac{a^{2} c^{2} d}{2} + \frac{a b c^{3}}{3}\right)"," ",0,"a**2*c**3*x**4/4 + b**2*d**3*x**14/14 + x**12*(a*b*d**3/6 + b**2*c*d**2/4) + x**10*(a**2*d**3/10 + 3*a*b*c*d**2/5 + 3*b**2*c**2*d/10) + x**8*(3*a**2*c*d**2/8 + 3*a*b*c**2*d/4 + b**2*c**3/8) + x**6*(a**2*c**2*d/2 + a*b*c**3/3)","A",0
161,1,143,0,0.093072," ","integrate(x**2*(b*x**2+a)**2*(d*x**2+c)**3,x)","\frac{a^{2} c^{3} x^{3}}{3} + \frac{b^{2} d^{3} x^{13}}{13} + x^{11} \left(\frac{2 a b d^{3}}{11} + \frac{3 b^{2} c d^{2}}{11}\right) + x^{9} \left(\frac{a^{2} d^{3}}{9} + \frac{2 a b c d^{2}}{3} + \frac{b^{2} c^{2} d}{3}\right) + x^{7} \left(\frac{3 a^{2} c d^{2}}{7} + \frac{6 a b c^{2} d}{7} + \frac{b^{2} c^{3}}{7}\right) + x^{5} \left(\frac{3 a^{2} c^{2} d}{5} + \frac{2 a b c^{3}}{5}\right)"," ",0,"a**2*c**3*x**3/3 + b**2*d**3*x**13/13 + x**11*(2*a*b*d**3/11 + 3*b**2*c*d**2/11) + x**9*(a**2*d**3/9 + 2*a*b*c*d**2/3 + b**2*c**2*d/3) + x**7*(3*a**2*c*d**2/7 + 6*a*b*c**2*d/7 + b**2*c**3/7) + x**5*(3*a**2*c**2*d/5 + 2*a*b*c**3/5)","A",0
162,1,136,0,0.091400," ","integrate(x*(b*x**2+a)**2*(d*x**2+c)**3,x)","\frac{a^{2} c^{3} x^{2}}{2} + \frac{b^{2} d^{3} x^{12}}{12} + x^{10} \left(\frac{a b d^{3}}{5} + \frac{3 b^{2} c d^{2}}{10}\right) + x^{8} \left(\frac{a^{2} d^{3}}{8} + \frac{3 a b c d^{2}}{4} + \frac{3 b^{2} c^{2} d}{8}\right) + x^{6} \left(\frac{a^{2} c d^{2}}{2} + a b c^{2} d + \frac{b^{2} c^{3}}{6}\right) + x^{4} \left(\frac{3 a^{2} c^{2} d}{4} + \frac{a b c^{3}}{2}\right)"," ",0,"a**2*c**3*x**2/2 + b**2*d**3*x**12/12 + x**10*(a*b*d**3/5 + 3*b**2*c*d**2/10) + x**8*(a**2*d**3/8 + 3*a*b*c*d**2/4 + 3*b**2*c**2*d/8) + x**6*(a**2*c*d**2/2 + a*b*c**2*d + b**2*c**3/6) + x**4*(3*a**2*c**2*d/4 + a*b*c**3/2)","B",0
163,1,136,0,0.090232," ","integrate((b*x**2+a)**2*(d*x**2+c)**3,x)","a^{2} c^{3} x + \frac{b^{2} d^{3} x^{11}}{11} + x^{9} \left(\frac{2 a b d^{3}}{9} + \frac{b^{2} c d^{2}}{3}\right) + x^{7} \left(\frac{a^{2} d^{3}}{7} + \frac{6 a b c d^{2}}{7} + \frac{3 b^{2} c^{2} d}{7}\right) + x^{5} \left(\frac{3 a^{2} c d^{2}}{5} + \frac{6 a b c^{2} d}{5} + \frac{b^{2} c^{3}}{5}\right) + x^{3} \left(a^{2} c^{2} d + \frac{2 a b c^{3}}{3}\right)"," ",0,"a**2*c**3*x + b**2*d**3*x**11/11 + x**9*(2*a*b*d**3/9 + b**2*c*d**2/3) + x**7*(a**2*d**3/7 + 6*a*b*c*d**2/7 + 3*b**2*c**2*d/7) + x**5*(3*a**2*c*d**2/5 + 6*a*b*c**2*d/5 + b**2*c**3/5) + x**3*(a**2*c**2*d + 2*a*b*c**3/3)","A",0
164,1,133,0,0.231940," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x,x)","a^{2} c^{3} \log{\left(x \right)} + \frac{b^{2} d^{3} x^{10}}{10} + x^{8} \left(\frac{a b d^{3}}{4} + \frac{3 b^{2} c d^{2}}{8}\right) + x^{6} \left(\frac{a^{2} d^{3}}{6} + a b c d^{2} + \frac{b^{2} c^{2} d}{2}\right) + x^{4} \left(\frac{3 a^{2} c d^{2}}{4} + \frac{3 a b c^{2} d}{2} + \frac{b^{2} c^{3}}{4}\right) + x^{2} \left(\frac{3 a^{2} c^{2} d}{2} + a b c^{3}\right)"," ",0,"a**2*c**3*log(x) + b**2*d**3*x**10/10 + x**8*(a*b*d**3/4 + 3*b**2*c*d**2/8) + x**6*(a**2*d**3/6 + a*b*c*d**2 + b**2*c**2*d/2) + x**4*(3*a**2*c*d**2/4 + 3*a*b*c**2*d/2 + b**2*c**3/4) + x**2*(3*a**2*c**2*d/2 + a*b*c**3)","A",0
165,1,131,0,0.224153," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x**2,x)","- \frac{a^{2} c^{3}}{x} + \frac{b^{2} d^{3} x^{9}}{9} + x^{7} \left(\frac{2 a b d^{3}}{7} + \frac{3 b^{2} c d^{2}}{7}\right) + x^{5} \left(\frac{a^{2} d^{3}}{5} + \frac{6 a b c d^{2}}{5} + \frac{3 b^{2} c^{2} d}{5}\right) + x^{3} \left(a^{2} c d^{2} + 2 a b c^{2} d + \frac{b^{2} c^{3}}{3}\right) + x \left(3 a^{2} c^{2} d + 2 a b c^{3}\right)"," ",0,"-a**2*c**3/x + b**2*d**3*x**9/9 + x**7*(2*a*b*d**3/7 + 3*b**2*c*d**2/7) + x**5*(a**2*d**3/5 + 6*a*b*c*d**2/5 + 3*b**2*c**2*d/5) + x**3*(a**2*c*d**2 + 2*a*b*c**2*d + b**2*c**3/3) + x*(3*a**2*c**2*d + 2*a*b*c**3)","A",0
166,1,133,0,0.325340," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x**3,x)","- \frac{a^{2} c^{3}}{2 x^{2}} + a c^{2} \left(3 a d + 2 b c\right) \log{\left(x \right)} + \frac{b^{2} d^{3} x^{8}}{8} + x^{6} \left(\frac{a b d^{3}}{3} + \frac{b^{2} c d^{2}}{2}\right) + x^{4} \left(\frac{a^{2} d^{3}}{4} + \frac{3 a b c d^{2}}{2} + \frac{3 b^{2} c^{2} d}{4}\right) + x^{2} \left(\frac{3 a^{2} c d^{2}}{2} + 3 a b c^{2} d + \frac{b^{2} c^{3}}{2}\right)"," ",0,"-a**2*c**3/(2*x**2) + a*c**2*(3*a*d + 2*b*c)*log(x) + b**2*d**3*x**8/8 + x**6*(a*b*d**3/3 + b**2*c*d**2/2) + x**4*(a**2*d**3/4 + 3*a*b*c*d**2/2 + 3*b**2*c**2*d/4) + x**2*(3*a**2*c*d**2/2 + 3*a*b*c**2*d + b**2*c**3/2)","A",0
167,1,131,0,0.345711," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x**4,x)","\frac{b^{2} d^{3} x^{7}}{7} + x^{5} \left(\frac{2 a b d^{3}}{5} + \frac{3 b^{2} c d^{2}}{5}\right) + x^{3} \left(\frac{a^{2} d^{3}}{3} + 2 a b c d^{2} + b^{2} c^{2} d\right) + x \left(3 a^{2} c d^{2} + 6 a b c^{2} d + b^{2} c^{3}\right) + \frac{- a^{2} c^{3} + x^{2} \left(- 9 a^{2} c^{2} d - 6 a b c^{3}\right)}{3 x^{3}}"," ",0,"b**2*d**3*x**7/7 + x**5*(2*a*b*d**3/5 + 3*b**2*c*d**2/5) + x**3*(a**2*d**3/3 + 2*a*b*c*d**2 + b**2*c**2*d) + x*(3*a**2*c*d**2 + 6*a*b*c**2*d + b**2*c**3) + (-a**2*c**3 + x**2*(-9*a**2*c**2*d - 6*a*b*c**3))/(3*x**3)","A",0
168,1,246,0,0.528259," ","integrate(x**4*(b*x**2+a)**2/(d*x**2+c),x)","\frac{b^{2} x^{7}}{7 d} + x^{5} \left(\frac{2 a b}{5 d} - \frac{b^{2} c}{5 d^{2}}\right) + x^{3} \left(\frac{a^{2}}{3 d} - \frac{2 a b c}{3 d^{2}} + \frac{b^{2} c^{2}}{3 d^{3}}\right) + x \left(- \frac{a^{2} c}{d^{2}} + \frac{2 a b c^{2}}{d^{3}} - \frac{b^{2} c^{3}}{d^{4}}\right) - \frac{\sqrt{- \frac{c^{3}}{d^{9}}} \left(a d - b c\right)^{2} \log{\left(- \frac{d^{4} \sqrt{- \frac{c^{3}}{d^{9}}} \left(a d - b c\right)^{2}}{a^{2} c d^{2} - 2 a b c^{2} d + b^{2} c^{3}} + x \right)}}{2} + \frac{\sqrt{- \frac{c^{3}}{d^{9}}} \left(a d - b c\right)^{2} \log{\left(\frac{d^{4} \sqrt{- \frac{c^{3}}{d^{9}}} \left(a d - b c\right)^{2}}{a^{2} c d^{2} - 2 a b c^{2} d + b^{2} c^{3}} + x \right)}}{2}"," ",0,"b**2*x**7/(7*d) + x**5*(2*a*b/(5*d) - b**2*c/(5*d**2)) + x**3*(a**2/(3*d) - 2*a*b*c/(3*d**2) + b**2*c**2/(3*d**3)) + x*(-a**2*c/d**2 + 2*a*b*c**2/d**3 - b**2*c**3/d**4) - sqrt(-c**3/d**9)*(a*d - b*c)**2*log(-d**4*sqrt(-c**3/d**9)*(a*d - b*c)**2/(a**2*c*d**2 - 2*a*b*c**2*d + b**2*c**3) + x)/2 + sqrt(-c**3/d**9)*(a*d - b*c)**2*log(d**4*sqrt(-c**3/d**9)*(a*d - b*c)**2/(a**2*c*d**2 - 2*a*b*c**2*d + b**2*c**3) + x)/2","B",0
169,1,83,0,0.415695," ","integrate(x**3*(b*x**2+a)**2/(d*x**2+c),x)","\frac{b^{2} x^{6}}{6 d} - \frac{c \left(a d - b c\right)^{2} \log{\left(c + d x^{2} \right)}}{2 d^{4}} + x^{4} \left(\frac{a b}{2 d} - \frac{b^{2} c}{4 d^{2}}\right) + x^{2} \left(\frac{a^{2}}{2 d} - \frac{a b c}{d^{2}} + \frac{b^{2} c^{2}}{2 d^{3}}\right)"," ",0,"b**2*x**6/(6*d) - c*(a*d - b*c)**2*log(c + d*x**2)/(2*d**4) + x**4*(a*b/(2*d) - b**2*c/(4*d**2)) + x**2*(a**2/(2*d) - a*b*c/d**2 + b**2*c**2/(2*d**3))","A",0
170,1,194,0,0.485359," ","integrate(x**2*(b*x**2+a)**2/(d*x**2+c),x)","\frac{b^{2} x^{5}}{5 d} + x^{3} \left(\frac{2 a b}{3 d} - \frac{b^{2} c}{3 d^{2}}\right) + x \left(\frac{a^{2}}{d} - \frac{2 a b c}{d^{2}} + \frac{b^{2} c^{2}}{d^{3}}\right) + \frac{\sqrt{- \frac{c}{d^{7}}} \left(a d - b c\right)^{2} \log{\left(- \frac{d^{3} \sqrt{- \frac{c}{d^{7}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} - \frac{\sqrt{- \frac{c}{d^{7}}} \left(a d - b c\right)^{2} \log{\left(\frac{d^{3} \sqrt{- \frac{c}{d^{7}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2}"," ",0,"b**2*x**5/(5*d) + x**3*(2*a*b/(3*d) - b**2*c/(3*d**2)) + x*(a**2/d - 2*a*b*c/d**2 + b**2*c**2/d**3) + sqrt(-c/d**7)*(a*d - b*c)**2*log(-d**3*sqrt(-c/d**7)*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 - sqrt(-c/d**7)*(a*d - b*c)**2*log(d**3*sqrt(-c/d**7)*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2","B",0
171,1,49,0,0.362867," ","integrate(x*(b*x**2+a)**2/(d*x**2+c),x)","\frac{b^{2} x^{4}}{4 d} + x^{2} \left(\frac{a b}{d} - \frac{b^{2} c}{2 d^{2}}\right) + \frac{\left(a d - b c\right)^{2} \log{\left(c + d x^{2} \right)}}{2 d^{3}}"," ",0,"b**2*x**4/(4*d) + x**2*(a*b/d - b**2*c/(2*d**2)) + (a*d - b*c)**2*log(c + d*x**2)/(2*d**3)","A",0
172,1,172,0,0.417513," ","integrate((b*x**2+a)**2/(d*x**2+c),x)","\frac{b^{2} x^{3}}{3 d} + x \left(\frac{2 a b}{d} - \frac{b^{2} c}{d^{2}}\right) - \frac{\sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2} \log{\left(- \frac{c d^{2} \sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2} \log{\left(\frac{c d^{2} \sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2}"," ",0,"b**2*x**3/(3*d) + x*(2*a*b/d - b**2*c/d**2) - sqrt(-1/(c*d**5))*(a*d - b*c)**2*log(-c*d**2*sqrt(-1/(c*d**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + sqrt(-1/(c*d**5))*(a*d - b*c)**2*log(c*d**2*sqrt(-1/(c*d**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2","B",0
173,1,41,0,1.214876," ","integrate((b*x**2+a)**2/x/(d*x**2+c),x)","\frac{a^{2} \log{\left(x \right)}}{c} + \frac{b^{2} x^{2}}{2 d} - \frac{\left(a d - b c\right)^{2} \log{\left(\frac{c}{d} + x^{2} \right)}}{2 c d^{2}}"," ",0,"a**2*log(x)/c + b**2*x**2/(2*d) - (a*d - b*c)**2*log(c/d + x**2)/(2*c*d**2)","A",0
174,1,165,0,0.543489," ","integrate((b*x**2+a)**2/x**2/(d*x**2+c),x)","- \frac{a^{2}}{c x} + \frac{b^{2} x}{d} + \frac{\sqrt{- \frac{1}{c^{3} d^{3}}} \left(a d - b c\right)^{2} \log{\left(- \frac{c^{2} d \sqrt{- \frac{1}{c^{3} d^{3}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{c^{3} d^{3}}} \left(a d - b c\right)^{2} \log{\left(\frac{c^{2} d \sqrt{- \frac{1}{c^{3} d^{3}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2}"," ",0,"-a**2/(c*x) + b**2*x/d + sqrt(-1/(c**3*d**3))*(a*d - b*c)**2*log(-c**2*d*sqrt(-1/(c**3*d**3))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 - sqrt(-1/(c**3*d**3))*(a*d - b*c)**2*log(c**2*d*sqrt(-1/(c**3*d**3))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2","B",0
175,1,49,0,1.396917," ","integrate((b*x**2+a)**2/x**3/(d*x**2+c),x)","- \frac{a^{2}}{2 c x^{2}} - \frac{a \left(a d - 2 b c\right) \log{\left(x \right)}}{c^{2}} + \frac{\left(a d - b c\right)^{2} \log{\left(\frac{c}{d} + x^{2} \right)}}{2 c^{2} d}"," ",0,"-a**2/(2*c*x**2) - a*(a*d - 2*b*c)*log(x)/c**2 + (a*d - b*c)**2*log(c/d + x**2)/(2*c**2*d)","A",0
176,1,172,0,0.645450," ","integrate((b*x**2+a)**2/x**4/(d*x**2+c),x)","- \frac{\sqrt{- \frac{1}{c^{5} d}} \left(a d - b c\right)^{2} \log{\left(- \frac{c^{3} \sqrt{- \frac{1}{c^{5} d}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{c^{5} d}} \left(a d - b c\right)^{2} \log{\left(\frac{c^{3} \sqrt{- \frac{1}{c^{5} d}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{- a^{2} c + x^{2} \left(3 a^{2} d - 6 a b c\right)}{3 c^{2} x^{3}}"," ",0,"-sqrt(-1/(c**5*d))*(a*d - b*c)**2*log(-c**3*sqrt(-1/(c**5*d))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + sqrt(-1/(c**5*d))*(a*d - b*c)**2*log(c**3*sqrt(-1/(c**5*d))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + (-a**2*c + x**2*(3*a**2*d - 6*a*b*c))/(3*c**2*x**3)","B",0
177,1,66,0,1.323810," ","integrate((b*x**2+a)**2/x**5/(d*x**2+c),x)","\frac{- a^{2} c + x^{2} \left(2 a^{2} d - 4 a b c\right)}{4 c^{2} x^{4}} + \frac{\left(a d - b c\right)^{2} \log{\left(x \right)}}{c^{3}} - \frac{\left(a d - b c\right)^{2} \log{\left(\frac{c}{d} + x^{2} \right)}}{2 c^{3}}"," ",0,"(-a**2*c + x**2*(2*a**2*d - 4*a*b*c))/(4*c**2*x**4) + (a*d - b*c)**2*log(x)/c**3 - (a*d - b*c)**2*log(c/d + x**2)/(2*c**3)","A",0
178,1,207,0,0.763024," ","integrate((b*x**2+a)**2/x**6/(d*x**2+c),x)","\frac{\sqrt{- \frac{d}{c^{7}}} \left(a d - b c\right)^{2} \log{\left(- \frac{c^{4} \sqrt{- \frac{d}{c^{7}}} \left(a d - b c\right)^{2}}{a^{2} d^{3} - 2 a b c d^{2} + b^{2} c^{2} d} + x \right)}}{2} - \frac{\sqrt{- \frac{d}{c^{7}}} \left(a d - b c\right)^{2} \log{\left(\frac{c^{4} \sqrt{- \frac{d}{c^{7}}} \left(a d - b c\right)^{2}}{a^{2} d^{3} - 2 a b c d^{2} + b^{2} c^{2} d} + x \right)}}{2} + \frac{- 3 a^{2} c^{2} + x^{4} \left(- 15 a^{2} d^{2} + 30 a b c d - 15 b^{2} c^{2}\right) + x^{2} \left(5 a^{2} c d - 10 a b c^{2}\right)}{15 c^{3} x^{5}}"," ",0,"sqrt(-d/c**7)*(a*d - b*c)**2*log(-c**4*sqrt(-d/c**7)*(a*d - b*c)**2/(a**2*d**3 - 2*a*b*c*d**2 + b**2*c**2*d) + x)/2 - sqrt(-d/c**7)*(a*d - b*c)**2*log(c**4*sqrt(-d/c**7)*(a*d - b*c)**2/(a**2*d**3 - 2*a*b*c*d**2 + b**2*c**2*d) + x)/2 + (-3*a**2*c**2 + x**4*(-15*a**2*d**2 + 30*a*b*c*d - 15*b**2*c**2) + x**2*(5*a**2*c*d - 10*a*b*c**2))/(15*c**3*x**5)","B",0
179,1,105,0,1.506659," ","integrate((b*x**2+a)**2/x**7/(d*x**2+c),x)","\frac{- 2 a^{2} c^{2} + x^{4} \left(- 6 a^{2} d^{2} + 12 a b c d - 6 b^{2} c^{2}\right) + x^{2} \left(3 a^{2} c d - 6 a b c^{2}\right)}{12 c^{3} x^{6}} - \frac{d \left(a d - b c\right)^{2} \log{\left(x \right)}}{c^{4}} + \frac{d \left(a d - b c\right)^{2} \log{\left(\frac{c}{d} + x^{2} \right)}}{2 c^{4}}"," ",0,"(-2*a**2*c**2 + x**4*(-6*a**2*d**2 + 12*a*b*c*d - 6*b**2*c**2) + x**2*(3*a**2*c*d - 6*a*b*c**2))/(12*c**3*x**6) - d*(a*d - b*c)**2*log(x)/c**4 + d*(a*d - b*c)**2*log(c/d + x**2)/(2*c**4)","A",0
180,1,286,0,0.990717," ","integrate(x**4*(b*x**2+a)**2/(d*x**2+c)**2,x)","\frac{b^{2} x^{5}}{5 d^{2}} + x^{3} \left(\frac{2 a b}{3 d^{2}} - \frac{2 b^{2} c}{3 d^{3}}\right) + x \left(\frac{a^{2}}{d^{2}} - \frac{4 a b c}{d^{3}} + \frac{3 b^{2} c^{2}}{d^{4}}\right) + \frac{x \left(a^{2} c d^{2} - 2 a b c^{2} d + b^{2} c^{3}\right)}{2 c d^{4} + 2 d^{5} x^{2}} + \frac{\sqrt{- \frac{c}{d^{9}}} \left(a d - b c\right) \left(3 a d - 7 b c\right) \log{\left(- \frac{d^{4} \sqrt{- \frac{c}{d^{9}}} \left(a d - b c\right) \left(3 a d - 7 b c\right)}{3 a^{2} d^{2} - 10 a b c d + 7 b^{2} c^{2}} + x \right)}}{4} - \frac{\sqrt{- \frac{c}{d^{9}}} \left(a d - b c\right) \left(3 a d - 7 b c\right) \log{\left(\frac{d^{4} \sqrt{- \frac{c}{d^{9}}} \left(a d - b c\right) \left(3 a d - 7 b c\right)}{3 a^{2} d^{2} - 10 a b c d + 7 b^{2} c^{2}} + x \right)}}{4}"," ",0,"b**2*x**5/(5*d**2) + x**3*(2*a*b/(3*d**2) - 2*b**2*c/(3*d**3)) + x*(a**2/d**2 - 4*a*b*c/d**3 + 3*b**2*c**2/d**4) + x*(a**2*c*d**2 - 2*a*b*c**2*d + b**2*c**3)/(2*c*d**4 + 2*d**5*x**2) + sqrt(-c/d**9)*(a*d - b*c)*(3*a*d - 7*b*c)*log(-d**4*sqrt(-c/d**9)*(a*d - b*c)*(3*a*d - 7*b*c)/(3*a**2*d**2 - 10*a*b*c*d + 7*b**2*c**2) + x)/4 - sqrt(-c/d**9)*(a*d - b*c)*(3*a*d - 7*b*c)*log(d**4*sqrt(-c/d**9)*(a*d - b*c)*(3*a*d - 7*b*c)/(3*a**2*d**2 - 10*a*b*c*d + 7*b**2*c**2) + x)/4","B",0
181,1,99,0,0.943199," ","integrate(x**3*(b*x**2+a)**2/(d*x**2+c)**2,x)","\frac{b^{2} x^{4}}{4 d^{2}} + x^{2} \left(\frac{a b}{d^{2}} - \frac{b^{2} c}{d^{3}}\right) + \frac{a^{2} c d^{2} - 2 a b c^{2} d + b^{2} c^{3}}{2 c d^{4} + 2 d^{5} x^{2}} + \frac{\left(a d - 3 b c\right) \left(a d - b c\right) \log{\left(c + d x^{2} \right)}}{2 d^{4}}"," ",0,"b**2*x**4/(4*d**2) + x**2*(a*b/d**2 - b**2*c/d**3) + (a**2*c*d**2 - 2*a*b*c**2*d + b**2*c**3)/(2*c*d**4 + 2*d**5*x**2) + (a*d - 3*b*c)*(a*d - b*c)*log(c + d*x**2)/(2*d**4)","A",0
182,1,246,0,0.871846," ","integrate(x**2*(b*x**2+a)**2/(d*x**2+c)**2,x)","\frac{b^{2} x^{3}}{3 d^{2}} + x \left(\frac{2 a b}{d^{2}} - \frac{2 b^{2} c}{d^{3}}\right) + \frac{x \left(- a^{2} d^{2} + 2 a b c d - b^{2} c^{2}\right)}{2 c d^{3} + 2 d^{4} x^{2}} - \frac{\sqrt{- \frac{1}{c d^{7}}} \left(a d - 5 b c\right) \left(a d - b c\right) \log{\left(- \frac{c d^{3} \sqrt{- \frac{1}{c d^{7}}} \left(a d - 5 b c\right) \left(a d - b c\right)}{a^{2} d^{2} - 6 a b c d + 5 b^{2} c^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{c d^{7}}} \left(a d - 5 b c\right) \left(a d - b c\right) \log{\left(\frac{c d^{3} \sqrt{- \frac{1}{c d^{7}}} \left(a d - 5 b c\right) \left(a d - b c\right)}{a^{2} d^{2} - 6 a b c d + 5 b^{2} c^{2}} + x \right)}}{4}"," ",0,"b**2*x**3/(3*d**2) + x*(2*a*b/d**2 - 2*b**2*c/d**3) + x*(-a**2*d**2 + 2*a*b*c*d - b**2*c**2)/(2*c*d**3 + 2*d**4*x**2) - sqrt(-1/(c*d**7))*(a*d - 5*b*c)*(a*d - b*c)*log(-c*d**3*sqrt(-1/(c*d**7))*(a*d - 5*b*c)*(a*d - b*c)/(a**2*d**2 - 6*a*b*c*d + 5*b**2*c**2) + x)/4 + sqrt(-1/(c*d**7))*(a*d - 5*b*c)*(a*d - b*c)*log(c*d**3*sqrt(-1/(c*d**7))*(a*d - 5*b*c)*(a*d - b*c)/(a**2*d**2 - 6*a*b*c*d + 5*b**2*c**2) + x)/4","B",0
183,1,68,0,0.772634," ","integrate(x*(b*x**2+a)**2/(d*x**2+c)**2,x)","\frac{b^{2} x^{2}}{2 d^{2}} + \frac{b \left(a d - b c\right) \log{\left(c + d x^{2} \right)}}{d^{3}} + \frac{- a^{2} d^{2} + 2 a b c d - b^{2} c^{2}}{2 c d^{3} + 2 d^{4} x^{2}}"," ",0,"b**2*x**2/(2*d**2) + b*(a*d - b*c)*log(c + d*x**2)/d**3 + (-a**2*d**2 + 2*a*b*c*d - b**2*c**2)/(2*c*d**3 + 2*d**4*x**2)","A",0
184,1,236,0,0.727538," ","integrate((b*x**2+a)**2/(d*x**2+c)**2,x)","\frac{b^{2} x}{d^{2}} + \frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{2 c^{2} d^{2} + 2 c d^{3} x^{2}} - \frac{\sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right) \log{\left(- \frac{c^{2} d^{2} \sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right)}{a^{2} d^{2} + 2 a b c d - 3 b^{2} c^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right) \log{\left(\frac{c^{2} d^{2} \sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right)}{a^{2} d^{2} + 2 a b c d - 3 b^{2} c^{2}} + x \right)}}{4}"," ",0,"b**2*x/d**2 + x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(2*c**2*d**2 + 2*c*d**3*x**2) - sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)*log(-c**2*d**2*sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)/(a**2*d**2 + 2*a*b*c*d - 3*b**2*c**2) + x)/4 + sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)*log(c**2*d**2*sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)/(a**2*d**2 + 2*a*b*c*d - 3*b**2*c**2) + x)/4","B",0
185,1,80,0,1.250600," ","integrate((b*x**2+a)**2/x/(d*x**2+c)**2,x)","\frac{a^{2} \log{\left(x \right)}}{c^{2}} + \frac{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}}{2 c^{2} d^{2} + 2 c d^{3} x^{2}} - \frac{\left(a d - b c\right) \left(a d + b c\right) \log{\left(\frac{c}{d} + x^{2} \right)}}{2 c^{2} d^{2}}"," ",0,"a**2*log(x)/c**2 + (a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(2*c**2*d**2 + 2*c*d**3*x**2) - (a*d - b*c)*(a*d + b*c)*log(c/d + x**2)/(2*c**2*d**2)","A",0
186,1,238,0,0.869307," ","integrate((b*x**2+a)**2/x**2/(d*x**2+c)**2,x)","\frac{\sqrt{- \frac{1}{c^{5} d^{3}}} \left(a d - b c\right) \left(3 a d + b c\right) \log{\left(- \frac{c^{3} d \sqrt{- \frac{1}{c^{5} d^{3}}} \left(a d - b c\right) \left(3 a d + b c\right)}{3 a^{2} d^{2} - 2 a b c d - b^{2} c^{2}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{c^{5} d^{3}}} \left(a d - b c\right) \left(3 a d + b c\right) \log{\left(\frac{c^{3} d \sqrt{- \frac{1}{c^{5} d^{3}}} \left(a d - b c\right) \left(3 a d + b c\right)}{3 a^{2} d^{2} - 2 a b c d - b^{2} c^{2}} + x \right)}}{4} + \frac{- 2 a^{2} c d + x^{2} \left(- 3 a^{2} d^{2} + 2 a b c d - b^{2} c^{2}\right)}{2 c^{3} d x + 2 c^{2} d^{2} x^{3}}"," ",0,"sqrt(-1/(c**5*d**3))*(a*d - b*c)*(3*a*d + b*c)*log(-c**3*d*sqrt(-1/(c**5*d**3))*(a*d - b*c)*(3*a*d + b*c)/(3*a**2*d**2 - 2*a*b*c*d - b**2*c**2) + x)/4 - sqrt(-1/(c**5*d**3))*(a*d - b*c)*(3*a*d + b*c)*log(c**3*d*sqrt(-1/(c**5*d**3))*(a*d - b*c)*(3*a*d + b*c)/(3*a**2*d**2 - 2*a*b*c*d - b**2*c**2) + x)/4 + (-2*a**2*c*d + x**2*(-3*a**2*d**2 + 2*a*b*c*d - b**2*c**2))/(2*c**3*d*x + 2*c**2*d**2*x**3)","B",0
187,1,92,0,1.362066," ","integrate((b*x**2+a)**2/x**3/(d*x**2+c)**2,x)","- \frac{2 a \left(a d - b c\right) \log{\left(x \right)}}{c^{3}} + \frac{a \left(a d - b c\right) \log{\left(\frac{c}{d} + x^{2} \right)}}{c^{3}} + \frac{- a^{2} c d + x^{2} \left(- 2 a^{2} d^{2} + 2 a b c d - b^{2} c^{2}\right)}{2 c^{3} d x^{2} + 2 c^{2} d^{2} x^{4}}"," ",0,"-2*a*(a*d - b*c)*log(x)/c**3 + a*(a*d - b*c)*log(c/d + x**2)/c**3 + (-a**2*c*d + x**2*(-2*a**2*d**2 + 2*a*b*c*d - b**2*c**2))/(2*c**3*d*x**2 + 2*c**2*d**2*x**4)","A",0
188,1,248,0,0.992751," ","integrate((b*x**2+a)**2/x**4/(d*x**2+c)**2,x)","- \frac{\sqrt{- \frac{1}{c^{7} d}} \left(a d - b c\right) \left(5 a d - b c\right) \log{\left(- \frac{c^{4} \sqrt{- \frac{1}{c^{7} d}} \left(a d - b c\right) \left(5 a d - b c\right)}{5 a^{2} d^{2} - 6 a b c d + b^{2} c^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{c^{7} d}} \left(a d - b c\right) \left(5 a d - b c\right) \log{\left(\frac{c^{4} \sqrt{- \frac{1}{c^{7} d}} \left(a d - b c\right) \left(5 a d - b c\right)}{5 a^{2} d^{2} - 6 a b c d + b^{2} c^{2}} + x \right)}}{4} + \frac{- 2 a^{2} c^{2} + x^{4} \left(15 a^{2} d^{2} - 18 a b c d + 3 b^{2} c^{2}\right) + x^{2} \left(10 a^{2} c d - 12 a b c^{2}\right)}{6 c^{4} x^{3} + 6 c^{3} d x^{5}}"," ",0,"-sqrt(-1/(c**7*d))*(a*d - b*c)*(5*a*d - b*c)*log(-c**4*sqrt(-1/(c**7*d))*(a*d - b*c)*(5*a*d - b*c)/(5*a**2*d**2 - 6*a*b*c*d + b**2*c**2) + x)/4 + sqrt(-1/(c**7*d))*(a*d - b*c)*(5*a*d - b*c)*log(c**4*sqrt(-1/(c**7*d))*(a*d - b*c)*(5*a*d - b*c)/(5*a**2*d**2 - 6*a*b*c*d + b**2*c**2) + x)/4 + (-2*a**2*c**2 + x**4*(15*a**2*d**2 - 18*a*b*c*d + 3*b**2*c**2) + x**2*(10*a**2*c*d - 12*a*b*c**2))/(6*c**4*x**3 + 6*c**3*d*x**5)","B",0
189,1,240,0,1.782453," ","integrate(x**4*(b*x**2+a)**2/(d*x**2+c)**3,x)","\frac{b^{2} x^{3}}{3 d^{3}} + x \left(\frac{2 a b}{d^{3}} - \frac{3 b^{2} c}{d^{4}}\right) - \frac{\sqrt{- \frac{1}{c d^{9}}} \left(3 a^{2} d^{2} - 30 a b c d + 35 b^{2} c^{2}\right) \log{\left(- c d^{4} \sqrt{- \frac{1}{c d^{9}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{c d^{9}}} \left(3 a^{2} d^{2} - 30 a b c d + 35 b^{2} c^{2}\right) \log{\left(c d^{4} \sqrt{- \frac{1}{c d^{9}}} + x \right)}}{16} + \frac{x^{3} \left(- 5 a^{2} d^{3} + 18 a b c d^{2} - 13 b^{2} c^{2} d\right) + x \left(- 3 a^{2} c d^{2} + 14 a b c^{2} d - 11 b^{2} c^{3}\right)}{8 c^{2} d^{4} + 16 c d^{5} x^{2} + 8 d^{6} x^{4}}"," ",0,"b**2*x**3/(3*d**3) + x*(2*a*b/d**3 - 3*b**2*c/d**4) - sqrt(-1/(c*d**9))*(3*a**2*d**2 - 30*a*b*c*d + 35*b**2*c**2)*log(-c*d**4*sqrt(-1/(c*d**9)) + x)/16 + sqrt(-1/(c*d**9))*(3*a**2*d**2 - 30*a*b*c*d + 35*b**2*c**2)*log(c*d**4*sqrt(-1/(c*d**9)) + x)/16 + (x**3*(-5*a**2*d**3 + 18*a*b*c*d**2 - 13*b**2*c**2*d) + x*(-3*a**2*c*d**2 + 14*a*b*c**2*d - 11*b**2*c**3))/(8*c**2*d**4 + 16*c*d**5*x**2 + 8*d**6*x**4)","A",0
190,1,122,0,2.107351," ","integrate(x**3*(b*x**2+a)**2/(d*x**2+c)**3,x)","\frac{b^{2} x^{2}}{2 d^{3}} + \frac{b \left(2 a d - 3 b c\right) \log{\left(c + d x^{2} \right)}}{2 d^{4}} + \frac{- a^{2} c d^{2} + 6 a b c^{2} d - 5 b^{2} c^{3} + x^{2} \left(- 2 a^{2} d^{3} + 8 a b c d^{2} - 6 b^{2} c^{2} d\right)}{4 c^{2} d^{4} + 8 c d^{5} x^{2} + 4 d^{6} x^{4}}"," ",0,"b**2*x**2/(2*d**3) + b*(2*a*d - 3*b*c)*log(c + d*x**2)/(2*d**4) + (-a**2*c*d**2 + 6*a*b*c**2*d - 5*b**2*c**3 + x**2*(-2*a**2*d**3 + 8*a*b*c*d**2 - 6*b**2*c**2*d))/(4*c**2*d**4 + 8*c*d**5*x**2 + 4*d**6*x**4)","A",0
191,1,223,0,1.498038," ","integrate(x**2*(b*x**2+a)**2/(d*x**2+c)**3,x)","\frac{b^{2} x}{d^{3}} - \frac{\sqrt{- \frac{1}{c^{3} d^{7}}} \left(a^{2} d^{2} + 6 a b c d - 15 b^{2} c^{2}\right) \log{\left(- c^{2} d^{3} \sqrt{- \frac{1}{c^{3} d^{7}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{c^{3} d^{7}}} \left(a^{2} d^{2} + 6 a b c d - 15 b^{2} c^{2}\right) \log{\left(c^{2} d^{3} \sqrt{- \frac{1}{c^{3} d^{7}}} + x \right)}}{16} + \frac{x^{3} \left(a^{2} d^{3} - 10 a b c d^{2} + 9 b^{2} c^{2} d\right) + x \left(- a^{2} c d^{2} - 6 a b c^{2} d + 7 b^{2} c^{3}\right)}{8 c^{3} d^{3} + 16 c^{2} d^{4} x^{2} + 8 c d^{5} x^{4}}"," ",0,"b**2*x/d**3 - sqrt(-1/(c**3*d**7))*(a**2*d**2 + 6*a*b*c*d - 15*b**2*c**2)*log(-c**2*d**3*sqrt(-1/(c**3*d**7)) + x)/16 + sqrt(-1/(c**3*d**7))*(a**2*d**2 + 6*a*b*c*d - 15*b**2*c**2)*log(c**2*d**3*sqrt(-1/(c**3*d**7)) + x)/16 + (x**3*(a**2*d**3 - 10*a*b*c*d**2 + 9*b**2*c**2*d) + x*(-a**2*c*d**2 - 6*a*b*c**2*d + 7*b**2*c**3))/(8*c**3*d**3 + 16*c**2*d**4*x**2 + 8*c*d**5*x**4)","A",0
192,1,87,0,1.273597," ","integrate(x*(b*x**2+a)**2/(d*x**2+c)**3,x)","\frac{b^{2} \log{\left(c + d x^{2} \right)}}{2 d^{3}} + \frac{- a^{2} d^{2} - 2 a b c d + 3 b^{2} c^{2} + x^{2} \left(- 4 a b d^{2} + 4 b^{2} c d\right)}{4 c^{2} d^{3} + 8 c d^{4} x^{2} + 4 d^{5} x^{4}}"," ",0,"b**2*log(c + d*x**2)/(2*d**3) + (-a**2*d**2 - 2*a*b*c*d + 3*b**2*c**2 + x**2*(-4*a*b*d**2 + 4*b**2*c*d))/(4*c**2*d**3 + 8*c*d**4*x**2 + 4*d**5*x**4)","A",0
193,1,223,0,0.995693," ","integrate((b*x**2+a)**2/(d*x**2+c)**3,x)","- \frac{\sqrt{- \frac{1}{c^{5} d^{5}}} \left(3 a^{2} d^{2} + 2 a b c d + 3 b^{2} c^{2}\right) \log{\left(- c^{3} d^{2} \sqrt{- \frac{1}{c^{5} d^{5}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{c^{5} d^{5}}} \left(3 a^{2} d^{2} + 2 a b c d + 3 b^{2} c^{2}\right) \log{\left(c^{3} d^{2} \sqrt{- \frac{1}{c^{5} d^{5}}} + x \right)}}{16} + \frac{x^{3} \left(3 a^{2} d^{3} + 2 a b c d^{2} - 5 b^{2} c^{2} d\right) + x \left(5 a^{2} c d^{2} - 2 a b c^{2} d - 3 b^{2} c^{3}\right)}{8 c^{4} d^{2} + 16 c^{3} d^{3} x^{2} + 8 c^{2} d^{4} x^{4}}"," ",0,"-sqrt(-1/(c**5*d**5))*(3*a**2*d**2 + 2*a*b*c*d + 3*b**2*c**2)*log(-c**3*d**2*sqrt(-1/(c**5*d**5)) + x)/16 + sqrt(-1/(c**5*d**5))*(3*a**2*d**2 + 2*a*b*c*d + 3*b**2*c**2)*log(c**3*d**2*sqrt(-1/(c**5*d**5)) + x)/16 + (x**3*(3*a**2*d**3 + 2*a*b*c*d**2 - 5*b**2*c**2*d) + x*(5*a**2*c*d**2 - 2*a*b*c**2*d - 3*b**2*c**3))/(8*c**4*d**2 + 16*c**3*d**3*x**2 + 8*c**2*d**4*x**4)","B",0
194,1,107,0,1.176652," ","integrate((b*x**2+a)**2/x/(d*x**2+c)**3,x)","\frac{a^{2} \log{\left(x \right)}}{c^{3}} - \frac{a^{2} \log{\left(\frac{c}{d} + x^{2} \right)}}{2 c^{3}} + \frac{3 a^{2} c d^{2} - 2 a b c^{2} d - b^{2} c^{3} + x^{2} \left(2 a^{2} d^{3} - 2 b^{2} c^{2} d\right)}{4 c^{4} d^{2} + 8 c^{3} d^{3} x^{2} + 4 c^{2} d^{4} x^{4}}"," ",0,"a**2*log(x)/c**3 - a**2*log(c/d + x**2)/(2*c**3) + (3*a**2*c*d**2 - 2*a*b*c**2*d - b**2*c**3 + x**2*(2*a**2*d**3 - 2*b**2*c**2*d))/(4*c**4*d**2 + 8*c**3*d**3*x**2 + 4*c**2*d**4*x**4)","A",0
195,1,224,0,1.198775," ","integrate((b*x**2+a)**2/x**2/(d*x**2+c)**3,x)","\frac{\sqrt{- \frac{1}{c^{7} d^{3}}} \left(15 a^{2} d^{2} - 6 a b c d - b^{2} c^{2}\right) \log{\left(- c^{4} d \sqrt{- \frac{1}{c^{7} d^{3}}} + x \right)}}{16} - \frac{\sqrt{- \frac{1}{c^{7} d^{3}}} \left(15 a^{2} d^{2} - 6 a b c d - b^{2} c^{2}\right) \log{\left(c^{4} d \sqrt{- \frac{1}{c^{7} d^{3}}} + x \right)}}{16} + \frac{- 8 a^{2} c^{2} d + x^{4} \left(- 15 a^{2} d^{3} + 6 a b c d^{2} + b^{2} c^{2} d\right) + x^{2} \left(- 25 a^{2} c d^{2} + 10 a b c^{2} d - b^{2} c^{3}\right)}{8 c^{5} d x + 16 c^{4} d^{2} x^{3} + 8 c^{3} d^{3} x^{5}}"," ",0,"sqrt(-1/(c**7*d**3))*(15*a**2*d**2 - 6*a*b*c*d - b**2*c**2)*log(-c**4*d*sqrt(-1/(c**7*d**3)) + x)/16 - sqrt(-1/(c**7*d**3))*(15*a**2*d**2 - 6*a*b*c*d - b**2*c**2)*log(c**4*d*sqrt(-1/(c**7*d**3)) + x)/16 + (-8*a**2*c**2*d + x**4*(-15*a**2*d**3 + 6*a*b*c*d**2 + b**2*c**2*d) + x**2*(-25*a**2*c*d**2 + 10*a*b*c**2*d - b**2*c**3))/(8*c**5*d*x + 16*c**4*d**2*x**3 + 8*c**3*d**3*x**5)","A",0
196,1,139,0,1.818988," ","integrate((b*x**2+a)**2/x**3/(d*x**2+c)**3,x)","- \frac{a \left(3 a d - 2 b c\right) \log{\left(x \right)}}{c^{4}} + \frac{a \left(3 a d - 2 b c\right) \log{\left(\frac{c}{d} + x^{2} \right)}}{2 c^{4}} + \frac{- 2 a^{2} c^{2} d + x^{4} \left(- 6 a^{2} d^{3} + 4 a b c d^{2}\right) + x^{2} \left(- 9 a^{2} c d^{2} + 6 a b c^{2} d - b^{2} c^{3}\right)}{4 c^{5} d x^{2} + 8 c^{4} d^{2} x^{4} + 4 c^{3} d^{3} x^{6}}"," ",0,"-a*(3*a*d - 2*b*c)*log(x)/c**4 + a*(3*a*d - 2*b*c)*log(c/d + x**2)/(2*c**4) + (-2*a**2*c**2*d + x**4*(-6*a**2*d**3 + 4*a*b*c*d**2) + x**2*(-9*a**2*c*d**2 + 6*a*b*c**2*d - b**2*c**3))/(4*c**5*d*x**2 + 8*c**4*d**2*x**4 + 4*c**3*d**3*x**6)","A",0
197,1,240,0,1.340348," ","integrate((b*x**2+a)**2/x**4/(d*x**2+c)**3,x)","- \frac{\sqrt{- \frac{1}{c^{9} d}} \left(35 a^{2} d^{2} - 30 a b c d + 3 b^{2} c^{2}\right) \log{\left(- c^{5} \sqrt{- \frac{1}{c^{9} d}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{c^{9} d}} \left(35 a^{2} d^{2} - 30 a b c d + 3 b^{2} c^{2}\right) \log{\left(c^{5} \sqrt{- \frac{1}{c^{9} d}} + x \right)}}{16} + \frac{- 8 a^{2} c^{3} + x^{6} \left(105 a^{2} d^{3} - 90 a b c d^{2} + 9 b^{2} c^{2} d\right) + x^{4} \left(175 a^{2} c d^{2} - 150 a b c^{2} d + 15 b^{2} c^{3}\right) + x^{2} \left(56 a^{2} c^{2} d - 48 a b c^{3}\right)}{24 c^{6} x^{3} + 48 c^{5} d x^{5} + 24 c^{4} d^{2} x^{7}}"," ",0,"-sqrt(-1/(c**9*d))*(35*a**2*d**2 - 30*a*b*c*d + 3*b**2*c**2)*log(-c**5*sqrt(-1/(c**9*d)) + x)/16 + sqrt(-1/(c**9*d))*(35*a**2*d**2 - 30*a*b*c*d + 3*b**2*c**2)*log(c**5*sqrt(-1/(c**9*d)) + x)/16 + (-8*a**2*c**3 + x**6*(105*a**2*d**3 - 90*a*b*c*d**2 + 9*b**2*c**2*d) + x**4*(175*a**2*c*d**2 - 150*a*b*c**2*d + 15*b**2*c**3) + x**2*(56*a**2*c**2*d - 48*a*b*c**3))/(24*c**6*x**3 + 48*c**5*d*x**5 + 24*c**4*d**2*x**7)","A",0
198,1,70,0,0.315840," ","integrate(x**5*(d*x**2+c)/(b*x**2+a),x)","- \frac{a^{2} \left(a d - b c\right) \log{\left(a + b x^{2} \right)}}{2 b^{4}} + x^{4} \left(- \frac{a d}{4 b^{2}} + \frac{c}{4 b}\right) + x^{2} \left(\frac{a^{2} d}{2 b^{3}} - \frac{a c}{2 b^{2}}\right) + \frac{d x^{6}}{6 b}"," ",0,"-a**2*(a*d - b*c)*log(a + b*x**2)/(2*b**4) + x**4*(-a*d/(4*b**2) + c/(4*b)) + x**2*(a**2*d/(2*b**3) - a*c/(2*b**2)) + d*x**6/(6*b)","A",0
199,1,153,0,0.363557," ","integrate(x**4*(d*x**2+c)/(b*x**2+a),x)","x^{3} \left(- \frac{a d}{3 b^{2}} + \frac{c}{3 b}\right) + x \left(\frac{a^{2} d}{b^{3}} - \frac{a c}{b^{2}}\right) + \frac{\sqrt{- \frac{a^{3}}{b^{7}}} \left(a d - b c\right) \log{\left(- \frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}} \left(a d - b c\right)}{a^{2} d - a b c} + x \right)}}{2} - \frac{\sqrt{- \frac{a^{3}}{b^{7}}} \left(a d - b c\right) \log{\left(\frac{b^{3} \sqrt{- \frac{a^{3}}{b^{7}}} \left(a d - b c\right)}{a^{2} d - a b c} + x \right)}}{2} + \frac{d x^{5}}{5 b}"," ",0,"x**3*(-a*d/(3*b**2) + c/(3*b)) + x*(a**2*d/b**3 - a*c/b**2) + sqrt(-a**3/b**7)*(a*d - b*c)*log(-b**3*sqrt(-a**3/b**7)*(a*d - b*c)/(a**2*d - a*b*c) + x)/2 - sqrt(-a**3/b**7)*(a*d - b*c)*log(b**3*sqrt(-a**3/b**7)*(a*d - b*c)/(a**2*d - a*b*c) + x)/2 + d*x**5/(5*b)","B",0
200,1,46,0,0.279463," ","integrate(x**3*(d*x**2+c)/(b*x**2+a),x)","\frac{a \left(a d - b c\right) \log{\left(a + b x^{2} \right)}}{2 b^{3}} + x^{2} \left(- \frac{a d}{2 b^{2}} + \frac{c}{2 b}\right) + \frac{d x^{4}}{4 b}"," ",0,"a*(a*d - b*c)*log(a + b*x**2)/(2*b**3) + x**2*(-a*d/(2*b**2) + c/(2*b)) + d*x**4/(4*b)","A",0
201,1,90,0,0.327239," ","integrate(x**2*(d*x**2+c)/(b*x**2+a),x)","x \left(- \frac{a d}{b^{2}} + \frac{c}{b}\right) - \frac{\sqrt{- \frac{a}{b^{5}}} \left(a d - b c\right) \log{\left(- b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{2} + \frac{\sqrt{- \frac{a}{b^{5}}} \left(a d - b c\right) \log{\left(b^{2} \sqrt{- \frac{a}{b^{5}}} + x \right)}}{2} + \frac{d x^{3}}{3 b}"," ",0,"x*(-a*d/b**2 + c/b) - sqrt(-a/b**5)*(a*d - b*c)*log(-b**2*sqrt(-a/b**5) + x)/2 + sqrt(-a/b**5)*(a*d - b*c)*log(b**2*sqrt(-a/b**5) + x)/2 + d*x**3/(3*b)","A",0
202,1,27,0,0.242417," ","integrate(x*(d*x**2+c)/(b*x**2+a),x)","\frac{d x^{2}}{2 b} - \frac{\left(a d - b c\right) \log{\left(a + b x^{2} \right)}}{2 b^{2}}"," ",0,"d*x**2/(2*b) - (a*d - b*c)*log(a + b*x**2)/(2*b**2)","A",0
203,1,82,0,0.277044," ","integrate((d*x**2+c)/(b*x**2+a),x)","\frac{\sqrt{- \frac{1}{a b^{3}}} \left(a d - b c\right) \log{\left(- a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a b^{3}}} \left(a d - b c\right) \log{\left(a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{2} + \frac{d x}{b}"," ",0,"sqrt(-1/(a*b**3))*(a*d - b*c)*log(-a*b*sqrt(-1/(a*b**3)) + x)/2 - sqrt(-1/(a*b**3))*(a*d - b*c)*log(a*b*sqrt(-1/(a*b**3)) + x)/2 + d*x/b","B",0
204,1,26,0,0.672861," ","integrate((d*x**2+c)/x/(b*x**2+a),x)","\frac{c \log{\left(x \right)}}{a} + \frac{\left(a d - b c\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a b}"," ",0,"c*log(x)/a + (a*d - b*c)*log(a/b + x**2)/(2*a*b)","A",0
205,1,82,0,0.329442," ","integrate((d*x**2+c)/x**2/(b*x**2+a),x)","- \frac{\sqrt{- \frac{1}{a^{3} b}} \left(a d - b c\right) \log{\left(- a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a^{3} b}} \left(a d - b c\right) \log{\left(a^{2} \sqrt{- \frac{1}{a^{3} b}} + x \right)}}{2} - \frac{c}{a x}"," ",0,"-sqrt(-1/(a**3*b))*(a*d - b*c)*log(-a**2*sqrt(-1/(a**3*b)) + x)/2 + sqrt(-1/(a**3*b))*(a*d - b*c)*log(a**2*sqrt(-1/(a**3*b)) + x)/2 - c/(a*x)","B",0
206,1,41,0,0.691560," ","integrate((d*x**2+c)/x**3/(b*x**2+a),x)","- \frac{c}{2 a x^{2}} + \frac{\left(a d - b c\right) \log{\left(x \right)}}{a^{2}} - \frac{\left(a d - b c\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"-c/(2*a*x**2) + (a*d - b*c)*log(x)/a**2 - (a*d - b*c)*log(a/b + x**2)/(2*a**2)","A",0
207,1,129,0,0.407635," ","integrate((d*x**2+c)/x**4/(b*x**2+a),x)","\frac{\sqrt{- \frac{b}{a^{5}}} \left(a d - b c\right) \log{\left(- \frac{a^{3} \sqrt{- \frac{b}{a^{5}}} \left(a d - b c\right)}{a b d - b^{2} c} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{a^{5}}} \left(a d - b c\right) \log{\left(\frac{a^{3} \sqrt{- \frac{b}{a^{5}}} \left(a d - b c\right)}{a b d - b^{2} c} + x \right)}}{2} + \frac{- a c + x^{2} \left(- 3 a d + 3 b c\right)}{3 a^{2} x^{3}}"," ",0,"sqrt(-b/a**5)*(a*d - b*c)*log(-a**3*sqrt(-b/a**5)*(a*d - b*c)/(a*b*d - b**2*c) + x)/2 - sqrt(-b/a**5)*(a*d - b*c)*log(a**3*sqrt(-b/a**5)*(a*d - b*c)/(a*b*d - b**2*c) + x)/2 + (-a*c + x**2*(-3*a*d + 3*b*c))/(3*a**2*x**3)","B",0
208,1,122,0,0.459793," ","integrate(x**5*(d*x**2+c)**2/(b*x**2+a),x)","\frac{a^{2} \left(a d - b c\right)^{2} \log{\left(a + b x^{2} \right)}}{2 b^{5}} + x^{6} \left(- \frac{a d^{2}}{6 b^{2}} + \frac{c d}{3 b}\right) + x^{4} \left(\frac{a^{2} d^{2}}{4 b^{3}} - \frac{a c d}{2 b^{2}} + \frac{c^{2}}{4 b}\right) + x^{2} \left(- \frac{a^{3} d^{2}}{2 b^{4}} + \frac{a^{2} c d}{b^{3}} - \frac{a c^{2}}{2 b^{2}}\right) + \frac{d^{2} x^{8}}{8 b}"," ",0,"a**2*(a*d - b*c)**2*log(a + b*x**2)/(2*b**5) + x**6*(-a*d**2/(6*b**2) + c*d/(3*b)) + x**4*(a**2*d**2/(4*b**3) - a*c*d/(2*b**2) + c**2/(4*b)) + x**2*(-a**3*d**2/(2*b**4) + a**2*c*d/b**3 - a*c**2/(2*b**2)) + d**2*x**8/(8*b)","A",0
209,1,246,0,0.540062," ","integrate(x**4*(d*x**2+c)**2/(b*x**2+a),x)","x^{5} \left(- \frac{a d^{2}}{5 b^{2}} + \frac{2 c d}{5 b}\right) + x^{3} \left(\frac{a^{2} d^{2}}{3 b^{3}} - \frac{2 a c d}{3 b^{2}} + \frac{c^{2}}{3 b}\right) + x \left(- \frac{a^{3} d^{2}}{b^{4}} + \frac{2 a^{2} c d}{b^{3}} - \frac{a c^{2}}{b^{2}}\right) - \frac{\sqrt{- \frac{a^{3}}{b^{9}}} \left(a d - b c\right)^{2} \log{\left(- \frac{b^{4} \sqrt{- \frac{a^{3}}{b^{9}}} \left(a d - b c\right)^{2}}{a^{3} d^{2} - 2 a^{2} b c d + a b^{2} c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{a^{3}}{b^{9}}} \left(a d - b c\right)^{2} \log{\left(\frac{b^{4} \sqrt{- \frac{a^{3}}{b^{9}}} \left(a d - b c\right)^{2}}{a^{3} d^{2} - 2 a^{2} b c d + a b^{2} c^{2}} + x \right)}}{2} + \frac{d^{2} x^{7}}{7 b}"," ",0,"x**5*(-a*d**2/(5*b**2) + 2*c*d/(5*b)) + x**3*(a**2*d**2/(3*b**3) - 2*a*c*d/(3*b**2) + c**2/(3*b)) + x*(-a**3*d**2/b**4 + 2*a**2*c*d/b**3 - a*c**2/b**2) - sqrt(-a**3/b**9)*(a*d - b*c)**2*log(-b**4*sqrt(-a**3/b**9)*(a*d - b*c)**2/(a**3*d**2 - 2*a**2*b*c*d + a*b**2*c**2) + x)/2 + sqrt(-a**3/b**9)*(a*d - b*c)**2*log(b**4*sqrt(-a**3/b**9)*(a*d - b*c)**2/(a**3*d**2 - 2*a**2*b*c*d + a*b**2*c**2) + x)/2 + d**2*x**7/(7*b)","B",0
210,1,83,0,0.420192," ","integrate(x**3*(d*x**2+c)**2/(b*x**2+a),x)","- \frac{a \left(a d - b c\right)^{2} \log{\left(a + b x^{2} \right)}}{2 b^{4}} + x^{4} \left(- \frac{a d^{2}}{4 b^{2}} + \frac{c d}{2 b}\right) + x^{2} \left(\frac{a^{2} d^{2}}{2 b^{3}} - \frac{a c d}{b^{2}} + \frac{c^{2}}{2 b}\right) + \frac{d^{2} x^{6}}{6 b}"," ",0,"-a*(a*d - b*c)**2*log(a + b*x**2)/(2*b**4) + x**4*(-a*d**2/(4*b**2) + c*d/(2*b)) + x**2*(a**2*d**2/(2*b**3) - a*c*d/b**2 + c**2/(2*b)) + d**2*x**6/(6*b)","A",0
211,1,194,0,0.489268," ","integrate(x**2*(d*x**2+c)**2/(b*x**2+a),x)","x^{3} \left(- \frac{a d^{2}}{3 b^{2}} + \frac{2 c d}{3 b}\right) + x \left(\frac{a^{2} d^{2}}{b^{3}} - \frac{2 a c d}{b^{2}} + \frac{c^{2}}{b}\right) + \frac{\sqrt{- \frac{a}{b^{7}}} \left(a d - b c\right)^{2} \log{\left(- \frac{b^{3} \sqrt{- \frac{a}{b^{7}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} - \frac{\sqrt{- \frac{a}{b^{7}}} \left(a d - b c\right)^{2} \log{\left(\frac{b^{3} \sqrt{- \frac{a}{b^{7}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{d^{2} x^{5}}{5 b}"," ",0,"x**3*(-a*d**2/(3*b**2) + 2*c*d/(3*b)) + x*(a**2*d**2/b**3 - 2*a*c*d/b**2 + c**2/b) + sqrt(-a/b**7)*(a*d - b*c)**2*log(-b**3*sqrt(-a/b**7)*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 - sqrt(-a/b**7)*(a*d - b*c)**2*log(b**3*sqrt(-a/b**7)*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + d**2*x**5/(5*b)","B",0
212,1,49,0,0.367522," ","integrate(x*(d*x**2+c)**2/(b*x**2+a),x)","x^{2} \left(- \frac{a d^{2}}{2 b^{2}} + \frac{c d}{b}\right) + \frac{d^{2} x^{4}}{4 b} + \frac{\left(a d - b c\right)^{2} \log{\left(a + b x^{2} \right)}}{2 b^{3}}"," ",0,"x**2*(-a*d**2/(2*b**2) + c*d/b) + d**2*x**4/(4*b) + (a*d - b*c)**2*log(a + b*x**2)/(2*b**3)","A",0
213,1,172,0,0.437025," ","integrate((d*x**2+c)**2/(b*x**2+a),x)","x \left(- \frac{a d^{2}}{b^{2}} + \frac{2 c d}{b}\right) - \frac{\sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2} \log{\left(- \frac{a b^{2} \sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2} \log{\left(\frac{a b^{2} \sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{d^{2} x^{3}}{3 b}"," ",0,"x*(-a*d**2/b**2 + 2*c*d/b) - sqrt(-1/(a*b**5))*(a*d - b*c)**2*log(-a*b**2*sqrt(-1/(a*b**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + sqrt(-1/(a*b**5))*(a*d - b*c)**2*log(a*b**2*sqrt(-1/(a*b**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + d**2*x**3/(3*b)","B",0
214,1,41,0,1.227368," ","integrate((d*x**2+c)**2/x/(b*x**2+a),x)","\frac{d^{2} x^{2}}{2 b} + \frac{c^{2} \log{\left(x \right)}}{a} - \frac{\left(a d - b c\right)^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a b^{2}}"," ",0,"d**2*x**2/(2*b) + c**2*log(x)/a - (a*d - b*c)**2*log(a/b + x**2)/(2*a*b**2)","A",0
215,1,165,0,0.555263," ","integrate((d*x**2+c)**2/x**2/(b*x**2+a),x)","\frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d - b c\right)^{2} \log{\left(- \frac{a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d - b c\right)^{2} \log{\left(\frac{a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{d^{2} x}{b} - \frac{c^{2}}{a x}"," ",0,"sqrt(-1/(a**3*b**3))*(a*d - b*c)**2*log(-a**2*b*sqrt(-1/(a**3*b**3))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 - sqrt(-1/(a**3*b**3))*(a*d - b*c)**2*log(a**2*b*sqrt(-1/(a**3*b**3))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + d**2*x/b - c**2/(a*x)","B",0
216,1,49,0,1.390756," ","integrate((d*x**2+c)**2/x**3/(b*x**2+a),x)","- \frac{c^{2}}{2 a x^{2}} + \frac{c \left(2 a d - b c\right) \log{\left(x \right)}}{a^{2}} + \frac{\left(a d - b c\right)^{2} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2} b}"," ",0,"-c**2/(2*a*x**2) + c*(2*a*d - b*c)*log(x)/a**2 + (a*d - b*c)**2*log(a/b + x**2)/(2*a**2*b)","A",0
217,1,172,0,0.672676," ","integrate((d*x**2+c)**2/x**4/(b*x**2+a),x)","- \frac{\sqrt{- \frac{1}{a^{5} b}} \left(a d - b c\right)^{2} \log{\left(- \frac{a^{3} \sqrt{- \frac{1}{a^{5} b}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a^{5} b}} \left(a d - b c\right)^{2} \log{\left(\frac{a^{3} \sqrt{- \frac{1}{a^{5} b}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{- a c^{2} + x^{2} \left(- 6 a c d + 3 b c^{2}\right)}{3 a^{2} x^{3}}"," ",0,"-sqrt(-1/(a**5*b))*(a*d - b*c)**2*log(-a**3*sqrt(-1/(a**5*b))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + sqrt(-1/(a**5*b))*(a*d - b*c)**2*log(a**3*sqrt(-1/(a**5*b))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + (-a*c**2 + x**2*(-6*a*c*d + 3*b*c**2))/(3*a**2*x**3)","B",0
218,1,201,0,0.603238," ","integrate(x**5*(d*x**2+c)**3/(b*x**2+a),x)","- \frac{a^{2} \left(a d - b c\right)^{3} \log{\left(a + b x^{2} \right)}}{2 b^{6}} + x^{8} \left(- \frac{a d^{3}}{8 b^{2}} + \frac{3 c d^{2}}{8 b}\right) + x^{6} \left(\frac{a^{2} d^{3}}{6 b^{3}} - \frac{a c d^{2}}{2 b^{2}} + \frac{c^{2} d}{2 b}\right) + x^{4} \left(- \frac{a^{3} d^{3}}{4 b^{4}} + \frac{3 a^{2} c d^{2}}{4 b^{3}} - \frac{3 a c^{2} d}{4 b^{2}} + \frac{c^{3}}{4 b}\right) + x^{2} \left(\frac{a^{4} d^{3}}{2 b^{5}} - \frac{3 a^{3} c d^{2}}{2 b^{4}} + \frac{3 a^{2} c^{2} d}{2 b^{3}} - \frac{a c^{3}}{2 b^{2}}\right) + \frac{d^{3} x^{10}}{10 b}"," ",0,"-a**2*(a*d - b*c)**3*log(a + b*x**2)/(2*b**6) + x**8*(-a*d**3/(8*b**2) + 3*c*d**2/(8*b)) + x**6*(a**2*d**3/(6*b**3) - a*c*d**2/(2*b**2) + c**2*d/(2*b)) + x**4*(-a**3*d**3/(4*b**4) + 3*a**2*c*d**2/(4*b**3) - 3*a*c**2*d/(4*b**2) + c**3/(4*b)) + x**2*(a**4*d**3/(2*b**5) - 3*a**3*c*d**2/(2*b**4) + 3*a**2*c**2*d/(2*b**3) - a*c**3/(2*b**2)) + d**3*x**10/(10*b)","A",0
219,1,343,0,0.721284," ","integrate(x**4*(d*x**2+c)**3/(b*x**2+a),x)","x^{7} \left(- \frac{a d^{3}}{7 b^{2}} + \frac{3 c d^{2}}{7 b}\right) + x^{5} \left(\frac{a^{2} d^{3}}{5 b^{3}} - \frac{3 a c d^{2}}{5 b^{2}} + \frac{3 c^{2} d}{5 b}\right) + x^{3} \left(- \frac{a^{3} d^{3}}{3 b^{4}} + \frac{a^{2} c d^{2}}{b^{3}} - \frac{a c^{2} d}{b^{2}} + \frac{c^{3}}{3 b}\right) + x \left(\frac{a^{4} d^{3}}{b^{5}} - \frac{3 a^{3} c d^{2}}{b^{4}} + \frac{3 a^{2} c^{2} d}{b^{3}} - \frac{a c^{3}}{b^{2}}\right) + \frac{\sqrt{- \frac{a^{3}}{b^{11}}} \left(a d - b c\right)^{3} \log{\left(- \frac{b^{5} \sqrt{- \frac{a^{3}}{b^{11}}} \left(a d - b c\right)^{3}}{a^{4} d^{3} - 3 a^{3} b c d^{2} + 3 a^{2} b^{2} c^{2} d - a b^{3} c^{3}} + x \right)}}{2} - \frac{\sqrt{- \frac{a^{3}}{b^{11}}} \left(a d - b c\right)^{3} \log{\left(\frac{b^{5} \sqrt{- \frac{a^{3}}{b^{11}}} \left(a d - b c\right)^{3}}{a^{4} d^{3} - 3 a^{3} b c d^{2} + 3 a^{2} b^{2} c^{2} d - a b^{3} c^{3}} + x \right)}}{2} + \frac{d^{3} x^{9}}{9 b}"," ",0,"x**7*(-a*d**3/(7*b**2) + 3*c*d**2/(7*b)) + x**5*(a**2*d**3/(5*b**3) - 3*a*c*d**2/(5*b**2) + 3*c**2*d/(5*b)) + x**3*(-a**3*d**3/(3*b**4) + a**2*c*d**2/b**3 - a*c**2*d/b**2 + c**3/(3*b)) + x*(a**4*d**3/b**5 - 3*a**3*c*d**2/b**4 + 3*a**2*c**2*d/b**3 - a*c**3/b**2) + sqrt(-a**3/b**11)*(a*d - b*c)**3*log(-b**5*sqrt(-a**3/b**11)*(a*d - b*c)**3/(a**4*d**3 - 3*a**3*b*c*d**2 + 3*a**2*b**2*c**2*d - a*b**3*c**3) + x)/2 - sqrt(-a**3/b**11)*(a*d - b*c)**3*log(b**5*sqrt(-a**3/b**11)*(a*d - b*c)**3/(a**4*d**3 - 3*a**3*b*c*d**2 + 3*a**2*b**2*c**2*d - a*b**3*c**3) + x)/2 + d**3*x**9/(9*b)","B",0
220,1,144,0,0.548371," ","integrate(x**3*(d*x**2+c)**3/(b*x**2+a),x)","\frac{a \left(a d - b c\right)^{3} \log{\left(a + b x^{2} \right)}}{2 b^{5}} + x^{6} \left(- \frac{a d^{3}}{6 b^{2}} + \frac{c d^{2}}{2 b}\right) + x^{4} \left(\frac{a^{2} d^{3}}{4 b^{3}} - \frac{3 a c d^{2}}{4 b^{2}} + \frac{3 c^{2} d}{4 b}\right) + x^{2} \left(- \frac{a^{3} d^{3}}{2 b^{4}} + \frac{3 a^{2} c d^{2}}{2 b^{3}} - \frac{3 a c^{2} d}{2 b^{2}} + \frac{c^{3}}{2 b}\right) + \frac{d^{3} x^{8}}{8 b}"," ",0,"a*(a*d - b*c)**3*log(a + b*x**2)/(2*b**5) + x**6*(-a*d**3/(6*b**2) + c*d**2/(2*b)) + x**4*(a**2*d**3/(4*b**3) - 3*a*c*d**2/(4*b**2) + 3*c**2*d/(4*b)) + x**2*(-a**3*d**3/(2*b**4) + 3*a**2*c*d**2/(2*b**3) - 3*a*c**2*d/(2*b**2) + c**3/(2*b)) + d**3*x**8/(8*b)","A",0
221,1,274,0,0.665848," ","integrate(x**2*(d*x**2+c)**3/(b*x**2+a),x)","x^{5} \left(- \frac{a d^{3}}{5 b^{2}} + \frac{3 c d^{2}}{5 b}\right) + x^{3} \left(\frac{a^{2} d^{3}}{3 b^{3}} - \frac{a c d^{2}}{b^{2}} + \frac{c^{2} d}{b}\right) + x \left(- \frac{a^{3} d^{3}}{b^{4}} + \frac{3 a^{2} c d^{2}}{b^{3}} - \frac{3 a c^{2} d}{b^{2}} + \frac{c^{3}}{b}\right) - \frac{\sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right)^{3} \log{\left(- \frac{b^{4} \sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{\sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right)^{3} \log{\left(\frac{b^{4} \sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{d^{3} x^{7}}{7 b}"," ",0,"x**5*(-a*d**3/(5*b**2) + 3*c*d**2/(5*b)) + x**3*(a**2*d**3/(3*b**3) - a*c*d**2/b**2 + c**2*d/b) + x*(-a**3*d**3/b**4 + 3*a**2*c*d**2/b**3 - 3*a*c**2*d/b**2 + c**3/b) - sqrt(-a/b**9)*(a*d - b*c)**3*log(-b**4*sqrt(-a/b**9)*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + sqrt(-a/b**9)*(a*d - b*c)**3*log(b**4*sqrt(-a/b**9)*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + d**3*x**7/(7*b)","B",0
222,1,94,0,0.494164," ","integrate(x*(d*x**2+c)**3/(b*x**2+a),x)","x^{4} \left(- \frac{a d^{3}}{4 b^{2}} + \frac{3 c d^{2}}{4 b}\right) + x^{2} \left(\frac{a^{2} d^{3}}{2 b^{3}} - \frac{3 a c d^{2}}{2 b^{2}} + \frac{3 c^{2} d}{2 b}\right) + \frac{d^{3} x^{6}}{6 b} - \frac{\left(a d - b c\right)^{3} \log{\left(a + b x^{2} \right)}}{2 b^{4}}"," ",0,"x**4*(-a*d**3/(4*b**2) + 3*c*d**2/(4*b)) + x**2*(a**2*d**3/(2*b**3) - 3*a*c*d**2/(2*b**2) + 3*c**2*d/(2*b)) + d**3*x**6/(6*b) - (a*d - b*c)**3*log(a + b*x**2)/(2*b**4)","A",0
223,1,238,0,0.603346," ","integrate((d*x**2+c)**3/(b*x**2+a),x)","x^{3} \left(- \frac{a d^{3}}{3 b^{2}} + \frac{c d^{2}}{b}\right) + x \left(\frac{a^{2} d^{3}}{b^{3}} - \frac{3 a c d^{2}}{b^{2}} + \frac{3 c^{2} d}{b}\right) + \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3} \log{\left(- \frac{a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3} \log{\left(\frac{a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{d^{3} x^{5}}{5 b}"," ",0,"x**3*(-a*d**3/(3*b**2) + c*d**2/b) + x*(a**2*d**3/b**3 - 3*a*c*d**2/b**2 + 3*c**2*d/b) + sqrt(-1/(a*b**7))*(a*d - b*c)**3*log(-a*b**3*sqrt(-1/(a*b**7))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 - sqrt(-1/(a*b**7))*(a*d - b*c)**3*log(a*b**3*sqrt(-1/(a*b**7))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + d**3*x**5/(5*b)","B",0
224,1,65,0,1.774496," ","integrate((d*x**2+c)**3/x/(b*x**2+a),x)","x^{2} \left(- \frac{a d^{3}}{2 b^{2}} + \frac{3 c d^{2}}{2 b}\right) + \frac{d^{3} x^{4}}{4 b} + \frac{c^{3} \log{\left(x \right)}}{a} + \frac{\left(a d - b c\right)^{3} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a b^{3}}"," ",0,"x**2*(-a*d**3/(2*b**2) + 3*c*d**2/(2*b)) + d**3*x**4/(4*b) + c**3*log(x)/a + (a*d - b*c)**3*log(a/b + x**2)/(2*a*b**3)","A",0
225,1,221,0,0.807154," ","integrate((d*x**2+c)**3/x**2/(b*x**2+a),x)","x \left(- \frac{a d^{3}}{b^{2}} + \frac{3 c d^{2}}{b}\right) - \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right)^{3} \log{\left(- \frac{a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right)^{3} \log{\left(\frac{a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{d^{3} x^{3}}{3 b} - \frac{c^{3}}{a x}"," ",0,"x*(-a*d**3/b**2 + 3*c*d**2/b) - sqrt(-1/(a**3*b**5))*(a*d - b*c)**3*log(-a**2*b**2*sqrt(-1/(a**3*b**5))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + sqrt(-1/(a**3*b**5))*(a*d - b*c)**3*log(a**2*b**2*sqrt(-1/(a**3*b**5))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + d**3*x**3/(3*b) - c**3/(a*x)","B",0
226,1,63,0,2.213682," ","integrate((d*x**2+c)**3/x**3/(b*x**2+a),x)","\frac{d^{3} x^{2}}{2 b} - \frac{c^{3}}{2 a x^{2}} + \frac{c^{2} \left(3 a d - b c\right) \log{\left(x \right)}}{a^{2}} - \frac{\left(a d - b c\right)^{3} \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2} b^{2}}"," ",0,"d**3*x**2/(2*b) - c**3/(2*a*x**2) + c**2*(3*a*d - b*c)*log(x)/a**2 - (a*d - b*c)**3*log(a/b + x**2)/(2*a**2*b**2)","A",0
227,1,221,0,1.129780," ","integrate((d*x**2+c)**3/x**4/(b*x**2+a),x)","\frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right)^{3} \log{\left(- \frac{a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right)^{3} \log{\left(\frac{a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{d^{3} x}{b} + \frac{- a c^{3} + x^{2} \left(- 9 a c^{2} d + 3 b c^{3}\right)}{3 a^{2} x^{3}}"," ",0,"sqrt(-1/(a**5*b**3))*(a*d - b*c)**3*log(-a**3*b*sqrt(-1/(a**5*b**3))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 - sqrt(-1/(a**5*b**3))*(a*d - b*c)**3*log(a**3*b*sqrt(-1/(a**5*b**3))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + d**3*x/b + (-a*c**3 + x**2*(-9*a*c**2*d + 3*b*c**3))/(3*a**2*x**3)","B",0
228,1,201,0,179.212506," ","integrate(x**5/(b*x**2+a)/(d*x**2+c),x)","- \frac{a^{2} \log{\left(x^{2} + \frac{\frac{a^{4} d^{3}}{b \left(a d - b c\right)} - \frac{2 a^{3} c d^{2}}{a d - b c} + \frac{a^{2} b c^{2} d}{a d - b c} + a^{2} c d + a b c^{2}}{a^{2} d^{2} + b^{2} c^{2}} \right)}}{2 b^{2} \left(a d - b c\right)} + \frac{c^{2} \log{\left(x^{2} + \frac{- \frac{a^{2} b c^{2} d}{a d - b c} + a^{2} c d + \frac{2 a b^{2} c^{3}}{a d - b c} + a b c^{2} - \frac{b^{3} c^{4}}{d \left(a d - b c\right)}}{a^{2} d^{2} + b^{2} c^{2}} \right)}}{2 d^{2} \left(a d - b c\right)} + \frac{x^{2}}{2 b d}"," ",0,"-a**2*log(x**2 + (a**4*d**3/(b*(a*d - b*c)) - 2*a**3*c*d**2/(a*d - b*c) + a**2*b*c**2*d/(a*d - b*c) + a**2*c*d + a*b*c**2)/(a**2*d**2 + b**2*c**2))/(2*b**2*(a*d - b*c)) + c**2*log(x**2 + (-a**2*b*c**2*d/(a*d - b*c) + a**2*c*d + 2*a*b**2*c**3/(a*d - b*c) + a*b*c**2 - b**3*c**4/(d*(a*d - b*c)))/(a**2*d**2 + b**2*c**2))/(2*d**2*(a*d - b*c)) + x**2/(2*b*d)","B",0
229,1,921,0,12.394741," ","integrate(x**4/(b*x**2+a)/(d*x**2+c),x)","- \frac{\sqrt{- \frac{a^{3}}{b^{3}}} \log{\left(x + \frac{- \frac{a^{4} d^{4} \sqrt{- \frac{a^{3}}{b^{3}}}}{a d - b c} - \frac{a^{3} b^{3} d^{6} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} b^{4} c d^{5} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a b^{5} c^{2} d^{4} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{6} c^{3} d^{3} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{4} c^{4} \sqrt{- \frac{a^{3}}{b^{3}}}}{a d - b c}}{a^{3} c d^{2} + a^{2} b c^{2} d + a b^{2} c^{3}} \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{a^{3}}{b^{3}}} \log{\left(x + \frac{\frac{a^{4} d^{4} \sqrt{- \frac{a^{3}}{b^{3}}}}{a d - b c} + \frac{a^{3} b^{3} d^{6} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} b^{4} c d^{5} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a b^{5} c^{2} d^{4} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{6} c^{3} d^{3} \left(- \frac{a^{3}}{b^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{4} c^{4} \sqrt{- \frac{a^{3}}{b^{3}}}}{a d - b c}}{a^{3} c d^{2} + a^{2} b c^{2} d + a b^{2} c^{3}} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{c^{3}}{d^{3}}} \log{\left(x + \frac{- \frac{a^{4} d^{4} \sqrt{- \frac{c^{3}}{d^{3}}}}{a d - b c} - \frac{a^{3} b^{3} d^{6} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} b^{4} c d^{5} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a b^{5} c^{2} d^{4} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{6} c^{3} d^{3} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{4} c^{4} \sqrt{- \frac{c^{3}}{d^{3}}}}{a d - b c}}{a^{3} c d^{2} + a^{2} b c^{2} d + a b^{2} c^{3}} \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{c^{3}}{d^{3}}} \log{\left(x + \frac{\frac{a^{4} d^{4} \sqrt{- \frac{c^{3}}{d^{3}}}}{a d - b c} + \frac{a^{3} b^{3} d^{6} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} b^{4} c d^{5} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a b^{5} c^{2} d^{4} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{6} c^{3} d^{3} \left(- \frac{c^{3}}{d^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{4} c^{4} \sqrt{- \frac{c^{3}}{d^{3}}}}{a d - b c}}{a^{3} c d^{2} + a^{2} b c^{2} d + a b^{2} c^{3}} \right)}}{2 \left(a d - b c\right)} + \frac{x}{b d}"," ",0,"-sqrt(-a**3/b**3)*log(x + (-a**4*d**4*sqrt(-a**3/b**3)/(a*d - b*c) - a**3*b**3*d**6*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 + a**2*b**4*c*d**5*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 + a*b**5*c**2*d**4*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 - b**6*c**3*d**3*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 - b**4*c**4*sqrt(-a**3/b**3)/(a*d - b*c))/(a**3*c*d**2 + a**2*b*c**2*d + a*b**2*c**3))/(2*(a*d - b*c)) + sqrt(-a**3/b**3)*log(x + (a**4*d**4*sqrt(-a**3/b**3)/(a*d - b*c) + a**3*b**3*d**6*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 - a**2*b**4*c*d**5*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 - a*b**5*c**2*d**4*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 + b**6*c**3*d**3*(-a**3/b**3)**(3/2)/(a*d - b*c)**3 + b**4*c**4*sqrt(-a**3/b**3)/(a*d - b*c))/(a**3*c*d**2 + a**2*b*c**2*d + a*b**2*c**3))/(2*(a*d - b*c)) - sqrt(-c**3/d**3)*log(x + (-a**4*d**4*sqrt(-c**3/d**3)/(a*d - b*c) - a**3*b**3*d**6*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 + a**2*b**4*c*d**5*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 + a*b**5*c**2*d**4*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 - b**6*c**3*d**3*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 - b**4*c**4*sqrt(-c**3/d**3)/(a*d - b*c))/(a**3*c*d**2 + a**2*b*c**2*d + a*b**2*c**3))/(2*(a*d - b*c)) + sqrt(-c**3/d**3)*log(x + (a**4*d**4*sqrt(-c**3/d**3)/(a*d - b*c) + a**3*b**3*d**6*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 - a**2*b**4*c*d**5*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 - a*b**5*c**2*d**4*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 + b**6*c**3*d**3*(-c**3/d**3)**(3/2)/(a*d - b*c)**3 + b**4*c**4*sqrt(-c**3/d**3)/(a*d - b*c))/(a**3*c*d**2 + a**2*b*c**2*d + a*b**2*c**3))/(2*(a*d - b*c)) + x/(b*d)","B",0
230,1,144,0,2.341233," ","integrate(x**3/(b*x**2+a)/(d*x**2+c),x)","\frac{a \log{\left(x^{2} + \frac{\frac{a^{3} d^{2}}{b \left(a d - b c\right)} - \frac{2 a^{2} c d}{a d - b c} + \frac{a b c^{2}}{a d - b c} + 2 a c}{a d + b c} \right)}}{2 b \left(a d - b c\right)} - \frac{c \log{\left(x^{2} + \frac{- \frac{a^{2} c d}{a d - b c} + \frac{2 a b c^{2}}{a d - b c} + 2 a c - \frac{b^{2} c^{3}}{d \left(a d - b c\right)}}{a d + b c} \right)}}{2 d \left(a d - b c\right)}"," ",0,"a*log(x**2 + (a**3*d**2/(b*(a*d - b*c)) - 2*a**2*c*d/(a*d - b*c) + a*b*c**2/(a*d - b*c) + 2*a*c)/(a*d + b*c))/(2*b*(a*d - b*c)) - c*log(x**2 + (-a**2*c*d/(a*d - b*c) + 2*a*b*c**2/(a*d - b*c) + 2*a*c - b**2*c**3/(d*(a*d - b*c)))/(a*d + b*c))/(2*d*(a*d - b*c))","B",0
231,1,570,0,2.182706," ","integrate(x**2/(b*x**2+a)/(d*x**2+c),x)","\frac{\sqrt{- \frac{a}{b}} \log{\left(- \frac{2 a^{2} b d^{3} \left(- \frac{a}{b}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{4 a b^{2} c d^{2} \left(- \frac{a}{b}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a d \sqrt{- \frac{a}{b}}}{a d - b c} - \frac{2 b^{3} c^{2} d \left(- \frac{a}{b}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b c \sqrt{- \frac{a}{b}}}{a d - b c} + x \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{a}{b}} \log{\left(\frac{2 a^{2} b d^{3} \left(- \frac{a}{b}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{4 a b^{2} c d^{2} \left(- \frac{a}{b}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a d \sqrt{- \frac{a}{b}}}{a d - b c} + \frac{2 b^{3} c^{2} d \left(- \frac{a}{b}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b c \sqrt{- \frac{a}{b}}}{a d - b c} + x \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{c}{d}} \log{\left(- \frac{2 a^{2} b d^{3} \left(- \frac{c}{d}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{4 a b^{2} c d^{2} \left(- \frac{c}{d}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a d \sqrt{- \frac{c}{d}}}{a d - b c} - \frac{2 b^{3} c^{2} d \left(- \frac{c}{d}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b c \sqrt{- \frac{c}{d}}}{a d - b c} + x \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{c}{d}} \log{\left(\frac{2 a^{2} b d^{3} \left(- \frac{c}{d}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{4 a b^{2} c d^{2} \left(- \frac{c}{d}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a d \sqrt{- \frac{c}{d}}}{a d - b c} + \frac{2 b^{3} c^{2} d \left(- \frac{c}{d}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b c \sqrt{- \frac{c}{d}}}{a d - b c} + x \right)}}{2 \left(a d - b c\right)}"," ",0,"sqrt(-a/b)*log(-2*a**2*b*d**3*(-a/b)**(3/2)/(a*d - b*c)**3 + 4*a*b**2*c*d**2*(-a/b)**(3/2)/(a*d - b*c)**3 - a*d*sqrt(-a/b)/(a*d - b*c) - 2*b**3*c**2*d*(-a/b)**(3/2)/(a*d - b*c)**3 - b*c*sqrt(-a/b)/(a*d - b*c) + x)/(2*(a*d - b*c)) - sqrt(-a/b)*log(2*a**2*b*d**3*(-a/b)**(3/2)/(a*d - b*c)**3 - 4*a*b**2*c*d**2*(-a/b)**(3/2)/(a*d - b*c)**3 + a*d*sqrt(-a/b)/(a*d - b*c) + 2*b**3*c**2*d*(-a/b)**(3/2)/(a*d - b*c)**3 + b*c*sqrt(-a/b)/(a*d - b*c) + x)/(2*(a*d - b*c)) + sqrt(-c/d)*log(-2*a**2*b*d**3*(-c/d)**(3/2)/(a*d - b*c)**3 + 4*a*b**2*c*d**2*(-c/d)**(3/2)/(a*d - b*c)**3 - a*d*sqrt(-c/d)/(a*d - b*c) - 2*b**3*c**2*d*(-c/d)**(3/2)/(a*d - b*c)**3 - b*c*sqrt(-c/d)/(a*d - b*c) + x)/(2*(a*d - b*c)) - sqrt(-c/d)*log(2*a**2*b*d**3*(-c/d)**(3/2)/(a*d - b*c)**3 - 4*a*b**2*c*d**2*(-c/d)**(3/2)/(a*d - b*c)**3 + a*d*sqrt(-c/d)/(a*d - b*c) + 2*b**3*c**2*d*(-c/d)**(3/2)/(a*d - b*c)**3 + b*c*sqrt(-c/d)/(a*d - b*c) + x)/(2*(a*d - b*c))","B",0
232,1,138,0,0.981658," ","integrate(x/(b*x**2+a)/(d*x**2+c),x)","\frac{\log{\left(x^{2} + \frac{- \frac{a^{2} d^{2}}{a d - b c} + \frac{2 a b c d}{a d - b c} + a d - \frac{b^{2} c^{2}}{a d - b c} + b c}{2 b d} \right)}}{2 \left(a d - b c\right)} - \frac{\log{\left(x^{2} + \frac{\frac{a^{2} d^{2}}{a d - b c} - \frac{2 a b c d}{a d - b c} + a d + \frac{b^{2} c^{2}}{a d - b c} + b c}{2 b d} \right)}}{2 \left(a d - b c\right)}"," ",0,"log(x**2 + (-a**2*d**2/(a*d - b*c) + 2*a*b*c*d/(a*d - b*c) + a*d - b**2*c**2/(a*d - b*c) + b*c)/(2*b*d))/(2*(a*d - b*c)) - log(x**2 + (a**2*d**2/(a*d - b*c) - 2*a*b*c*d/(a*d - b*c) + a*d + b**2*c**2/(a*d - b*c) + b*c)/(2*b*d))/(2*(a*d - b*c))","B",0
233,1,712,0,2.824749," ","integrate(1/(b*x**2+a)/(d*x**2+c),x)","\frac{\sqrt{- \frac{b}{a}} \log{\left(x + \frac{- \frac{a^{4} c d^{3} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{3} b c^{2} d^{2} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} b^{2} c^{3} d \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} d^{2} \sqrt{- \frac{b}{a}}}{a d - b c} - \frac{a b^{3} c^{4} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{2} c^{2} \sqrt{- \frac{b}{a}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{b}{a}} \log{\left(x + \frac{\frac{a^{4} c d^{3} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{3} b c^{2} d^{2} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} b^{2} c^{3} d \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} d^{2} \sqrt{- \frac{b}{a}}}{a d - b c} + \frac{a b^{3} c^{4} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{2} c^{2} \sqrt{- \frac{b}{a}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{d}{c}} \log{\left(x + \frac{- \frac{a^{4} c d^{3} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{3} b c^{2} d^{2} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} b^{2} c^{3} d \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} d^{2} \sqrt{- \frac{d}{c}}}{a d - b c} - \frac{a b^{3} c^{4} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{2} c^{2} \sqrt{- \frac{d}{c}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{d}{c}} \log{\left(x + \frac{\frac{a^{4} c d^{3} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{3} b c^{2} d^{2} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} b^{2} c^{3} d \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} d^{2} \sqrt{- \frac{d}{c}}}{a d - b c} + \frac{a b^{3} c^{4} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{2} c^{2} \sqrt{- \frac{d}{c}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)}"," ",0,"sqrt(-b/a)*log(x + (-a**4*c*d**3*(-b/a)**(3/2)/(a*d - b*c)**3 + a**3*b*c**2*d**2*(-b/a)**(3/2)/(a*d - b*c)**3 + a**2*b**2*c**3*d*(-b/a)**(3/2)/(a*d - b*c)**3 - a**2*d**2*sqrt(-b/a)/(a*d - b*c) - a*b**3*c**4*(-b/a)**(3/2)/(a*d - b*c)**3 - b**2*c**2*sqrt(-b/a)/(a*d - b*c))/(b*d))/(2*(a*d - b*c)) - sqrt(-b/a)*log(x + (a**4*c*d**3*(-b/a)**(3/2)/(a*d - b*c)**3 - a**3*b*c**2*d**2*(-b/a)**(3/2)/(a*d - b*c)**3 - a**2*b**2*c**3*d*(-b/a)**(3/2)/(a*d - b*c)**3 + a**2*d**2*sqrt(-b/a)/(a*d - b*c) + a*b**3*c**4*(-b/a)**(3/2)/(a*d - b*c)**3 + b**2*c**2*sqrt(-b/a)/(a*d - b*c))/(b*d))/(2*(a*d - b*c)) + sqrt(-d/c)*log(x + (-a**4*c*d**3*(-d/c)**(3/2)/(a*d - b*c)**3 + a**3*b*c**2*d**2*(-d/c)**(3/2)/(a*d - b*c)**3 + a**2*b**2*c**3*d*(-d/c)**(3/2)/(a*d - b*c)**3 - a**2*d**2*sqrt(-d/c)/(a*d - b*c) - a*b**3*c**4*(-d/c)**(3/2)/(a*d - b*c)**3 - b**2*c**2*sqrt(-d/c)/(a*d - b*c))/(b*d))/(2*(a*d - b*c)) - sqrt(-d/c)*log(x + (a**4*c*d**3*(-d/c)**(3/2)/(a*d - b*c)**3 - a**3*b*c**2*d**2*(-d/c)**(3/2)/(a*d - b*c)**3 - a**2*b**2*c**3*d*(-d/c)**(3/2)/(a*d - b*c)**3 + a**2*d**2*sqrt(-d/c)/(a*d - b*c) + a*b**3*c**4*(-d/c)**(3/2)/(a*d - b*c)**3 + b**2*c**2*sqrt(-d/c)/(a*d - b*c))/(b*d))/(2*(a*d - b*c))","B",0
234,-1,0,0,0.000000," ","integrate(1/x/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,1,1093,0,12.233366," ","integrate(1/x**2/(b*x**2+a)/(d*x**2+c),x)","- \frac{\sqrt{- \frac{b^{3}}{a^{3}}} \log{\left(x + \frac{- \frac{a^{7} c^{3} d^{4} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{6} b c^{4} d^{3} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{5} b^{2} c^{5} d^{2} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{5} d^{5} \sqrt{- \frac{b^{3}}{a^{3}}}}{a d - b c} + \frac{2 a^{4} b^{3} c^{6} d \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{3} b^{4} c^{7} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{5} c^{5} \sqrt{- \frac{b^{3}}{a^{3}}}}{a d - b c}}{a^{2} b^{2} d^{4} + a b^{3} c d^{3} + b^{4} c^{2} d^{2}} \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{b^{3}}{a^{3}}} \log{\left(x + \frac{\frac{a^{7} c^{3} d^{4} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{6} b c^{4} d^{3} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{5} b^{2} c^{5} d^{2} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{5} d^{5} \sqrt{- \frac{b^{3}}{a^{3}}}}{a d - b c} - \frac{2 a^{4} b^{3} c^{6} d \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{3} b^{4} c^{7} \left(- \frac{b^{3}}{a^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{5} c^{5} \sqrt{- \frac{b^{3}}{a^{3}}}}{a d - b c}}{a^{2} b^{2} d^{4} + a b^{3} c d^{3} + b^{4} c^{2} d^{2}} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{d^{3}}{c^{3}}} \log{\left(x + \frac{- \frac{a^{7} c^{3} d^{4} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{6} b c^{4} d^{3} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{5} b^{2} c^{5} d^{2} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{5} d^{5} \sqrt{- \frac{d^{3}}{c^{3}}}}{a d - b c} + \frac{2 a^{4} b^{3} c^{6} d \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{3} b^{4} c^{7} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{5} c^{5} \sqrt{- \frac{d^{3}}{c^{3}}}}{a d - b c}}{a^{2} b^{2} d^{4} + a b^{3} c d^{3} + b^{4} c^{2} d^{2}} \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{d^{3}}{c^{3}}} \log{\left(x + \frac{\frac{a^{7} c^{3} d^{4} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{6} b c^{4} d^{3} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{5} b^{2} c^{5} d^{2} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{5} d^{5} \sqrt{- \frac{d^{3}}{c^{3}}}}{a d - b c} - \frac{2 a^{4} b^{3} c^{6} d \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{3} b^{4} c^{7} \left(- \frac{d^{3}}{c^{3}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{5} c^{5} \sqrt{- \frac{d^{3}}{c^{3}}}}{a d - b c}}{a^{2} b^{2} d^{4} + a b^{3} c d^{3} + b^{4} c^{2} d^{2}} \right)}}{2 \left(a d - b c\right)} - \frac{1}{a c x}"," ",0,"-sqrt(-b**3/a**3)*log(x + (-a**7*c**3*d**4*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 + 2*a**6*b*c**4*d**3*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 - 2*a**5*b**2*c**5*d**2*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 - a**5*d**5*sqrt(-b**3/a**3)/(a*d - b*c) + 2*a**4*b**3*c**6*d*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 - a**3*b**4*c**7*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 - b**5*c**5*sqrt(-b**3/a**3)/(a*d - b*c))/(a**2*b**2*d**4 + a*b**3*c*d**3 + b**4*c**2*d**2))/(2*(a*d - b*c)) + sqrt(-b**3/a**3)*log(x + (a**7*c**3*d**4*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 - 2*a**6*b*c**4*d**3*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 + 2*a**5*b**2*c**5*d**2*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 + a**5*d**5*sqrt(-b**3/a**3)/(a*d - b*c) - 2*a**4*b**3*c**6*d*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 + a**3*b**4*c**7*(-b**3/a**3)**(3/2)/(a*d - b*c)**3 + b**5*c**5*sqrt(-b**3/a**3)/(a*d - b*c))/(a**2*b**2*d**4 + a*b**3*c*d**3 + b**4*c**2*d**2))/(2*(a*d - b*c)) - sqrt(-d**3/c**3)*log(x + (-a**7*c**3*d**4*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 + 2*a**6*b*c**4*d**3*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 - 2*a**5*b**2*c**5*d**2*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 - a**5*d**5*sqrt(-d**3/c**3)/(a*d - b*c) + 2*a**4*b**3*c**6*d*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 - a**3*b**4*c**7*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 - b**5*c**5*sqrt(-d**3/c**3)/(a*d - b*c))/(a**2*b**2*d**4 + a*b**3*c*d**3 + b**4*c**2*d**2))/(2*(a*d - b*c)) + sqrt(-d**3/c**3)*log(x + (a**7*c**3*d**4*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 - 2*a**6*b*c**4*d**3*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 + 2*a**5*b**2*c**5*d**2*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 + a**5*d**5*sqrt(-d**3/c**3)/(a*d - b*c) - 2*a**4*b**3*c**6*d*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 + a**3*b**4*c**7*(-d**3/c**3)**(3/2)/(a*d - b*c)**3 + b**5*c**5*sqrt(-d**3/c**3)/(a*d - b*c))/(a**2*b**2*d**4 + a*b**3*c*d**3 + b**4*c**2*d**2))/(2*(a*d - b*c)) - 1/(a*c*x)","B",0
236,-1,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,1,1353,0,40.892138," ","integrate(1/x**4/(b*x**2+a)/(d*x**2+c),x)","\frac{\sqrt{- \frac{b^{5}}{a^{5}}} \log{\left(x + \frac{- \frac{a^{10} c^{5} d^{5} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{9} b c^{6} d^{4} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{8} b^{2} c^{7} d^{3} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{8} d^{8} \sqrt{- \frac{b^{5}}{a^{5}}}}{a d - b c} - \frac{a^{7} b^{3} c^{8} d^{2} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{6} b^{4} c^{9} d \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{5} b^{5} c^{10} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{8} c^{8} \sqrt{- \frac{b^{5}}{a^{5}}}}{a d - b c}}{a^{4} b^{3} d^{7} + a^{3} b^{4} c d^{6} + a^{2} b^{5} c^{2} d^{5} + a b^{6} c^{3} d^{4} + b^{7} c^{4} d^{3}} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{b^{5}}{a^{5}}} \log{\left(x + \frac{\frac{a^{10} c^{5} d^{5} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{9} b c^{6} d^{4} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{8} b^{2} c^{7} d^{3} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{8} d^{8} \sqrt{- \frac{b^{5}}{a^{5}}}}{a d - b c} + \frac{a^{7} b^{3} c^{8} d^{2} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{6} b^{4} c^{9} d \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{5} b^{5} c^{10} \left(- \frac{b^{5}}{a^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{8} c^{8} \sqrt{- \frac{b^{5}}{a^{5}}}}{a d - b c}}{a^{4} b^{3} d^{7} + a^{3} b^{4} c d^{6} + a^{2} b^{5} c^{2} d^{5} + a b^{6} c^{3} d^{4} + b^{7} c^{4} d^{3}} \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{d^{5}}{c^{5}}} \log{\left(x + \frac{- \frac{a^{10} c^{5} d^{5} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{9} b c^{6} d^{4} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{8} b^{2} c^{7} d^{3} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{8} d^{8} \sqrt{- \frac{d^{5}}{c^{5}}}}{a d - b c} - \frac{a^{7} b^{3} c^{8} d^{2} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{2 a^{6} b^{4} c^{9} d \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{5} b^{5} c^{10} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{8} c^{8} \sqrt{- \frac{d^{5}}{c^{5}}}}{a d - b c}}{a^{4} b^{3} d^{7} + a^{3} b^{4} c d^{6} + a^{2} b^{5} c^{2} d^{5} + a b^{6} c^{3} d^{4} + b^{7} c^{4} d^{3}} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{d^{5}}{c^{5}}} \log{\left(x + \frac{\frac{a^{10} c^{5} d^{5} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{9} b c^{6} d^{4} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{8} b^{2} c^{7} d^{3} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{8} d^{8} \sqrt{- \frac{d^{5}}{c^{5}}}}{a d - b c} + \frac{a^{7} b^{3} c^{8} d^{2} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{2 a^{6} b^{4} c^{9} d \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{5} b^{5} c^{10} \left(- \frac{d^{5}}{c^{5}}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{8} c^{8} \sqrt{- \frac{d^{5}}{c^{5}}}}{a d - b c}}{a^{4} b^{3} d^{7} + a^{3} b^{4} c d^{6} + a^{2} b^{5} c^{2} d^{5} + a b^{6} c^{3} d^{4} + b^{7} c^{4} d^{3}} \right)}}{2 \left(a d - b c\right)} + \frac{- a c + x^{2} \left(3 a d + 3 b c\right)}{3 a^{2} c^{2} x^{3}}"," ",0,"sqrt(-b**5/a**5)*log(x + (-a**10*c**5*d**5*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 + 2*a**9*b*c**6*d**4*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 - a**8*b**2*c**7*d**3*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 - a**8*d**8*sqrt(-b**5/a**5)/(a*d - b*c) - a**7*b**3*c**8*d**2*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 + 2*a**6*b**4*c**9*d*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 - a**5*b**5*c**10*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 - b**8*c**8*sqrt(-b**5/a**5)/(a*d - b*c))/(a**4*b**3*d**7 + a**3*b**4*c*d**6 + a**2*b**5*c**2*d**5 + a*b**6*c**3*d**4 + b**7*c**4*d**3))/(2*(a*d - b*c)) - sqrt(-b**5/a**5)*log(x + (a**10*c**5*d**5*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 - 2*a**9*b*c**6*d**4*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 + a**8*b**2*c**7*d**3*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 + a**8*d**8*sqrt(-b**5/a**5)/(a*d - b*c) + a**7*b**3*c**8*d**2*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 - 2*a**6*b**4*c**9*d*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 + a**5*b**5*c**10*(-b**5/a**5)**(3/2)/(a*d - b*c)**3 + b**8*c**8*sqrt(-b**5/a**5)/(a*d - b*c))/(a**4*b**3*d**7 + a**3*b**4*c*d**6 + a**2*b**5*c**2*d**5 + a*b**6*c**3*d**4 + b**7*c**4*d**3))/(2*(a*d - b*c)) + sqrt(-d**5/c**5)*log(x + (-a**10*c**5*d**5*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 + 2*a**9*b*c**6*d**4*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 - a**8*b**2*c**7*d**3*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 - a**8*d**8*sqrt(-d**5/c**5)/(a*d - b*c) - a**7*b**3*c**8*d**2*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 + 2*a**6*b**4*c**9*d*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 - a**5*b**5*c**10*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 - b**8*c**8*sqrt(-d**5/c**5)/(a*d - b*c))/(a**4*b**3*d**7 + a**3*b**4*c*d**6 + a**2*b**5*c**2*d**5 + a*b**6*c**3*d**4 + b**7*c**4*d**3))/(2*(a*d - b*c)) - sqrt(-d**5/c**5)*log(x + (a**10*c**5*d**5*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 - 2*a**9*b*c**6*d**4*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 + a**8*b**2*c**7*d**3*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 + a**8*d**8*sqrt(-d**5/c**5)/(a*d - b*c) + a**7*b**3*c**8*d**2*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 - 2*a**6*b**4*c**9*d*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 + a**5*b**5*c**10*(-d**5/c**5)**(3/2)/(a*d - b*c)**3 + b**8*c**8*sqrt(-d**5/c**5)/(a*d - b*c))/(a**4*b**3*d**7 + a**3*b**4*c*d**6 + a**2*b**5*c**2*d**5 + a*b**6*c**3*d**4 + b**7*c**4*d**3))/(2*(a*d - b*c)) + (-a*c + x**2*(3*a*d + 3*b*c))/(3*a**2*c**2*x**3)","B",0
238,-1,0,0,0.000000," ","integrate(1/x**5/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate(1/x**6/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,-1,0,0,0.000000," ","integrate(1/x**7/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate(x**5/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate(x**4/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,1,253,0,1.919441," ","integrate(x**3/(b*x**2+a)/(d*x**2+c)**2,x)","\frac{a \log{\left(x^{2} + \frac{- \frac{a^{4} d^{3}}{\left(a d - b c\right)^{2}} + \frac{3 a^{3} b c d^{2}}{\left(a d - b c\right)^{2}} - \frac{3 a^{2} b^{2} c^{2} d}{\left(a d - b c\right)^{2}} + a^{2} d + \frac{a b^{3} c^{3}}{\left(a d - b c\right)^{2}} + a b c}{2 a b d} \right)}}{2 \left(a d - b c\right)^{2}} - \frac{a \log{\left(x^{2} + \frac{\frac{a^{4} d^{3}}{\left(a d - b c\right)^{2}} - \frac{3 a^{3} b c d^{2}}{\left(a d - b c\right)^{2}} + \frac{3 a^{2} b^{2} c^{2} d}{\left(a d - b c\right)^{2}} + a^{2} d - \frac{a b^{3} c^{3}}{\left(a d - b c\right)^{2}} + a b c}{2 a b d} \right)}}{2 \left(a d - b c\right)^{2}} + \frac{c}{2 a c d^{2} - 2 b c^{2} d + x^{2} \left(2 a d^{3} - 2 b c d^{2}\right)}"," ",0,"a*log(x**2 + (-a**4*d**3/(a*d - b*c)**2 + 3*a**3*b*c*d**2/(a*d - b*c)**2 - 3*a**2*b**2*c**2*d/(a*d - b*c)**2 + a**2*d + a*b**3*c**3/(a*d - b*c)**2 + a*b*c)/(2*a*b*d))/(2*(a*d - b*c)**2) - a*log(x**2 + (a**4*d**3/(a*d - b*c)**2 - 3*a**3*b*c*d**2/(a*d - b*c)**2 + 3*a**2*b**2*c**2*d/(a*d - b*c)**2 + a**2*d - a*b**3*c**3/(a*d - b*c)**2 + a*b*c)/(2*a*b*d))/(2*(a*d - b*c)**2) + c/(2*a*c*d**2 - 2*b*c**2*d + x**2*(2*a*d**3 - 2*b*c*d**2))","B",0
244,-1,0,0,0.000000," ","integrate(x**2/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,1,248,0,1.889797," ","integrate(x/(b*x**2+a)/(d*x**2+c)**2,x)","- \frac{b \log{\left(x^{2} + \frac{- \frac{a^{3} b d^{3}}{\left(a d - b c\right)^{2}} + \frac{3 a^{2} b^{2} c d^{2}}{\left(a d - b c\right)^{2}} - \frac{3 a b^{3} c^{2} d}{\left(a d - b c\right)^{2}} + a b d + \frac{b^{4} c^{3}}{\left(a d - b c\right)^{2}} + b^{2} c}{2 b^{2} d} \right)}}{2 \left(a d - b c\right)^{2}} + \frac{b \log{\left(x^{2} + \frac{\frac{a^{3} b d^{3}}{\left(a d - b c\right)^{2}} - \frac{3 a^{2} b^{2} c d^{2}}{\left(a d - b c\right)^{2}} + \frac{3 a b^{3} c^{2} d}{\left(a d - b c\right)^{2}} + a b d - \frac{b^{4} c^{3}}{\left(a d - b c\right)^{2}} + b^{2} c}{2 b^{2} d} \right)}}{2 \left(a d - b c\right)^{2}} - \frac{1}{2 a c d - 2 b c^{2} + x^{2} \left(2 a d^{2} - 2 b c d\right)}"," ",0,"-b*log(x**2 + (-a**3*b*d**3/(a*d - b*c)**2 + 3*a**2*b**2*c*d**2/(a*d - b*c)**2 - 3*a*b**3*c**2*d/(a*d - b*c)**2 + a*b*d + b**4*c**3/(a*d - b*c)**2 + b**2*c)/(2*b**2*d))/(2*(a*d - b*c)**2) + b*log(x**2 + (a**3*b*d**3/(a*d - b*c)**2 - 3*a**2*b**2*c*d**2/(a*d - b*c)**2 + 3*a*b**3*c**2*d/(a*d - b*c)**2 + a*b*d - b**4*c**3/(a*d - b*c)**2 + b**2*c)/(2*b**2*d))/(2*(a*d - b*c)**2) - 1/(2*a*c*d - 2*b*c**2 + x**2*(2*a*d**2 - 2*b*c*d))","B",0
246,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate(1/x/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,1,418,0,3.262809," ","integrate(x**5/(b*x**2+a)**3/(d*x**2+c),x)","\frac{c^{2} \log{\left(x^{2} + \frac{- \frac{a^{4} c^{2} d^{4}}{\left(a d - b c\right)^{3}} + \frac{4 a^{3} b c^{3} d^{3}}{\left(a d - b c\right)^{3}} - \frac{6 a^{2} b^{2} c^{4} d^{2}}{\left(a d - b c\right)^{3}} + \frac{4 a b^{3} c^{5} d}{\left(a d - b c\right)^{3}} + a c^{2} d - \frac{b^{4} c^{6}}{\left(a d - b c\right)^{3}} + b c^{3}}{2 b c^{2} d} \right)}}{2 \left(a d - b c\right)^{3}} - \frac{c^{2} \log{\left(x^{2} + \frac{\frac{a^{4} c^{2} d^{4}}{\left(a d - b c\right)^{3}} - \frac{4 a^{3} b c^{3} d^{3}}{\left(a d - b c\right)^{3}} + \frac{6 a^{2} b^{2} c^{4} d^{2}}{\left(a d - b c\right)^{3}} - \frac{4 a b^{3} c^{5} d}{\left(a d - b c\right)^{3}} + a c^{2} d + \frac{b^{4} c^{6}}{\left(a d - b c\right)^{3}} + b c^{3}}{2 b c^{2} d} \right)}}{2 \left(a d - b c\right)^{3}} + \frac{- a^{3} d + 3 a^{2} b c + x^{2} \left(- 2 a^{2} b d + 4 a b^{2} c\right)}{4 a^{4} b^{2} d^{2} - 8 a^{3} b^{3} c d + 4 a^{2} b^{4} c^{2} + x^{4} \left(4 a^{2} b^{4} d^{2} - 8 a b^{5} c d + 4 b^{6} c^{2}\right) + x^{2} \left(8 a^{3} b^{3} d^{2} - 16 a^{2} b^{4} c d + 8 a b^{5} c^{2}\right)}"," ",0,"c**2*log(x**2 + (-a**4*c**2*d**4/(a*d - b*c)**3 + 4*a**3*b*c**3*d**3/(a*d - b*c)**3 - 6*a**2*b**2*c**4*d**2/(a*d - b*c)**3 + 4*a*b**3*c**5*d/(a*d - b*c)**3 + a*c**2*d - b**4*c**6/(a*d - b*c)**3 + b*c**3)/(2*b*c**2*d))/(2*(a*d - b*c)**3) - c**2*log(x**2 + (a**4*c**2*d**4/(a*d - b*c)**3 - 4*a**3*b*c**3*d**3/(a*d - b*c)**3 + 6*a**2*b**2*c**4*d**2/(a*d - b*c)**3 - 4*a*b**3*c**5*d/(a*d - b*c)**3 + a*c**2*d + b**4*c**6/(a*d - b*c)**3 + b*c**3)/(2*b*c**2*d))/(2*(a*d - b*c)**3) + (-a**3*d + 3*a**2*b*c + x**2*(-2*a**2*b*d + 4*a*b**2*c))/(4*a**4*b**2*d**2 - 8*a**3*b**3*c*d + 4*a**2*b**4*c**2 + x**4*(4*a**2*b**4*d**2 - 8*a*b**5*c*d + 4*b**6*c**2) + x**2*(8*a**3*b**3*d**2 - 16*a**2*b**4*c*d + 8*a*b**5*c**2))","B",0
252,-1,0,0,0.000000," ","integrate(x**4/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,1,411,0,2.973662," ","integrate(x**3/(b*x**2+a)/(d*x**2+c)**3,x)","- \frac{a b \log{\left(x^{2} + \frac{- \frac{a^{5} b d^{4}}{\left(a d - b c\right)^{3}} + \frac{4 a^{4} b^{2} c d^{3}}{\left(a d - b c\right)^{3}} - \frac{6 a^{3} b^{3} c^{2} d^{2}}{\left(a d - b c\right)^{3}} + \frac{4 a^{2} b^{4} c^{3} d}{\left(a d - b c\right)^{3}} + a^{2} b d - \frac{a b^{5} c^{4}}{\left(a d - b c\right)^{3}} + a b^{2} c}{2 a b^{2} d} \right)}}{2 \left(a d - b c\right)^{3}} + \frac{a b \log{\left(x^{2} + \frac{\frac{a^{5} b d^{4}}{\left(a d - b c\right)^{3}} - \frac{4 a^{4} b^{2} c d^{3}}{\left(a d - b c\right)^{3}} + \frac{6 a^{3} b^{3} c^{2} d^{2}}{\left(a d - b c\right)^{3}} - \frac{4 a^{2} b^{4} c^{3} d}{\left(a d - b c\right)^{3}} + a^{2} b d + \frac{a b^{5} c^{4}}{\left(a d - b c\right)^{3}} + a b^{2} c}{2 a b^{2} d} \right)}}{2 \left(a d - b c\right)^{3}} + \frac{- a c d - 2 a d^{2} x^{2} - b c^{2}}{4 a^{2} c^{2} d^{3} - 8 a b c^{3} d^{2} + 4 b^{2} c^{4} d + x^{4} \left(4 a^{2} d^{5} - 8 a b c d^{4} + 4 b^{2} c^{2} d^{3}\right) + x^{2} \left(8 a^{2} c d^{4} - 16 a b c^{2} d^{3} + 8 b^{2} c^{3} d^{2}\right)}"," ",0,"-a*b*log(x**2 + (-a**5*b*d**4/(a*d - b*c)**3 + 4*a**4*b**2*c*d**3/(a*d - b*c)**3 - 6*a**3*b**3*c**2*d**2/(a*d - b*c)**3 + 4*a**2*b**4*c**3*d/(a*d - b*c)**3 + a**2*b*d - a*b**5*c**4/(a*d - b*c)**3 + a*b**2*c)/(2*a*b**2*d))/(2*(a*d - b*c)**3) + a*b*log(x**2 + (a**5*b*d**4/(a*d - b*c)**3 - 4*a**4*b**2*c*d**3/(a*d - b*c)**3 + 6*a**3*b**3*c**2*d**2/(a*d - b*c)**3 - 4*a**2*b**4*c**3*d/(a*d - b*c)**3 + a**2*b*d + a*b**5*c**4/(a*d - b*c)**3 + a*b**2*c)/(2*a*b**2*d))/(2*(a*d - b*c)**3) + (-a*c*d - 2*a*d**2*x**2 - b*c**2)/(4*a**2*c**2*d**3 - 8*a*b*c**3*d**2 + 4*b**2*c**4*d + x**4*(4*a**2*d**5 - 8*a*b*c*d**4 + 4*b**2*c**2*d**3) + x**2*(8*a**2*c*d**4 - 16*a*b*c**2*d**3 + 8*b**2*c**3*d**2))","B",0
254,-1,0,0,0.000000," ","integrate(x**2/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,1,391,0,2.866581," ","integrate(x/(b*x**2+a)/(d*x**2+c)**3,x)","\frac{b^{2} \log{\left(x^{2} + \frac{- \frac{a^{4} b^{2} d^{4}}{\left(a d - b c\right)^{3}} + \frac{4 a^{3} b^{3} c d^{3}}{\left(a d - b c\right)^{3}} - \frac{6 a^{2} b^{4} c^{2} d^{2}}{\left(a d - b c\right)^{3}} + \frac{4 a b^{5} c^{3} d}{\left(a d - b c\right)^{3}} + a b^{2} d - \frac{b^{6} c^{4}}{\left(a d - b c\right)^{3}} + b^{3} c}{2 b^{3} d} \right)}}{2 \left(a d - b c\right)^{3}} - \frac{b^{2} \log{\left(x^{2} + \frac{\frac{a^{4} b^{2} d^{4}}{\left(a d - b c\right)^{3}} - \frac{4 a^{3} b^{3} c d^{3}}{\left(a d - b c\right)^{3}} + \frac{6 a^{2} b^{4} c^{2} d^{2}}{\left(a d - b c\right)^{3}} - \frac{4 a b^{5} c^{3} d}{\left(a d - b c\right)^{3}} + a b^{2} d + \frac{b^{6} c^{4}}{\left(a d - b c\right)^{3}} + b^{3} c}{2 b^{3} d} \right)}}{2 \left(a d - b c\right)^{3}} + \frac{- a d + 3 b c + 2 b d x^{2}}{4 a^{2} c^{2} d^{2} - 8 a b c^{3} d + 4 b^{2} c^{4} + x^{4} \left(4 a^{2} d^{4} - 8 a b c d^{3} + 4 b^{2} c^{2} d^{2}\right) + x^{2} \left(8 a^{2} c d^{3} - 16 a b c^{2} d^{2} + 8 b^{2} c^{3} d\right)}"," ",0,"b**2*log(x**2 + (-a**4*b**2*d**4/(a*d - b*c)**3 + 4*a**3*b**3*c*d**3/(a*d - b*c)**3 - 6*a**2*b**4*c**2*d**2/(a*d - b*c)**3 + 4*a*b**5*c**3*d/(a*d - b*c)**3 + a*b**2*d - b**6*c**4/(a*d - b*c)**3 + b**3*c)/(2*b**3*d))/(2*(a*d - b*c)**3) - b**2*log(x**2 + (a**4*b**2*d**4/(a*d - b*c)**3 - 4*a**3*b**3*c*d**3/(a*d - b*c)**3 + 6*a**2*b**4*c**2*d**2/(a*d - b*c)**3 - 4*a*b**5*c**3*d/(a*d - b*c)**3 + a*b**2*d + b**6*c**4/(a*d - b*c)**3 + b**3*c)/(2*b**3*d))/(2*(a*d - b*c)**3) + (-a*d + 3*b*c + 2*b*d*x**2)/(4*a**2*c**2*d**2 - 8*a*b*c**3*d + 4*b**2*c**4 + x**4*(4*a**2*d**4 - 8*a*b*c*d**3 + 4*b**2*c**2*d**2) + x**2*(8*a**2*c*d**3 - 16*a*b*c**2*d**2 + 8*b**2*c**3*d))","B",0
256,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate(1/x/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,1,15,0,0.107970," ","integrate(x/(x**2+1)/(x**2+4),x)","\frac{\log{\left(x^{2} + 1 \right)}}{6} - \frac{\log{\left(x^{2} + 4 \right)}}{6}"," ",0,"log(x**2 + 1)/6 - log(x**2 + 4)/6","A",0
262,1,129,0,0.629439," ","integrate(x**4*(d*x**2+c)/(b*x**2+a)**2,x)","x \left(- \frac{2 a d}{b^{3}} + \frac{c}{b^{2}}\right) + \frac{x \left(- a^{2} d + a b c\right)}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{\sqrt{- \frac{a}{b^{7}}} \left(5 a d - 3 b c\right) \log{\left(- b^{3} \sqrt{- \frac{a}{b^{7}}} + x \right)}}{4} + \frac{\sqrt{- \frac{a}{b^{7}}} \left(5 a d - 3 b c\right) \log{\left(b^{3} \sqrt{- \frac{a}{b^{7}}} + x \right)}}{4} + \frac{d x^{3}}{3 b^{2}}"," ",0,"x*(-2*a*d/b**3 + c/b**2) + x*(-a**2*d + a*b*c)/(2*a*b**3 + 2*b**4*x**2) - sqrt(-a/b**7)*(5*a*d - 3*b*c)*log(-b**3*sqrt(-a/b**7) + x)/4 + sqrt(-a/b**7)*(5*a*d - 3*b*c)*log(b**3*sqrt(-a/b**7) + x)/4 + d*x**3/(3*b**2)","A",0
263,1,56,0,0.563250," ","integrate(x**3*(d*x**2+c)/(b*x**2+a)**2,x)","\frac{- a^{2} d + a b c}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{d x^{2}}{2 b^{2}} - \frac{\left(2 a d - b c\right) \log{\left(a + b x^{2} \right)}}{2 b^{3}}"," ",0,"(-a**2*d + a*b*c)/(2*a*b**3 + 2*b**4*x**2) + d*x**2/(2*b**2) - (2*a*d - b*c)*log(a + b*x**2)/(2*b**3)","A",0
264,1,114,0,0.527437," ","integrate(x**2*(d*x**2+c)/(b*x**2+a)**2,x)","\frac{x \left(a d - b c\right)}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{\sqrt{- \frac{1}{a b^{5}}} \left(3 a d - b c\right) \log{\left(- a b^{2} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a b^{5}}} \left(3 a d - b c\right) \log{\left(a b^{2} \sqrt{- \frac{1}{a b^{5}}} + x \right)}}{4} + \frac{d x}{b^{2}}"," ",0,"x*(a*d - b*c)/(2*a*b**2 + 2*b**3*x**2) + sqrt(-1/(a*b**5))*(3*a*d - b*c)*log(-a*b**2*sqrt(-1/(a*b**5)) + x)/4 - sqrt(-1/(a*b**5))*(3*a*d - b*c)*log(a*b**2*sqrt(-1/(a*b**5)) + x)/4 + d*x/b**2","A",0
265,1,36,0,0.360921," ","integrate(x*(d*x**2+c)/(b*x**2+a)**2,x)","\frac{a d - b c}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{d \log{\left(a + b x^{2} \right)}}{2 b^{2}}"," ",0,"(a*d - b*c)/(2*a*b**2 + 2*b**3*x**2) + d*log(a + b*x**2)/(2*b**2)","A",0
266,1,112,0,0.395048," ","integrate((d*x**2+c)/(b*x**2+a)**2,x)","\frac{x \left(- a d + b c\right)}{2 a^{2} b + 2 a b^{2} x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d + b c\right) \log{\left(- a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d + b c\right) \log{\left(a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{4}"," ",0,"x*(-a*d + b*c)/(2*a**2*b + 2*a*b**2*x**2) - sqrt(-1/(a**3*b**3))*(a*d + b*c)*log(-a**2*b*sqrt(-1/(a**3*b**3)) + x)/4 + sqrt(-1/(a**3*b**3))*(a*d + b*c)*log(a**2*b*sqrt(-1/(a**3*b**3)) + x)/4","B",0
267,1,46,0,0.414681," ","integrate((d*x**2+c)/x/(b*x**2+a)**2,x)","\frac{- a d + b c}{2 a^{2} b + 2 a b^{2} x^{2}} + \frac{c \log{\left(x \right)}}{a^{2}} - \frac{c \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2}}"," ",0,"(-a*d + b*c)/(2*a**2*b + 2*a*b**2*x**2) + c*log(x)/a**2 - c*log(a/b + x**2)/(2*a**2)","A",0
268,1,114,0,0.488320," ","integrate((d*x**2+c)/x**2/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{5} b}} \left(a d - 3 b c\right) \log{\left(- a^{3} \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{5} b}} \left(a d - 3 b c\right) \log{\left(a^{3} \sqrt{- \frac{1}{a^{5} b}} + x \right)}}{4} + \frac{- 2 a c + x^{2} \left(a d - 3 b c\right)}{2 a^{3} x + 2 a^{2} b x^{3}}"," ",0,"-sqrt(-1/(a**5*b))*(a*d - 3*b*c)*log(-a**3*sqrt(-1/(a**5*b)) + x)/4 + sqrt(-1/(a**5*b))*(a*d - 3*b*c)*log(a**3*sqrt(-1/(a**5*b)) + x)/4 + (-2*a*c + x**2*(a*d - 3*b*c))/(2*a**3*x + 2*a**2*b*x**3)","A",0
269,1,70,0,0.866676," ","integrate((d*x**2+c)/x**3/(b*x**2+a)**2,x)","\frac{- a c + x^{2} \left(a d - 2 b c\right)}{2 a^{3} x^{2} + 2 a^{2} b x^{4}} + \frac{\left(a d - 2 b c\right) \log{\left(x \right)}}{a^{3}} - \frac{\left(a d - 2 b c\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{3}}"," ",0,"(-a*c + x**2*(a*d - 2*b*c))/(2*a**3*x**2 + 2*a**2*b*x**4) + (a*d - 2*b*c)*log(x)/a**3 - (a*d - 2*b*c)*log(a/b + x**2)/(2*a**3)","A",0
270,1,184,0,0.589964," ","integrate((d*x**2+c)/x**4/(b*x**2+a)**2,x)","\frac{\sqrt{- \frac{b}{a^{7}}} \left(3 a d - 5 b c\right) \log{\left(- \frac{a^{4} \sqrt{- \frac{b}{a^{7}}} \left(3 a d - 5 b c\right)}{3 a b d - 5 b^{2} c} + x \right)}}{4} - \frac{\sqrt{- \frac{b}{a^{7}}} \left(3 a d - 5 b c\right) \log{\left(\frac{a^{4} \sqrt{- \frac{b}{a^{7}}} \left(3 a d - 5 b c\right)}{3 a b d - 5 b^{2} c} + x \right)}}{4} + \frac{- 2 a^{2} c + x^{4} \left(- 9 a b d + 15 b^{2} c\right) + x^{2} \left(- 6 a^{2} d + 10 a b c\right)}{6 a^{4} x^{3} + 6 a^{3} b x^{5}}"," ",0,"sqrt(-b/a**7)*(3*a*d - 5*b*c)*log(-a**4*sqrt(-b/a**7)*(3*a*d - 5*b*c)/(3*a*b*d - 5*b**2*c) + x)/4 - sqrt(-b/a**7)*(3*a*d - 5*b*c)*log(a**4*sqrt(-b/a**7)*(3*a*d - 5*b*c)/(3*a*b*d - 5*b**2*c) + x)/4 + (-2*a**2*c + x**4*(-9*a*b*d + 15*b**2*c) + x**2*(-6*a**2*d + 10*a*b*c))/(6*a**4*x**3 + 6*a**3*b*x**5)","B",0
271,1,286,0,0.982427," ","integrate(x**4*(d*x**2+c)**2/(b*x**2+a)**2,x)","x^{3} \left(- \frac{2 a d^{2}}{3 b^{3}} + \frac{2 c d}{3 b^{2}}\right) + x \left(\frac{3 a^{2} d^{2}}{b^{4}} - \frac{4 a c d}{b^{3}} + \frac{c^{2}}{b^{2}}\right) + \frac{x \left(a^{3} d^{2} - 2 a^{2} b c d + a b^{2} c^{2}\right)}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{\sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right) \left(7 a d - 3 b c\right) \log{\left(- \frac{b^{4} \sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right) \left(7 a d - 3 b c\right)}{7 a^{2} d^{2} - 10 a b c d + 3 b^{2} c^{2}} + x \right)}}{4} - \frac{\sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right) \left(7 a d - 3 b c\right) \log{\left(\frac{b^{4} \sqrt{- \frac{a}{b^{9}}} \left(a d - b c\right) \left(7 a d - 3 b c\right)}{7 a^{2} d^{2} - 10 a b c d + 3 b^{2} c^{2}} + x \right)}}{4} + \frac{d^{2} x^{5}}{5 b^{2}}"," ",0,"x**3*(-2*a*d**2/(3*b**3) + 2*c*d/(3*b**2)) + x*(3*a**2*d**2/b**4 - 4*a*c*d/b**3 + c**2/b**2) + x*(a**3*d**2 - 2*a**2*b*c*d + a*b**2*c**2)/(2*a*b**4 + 2*b**5*x**2) + sqrt(-a/b**9)*(a*d - b*c)*(7*a*d - 3*b*c)*log(-b**4*sqrt(-a/b**9)*(a*d - b*c)*(7*a*d - 3*b*c)/(7*a**2*d**2 - 10*a*b*c*d + 3*b**2*c**2) + x)/4 - sqrt(-a/b**9)*(a*d - b*c)*(7*a*d - 3*b*c)*log(b**4*sqrt(-a/b**9)*(a*d - b*c)*(7*a*d - 3*b*c)/(7*a**2*d**2 - 10*a*b*c*d + 3*b**2*c**2) + x)/4 + d**2*x**5/(5*b**2)","B",0
272,1,99,0,0.926293," ","integrate(x**3*(d*x**2+c)**2/(b*x**2+a)**2,x)","x^{2} \left(- \frac{a d^{2}}{b^{3}} + \frac{c d}{b^{2}}\right) + \frac{a^{3} d^{2} - 2 a^{2} b c d + a b^{2} c^{2}}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{d^{2} x^{4}}{4 b^{2}} + \frac{\left(a d - b c\right) \left(3 a d - b c\right) \log{\left(a + b x^{2} \right)}}{2 b^{4}}"," ",0,"x**2*(-a*d**2/b**3 + c*d/b**2) + (a**3*d**2 - 2*a**2*b*c*d + a*b**2*c**2)/(2*a*b**4 + 2*b**5*x**2) + d**2*x**4/(4*b**2) + (a*d - b*c)*(3*a*d - b*c)*log(a + b*x**2)/(2*b**4)","A",0
273,1,246,0,0.857901," ","integrate(x**2*(d*x**2+c)**2/(b*x**2+a)**2,x)","x \left(- \frac{2 a d^{2}}{b^{3}} + \frac{2 c d}{b^{2}}\right) + \frac{x \left(- a^{2} d^{2} + 2 a b c d - b^{2} c^{2}\right)}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right) \left(5 a d - b c\right) \log{\left(- \frac{a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right) \left(5 a d - b c\right)}{5 a^{2} d^{2} - 6 a b c d + b^{2} c^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right) \left(5 a d - b c\right) \log{\left(\frac{a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right) \left(5 a d - b c\right)}{5 a^{2} d^{2} - 6 a b c d + b^{2} c^{2}} + x \right)}}{4} + \frac{d^{2} x^{3}}{3 b^{2}}"," ",0,"x*(-2*a*d**2/b**3 + 2*c*d/b**2) + x*(-a**2*d**2 + 2*a*b*c*d - b**2*c**2)/(2*a*b**3 + 2*b**4*x**2) - sqrt(-1/(a*b**7))*(a*d - b*c)*(5*a*d - b*c)*log(-a*b**3*sqrt(-1/(a*b**7))*(a*d - b*c)*(5*a*d - b*c)/(5*a**2*d**2 - 6*a*b*c*d + b**2*c**2) + x)/4 + sqrt(-1/(a*b**7))*(a*d - b*c)*(5*a*d - b*c)*log(a*b**3*sqrt(-1/(a*b**7))*(a*d - b*c)*(5*a*d - b*c)/(5*a**2*d**2 - 6*a*b*c*d + b**2*c**2) + x)/4 + d**2*x**3/(3*b**2)","B",0
274,1,68,0,0.756861," ","integrate(x*(d*x**2+c)**2/(b*x**2+a)**2,x)","\frac{- a^{2} d^{2} + 2 a b c d - b^{2} c^{2}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{d^{2} x^{2}}{2 b^{2}} - \frac{d \left(a d - b c\right) \log{\left(a + b x^{2} \right)}}{b^{3}}"," ",0,"(-a**2*d**2 + 2*a*b*c*d - b**2*c**2)/(2*a*b**3 + 2*b**4*x**2) + d**2*x**2/(2*b**2) - d*(a*d - b*c)*log(a + b*x**2)/b**3","A",0
275,1,236,0,0.713147," ","integrate((d*x**2+c)**2/(b*x**2+a)**2,x)","\frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{2 a^{2} b^{2} + 2 a b^{3} x^{2}} + \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right) \log{\left(- \frac{a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right)}{3 a^{2} d^{2} - 2 a b c d - b^{2} c^{2}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right) \log{\left(\frac{a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right)}{3 a^{2} d^{2} - 2 a b c d - b^{2} c^{2}} + x \right)}}{4} + \frac{d^{2} x}{b^{2}}"," ",0,"x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(2*a**2*b**2 + 2*a*b**3*x**2) + sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)*log(-a**2*b**2*sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)/(3*a**2*d**2 - 2*a*b*c*d - b**2*c**2) + x)/4 - sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)*log(a**2*b**2*sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)/(3*a**2*d**2 - 2*a*b*c*d - b**2*c**2) + x)/4 + d**2*x/b**2","B",0
276,1,80,0,1.240166," ","integrate((d*x**2+c)**2/x/(b*x**2+a)**2,x)","\frac{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}}{2 a^{2} b^{2} + 2 a b^{3} x^{2}} + \frac{c^{2} \log{\left(x \right)}}{a^{2}} + \frac{\left(a d - b c\right) \left(a d + b c\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2} b^{2}}"," ",0,"(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(2*a**2*b**2 + 2*a*b**3*x**2) + c**2*log(x)/a**2 + (a*d - b*c)*(a*d + b*c)*log(a/b + x**2)/(2*a**2*b**2)","A",0
277,1,238,0,0.872523," ","integrate((d*x**2+c)**2/x**2/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right) \left(a d + 3 b c\right) \log{\left(- \frac{a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right) \left(a d + 3 b c\right)}{a^{2} d^{2} + 2 a b c d - 3 b^{2} c^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right) \left(a d + 3 b c\right) \log{\left(\frac{a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d - b c\right) \left(a d + 3 b c\right)}{a^{2} d^{2} + 2 a b c d - 3 b^{2} c^{2}} + x \right)}}{4} + \frac{- 2 a b c^{2} + x^{2} \left(- a^{2} d^{2} + 2 a b c d - 3 b^{2} c^{2}\right)}{2 a^{3} b x + 2 a^{2} b^{2} x^{3}}"," ",0,"-sqrt(-1/(a**5*b**3))*(a*d - b*c)*(a*d + 3*b*c)*log(-a**3*b*sqrt(-1/(a**5*b**3))*(a*d - b*c)*(a*d + 3*b*c)/(a**2*d**2 + 2*a*b*c*d - 3*b**2*c**2) + x)/4 + sqrt(-1/(a**5*b**3))*(a*d - b*c)*(a*d + 3*b*c)*log(a**3*b*sqrt(-1/(a**5*b**3))*(a*d - b*c)*(a*d + 3*b*c)/(a**2*d**2 + 2*a*b*c*d - 3*b**2*c**2) + x)/4 + (-2*a*b*c**2 + x**2*(-a**2*d**2 + 2*a*b*c*d - 3*b**2*c**2))/(2*a**3*b*x + 2*a**2*b**2*x**3)","B",0
278,1,92,0,1.364944," ","integrate((d*x**2+c)**2/x**3/(b*x**2+a)**2,x)","\frac{- a b c^{2} + x^{2} \left(- a^{2} d^{2} + 2 a b c d - 2 b^{2} c^{2}\right)}{2 a^{3} b x^{2} + 2 a^{2} b^{2} x^{4}} + \frac{2 c \left(a d - b c\right) \log{\left(x \right)}}{a^{3}} - \frac{c \left(a d - b c\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{a^{3}}"," ",0,"(-a*b*c**2 + x**2*(-a**2*d**2 + 2*a*b*c*d - 2*b**2*c**2))/(2*a**3*b*x**2 + 2*a**2*b**2*x**4) + 2*c*(a*d - b*c)*log(x)/a**3 - c*(a*d - b*c)*log(a/b + x**2)/a**3","A",0
279,1,248,0,0.996331," ","integrate((d*x**2+c)**2/x**4/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{7} b}} \left(a d - 5 b c\right) \left(a d - b c\right) \log{\left(- \frac{a^{4} \sqrt{- \frac{1}{a^{7} b}} \left(a d - 5 b c\right) \left(a d - b c\right)}{a^{2} d^{2} - 6 a b c d + 5 b^{2} c^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{7} b}} \left(a d - 5 b c\right) \left(a d - b c\right) \log{\left(\frac{a^{4} \sqrt{- \frac{1}{a^{7} b}} \left(a d - 5 b c\right) \left(a d - b c\right)}{a^{2} d^{2} - 6 a b c d + 5 b^{2} c^{2}} + x \right)}}{4} + \frac{- 2 a^{2} c^{2} + x^{4} \left(3 a^{2} d^{2} - 18 a b c d + 15 b^{2} c^{2}\right) + x^{2} \left(- 12 a^{2} c d + 10 a b c^{2}\right)}{6 a^{4} x^{3} + 6 a^{3} b x^{5}}"," ",0,"-sqrt(-1/(a**7*b))*(a*d - 5*b*c)*(a*d - b*c)*log(-a**4*sqrt(-1/(a**7*b))*(a*d - 5*b*c)*(a*d - b*c)/(a**2*d**2 - 6*a*b*c*d + 5*b**2*c**2) + x)/4 + sqrt(-1/(a**7*b))*(a*d - 5*b*c)*(a*d - b*c)*log(a**4*sqrt(-1/(a**7*b))*(a*d - 5*b*c)*(a*d - b*c)/(a**2*d**2 - 6*a*b*c*d + 5*b**2*c**2) + x)/4 + (-2*a**2*c**2 + x**4*(3*a**2*d**2 - 18*a*b*c*d + 15*b**2*c**2) + x**2*(-12*a**2*c*d + 10*a*b*c**2))/(6*a**4*x**3 + 6*a**3*b*x**5)","B",0
280,1,389,0,1.361623," ","integrate(x**4*(d*x**2+c)**3/(b*x**2+a)**2,x)","x^{5} \left(- \frac{2 a d^{3}}{5 b^{3}} + \frac{3 c d^{2}}{5 b^{2}}\right) + x^{3} \left(\frac{a^{2} d^{3}}{b^{4}} - \frac{2 a c d^{2}}{b^{3}} + \frac{c^{2} d}{b^{2}}\right) + x \left(- \frac{4 a^{3} d^{3}}{b^{5}} + \frac{9 a^{2} c d^{2}}{b^{4}} - \frac{6 a c^{2} d}{b^{3}} + \frac{c^{3}}{b^{2}}\right) + \frac{x \left(- a^{4} d^{3} + 3 a^{3} b c d^{2} - 3 a^{2} b^{2} c^{2} d + a b^{3} c^{3}\right)}{2 a b^{5} + 2 b^{6} x^{2}} - \frac{3 \sqrt{- \frac{a}{b^{11}}} \left(a d - b c\right)^{2} \left(3 a d - b c\right) \log{\left(- \frac{3 b^{5} \sqrt{- \frac{a}{b^{11}}} \left(a d - b c\right)^{2} \left(3 a d - b c\right)}{9 a^{3} d^{3} - 21 a^{2} b c d^{2} + 15 a b^{2} c^{2} d - 3 b^{3} c^{3}} + x \right)}}{4} + \frac{3 \sqrt{- \frac{a}{b^{11}}} \left(a d - b c\right)^{2} \left(3 a d - b c\right) \log{\left(\frac{3 b^{5} \sqrt{- \frac{a}{b^{11}}} \left(a d - b c\right)^{2} \left(3 a d - b c\right)}{9 a^{3} d^{3} - 21 a^{2} b c d^{2} + 15 a b^{2} c^{2} d - 3 b^{3} c^{3}} + x \right)}}{4} + \frac{d^{3} x^{7}}{7 b^{2}}"," ",0,"x**5*(-2*a*d**3/(5*b**3) + 3*c*d**2/(5*b**2)) + x**3*(a**2*d**3/b**4 - 2*a*c*d**2/b**3 + c**2*d/b**2) + x*(-4*a**3*d**3/b**5 + 9*a**2*c*d**2/b**4 - 6*a*c**2*d/b**3 + c**3/b**2) + x*(-a**4*d**3 + 3*a**3*b*c*d**2 - 3*a**2*b**2*c**2*d + a*b**3*c**3)/(2*a*b**5 + 2*b**6*x**2) - 3*sqrt(-a/b**11)*(a*d - b*c)**2*(3*a*d - b*c)*log(-3*b**5*sqrt(-a/b**11)*(a*d - b*c)**2*(3*a*d - b*c)/(9*a**3*d**3 - 21*a**2*b*c*d**2 + 15*a*b**2*c**2*d - 3*b**3*c**3) + x)/4 + 3*sqrt(-a/b**11)*(a*d - b*c)**2*(3*a*d - b*c)*log(3*b**5*sqrt(-a/b**11)*(a*d - b*c)**2*(3*a*d - b*c)/(9*a**3*d**3 - 21*a**2*b*c*d**2 + 15*a*b**2*c**2*d - 3*b**3*c**3) + x)/4 + d**3*x**7/(7*b**2)","B",0
281,1,163,0,1.343007," ","integrate(x**3*(d*x**2+c)**3/(b*x**2+a)**2,x)","x^{4} \left(- \frac{a d^{3}}{2 b^{3}} + \frac{3 c d^{2}}{4 b^{2}}\right) + x^{2} \left(\frac{3 a^{2} d^{3}}{2 b^{4}} - \frac{3 a c d^{2}}{b^{3}} + \frac{3 c^{2} d}{2 b^{2}}\right) + \frac{- a^{4} d^{3} + 3 a^{3} b c d^{2} - 3 a^{2} b^{2} c^{2} d + a b^{3} c^{3}}{2 a b^{5} + 2 b^{6} x^{2}} + \frac{d^{3} x^{6}}{6 b^{2}} - \frac{\left(a d - b c\right)^{2} \left(4 a d - b c\right) \log{\left(a + b x^{2} \right)}}{2 b^{5}}"," ",0,"x**4*(-a*d**3/(2*b**3) + 3*c*d**2/(4*b**2)) + x**2*(3*a**2*d**3/(2*b**4) - 3*a*c*d**2/b**3 + 3*c**2*d/(2*b**2)) + (-a**4*d**3 + 3*a**3*b*c*d**2 - 3*a**2*b**2*c**2*d + a*b**3*c**3)/(2*a*b**5 + 2*b**6*x**2) + d**3*x**6/(6*b**2) - (a*d - b*c)**2*(4*a*d - b*c)*log(a + b*x**2)/(2*b**5)","A",0
282,1,338,0,1.222280," ","integrate(x**2*(d*x**2+c)**3/(b*x**2+a)**2,x)","x^{3} \left(- \frac{2 a d^{3}}{3 b^{3}} + \frac{c d^{2}}{b^{2}}\right) + x \left(\frac{3 a^{2} d^{3}}{b^{4}} - \frac{6 a c d^{2}}{b^{3}} + \frac{3 c^{2} d}{b^{2}}\right) + \frac{x \left(a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}\right)}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{\sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{2} \left(7 a d - b c\right) \log{\left(- \frac{a b^{4} \sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{2} \left(7 a d - b c\right)}{7 a^{3} d^{3} - 15 a^{2} b c d^{2} + 9 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{2} \left(7 a d - b c\right) \log{\left(\frac{a b^{4} \sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{2} \left(7 a d - b c\right)}{7 a^{3} d^{3} - 15 a^{2} b c d^{2} + 9 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{4} + \frac{d^{3} x^{5}}{5 b^{2}}"," ",0,"x**3*(-2*a*d**3/(3*b**3) + c*d**2/b**2) + x*(3*a**2*d**3/b**4 - 6*a*c*d**2/b**3 + 3*c**2*d/b**2) + x*(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3)/(2*a*b**4 + 2*b**5*x**2) + sqrt(-1/(a*b**9))*(a*d - b*c)**2*(7*a*d - b*c)*log(-a*b**4*sqrt(-1/(a*b**9))*(a*d - b*c)**2*(7*a*d - b*c)/(7*a**3*d**3 - 15*a**2*b*c*d**2 + 9*a*b**2*c**2*d - b**3*c**3) + x)/4 - sqrt(-1/(a*b**9))*(a*d - b*c)**2*(7*a*d - b*c)*log(a*b**4*sqrt(-1/(a*b**9))*(a*d - b*c)**2*(7*a*d - b*c)/(7*a**3*d**3 - 15*a**2*b*c*d**2 + 9*a*b**2*c**2*d - b**3*c**3) + x)/4 + d**3*x**5/(5*b**2)","B",0
283,1,112,0,1.155771," ","integrate(x*(d*x**2+c)**3/(b*x**2+a)**2,x)","x^{2} \left(- \frac{a d^{3}}{b^{3}} + \frac{3 c d^{2}}{2 b^{2}}\right) + \frac{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{d^{3} x^{4}}{4 b^{2}} + \frac{3 d \left(a d - b c\right)^{2} \log{\left(a + b x^{2} \right)}}{2 b^{4}}"," ",0,"x**2*(-a*d**3/b**3 + 3*c*d**2/(2*b**2)) + (a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3)/(2*a*b**4 + 2*b**5*x**2) + d**3*x**4/(4*b**2) + 3*d*(a*d - b*c)**2*log(a + b*x**2)/(2*b**4)","A",0
284,1,314,0,1.062264," ","integrate((d*x**2+c)**3/(b*x**2+a)**2,x)","x \left(- \frac{2 a d^{3}}{b^{3}} + \frac{3 c d^{2}}{b^{2}}\right) + \frac{x \left(- a^{3} d^{3} + 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + b^{3} c^{3}\right)}{2 a^{2} b^{3} + 2 a b^{4} x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right) \log{\left(- \frac{a^{2} b^{3} \sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right)}{5 a^{3} d^{3} - 9 a^{2} b c d^{2} + 3 a b^{2} c^{2} d + b^{3} c^{3}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right) \log{\left(\frac{a^{2} b^{3} \sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right)}{5 a^{3} d^{3} - 9 a^{2} b c d^{2} + 3 a b^{2} c^{2} d + b^{3} c^{3}} + x \right)}}{4} + \frac{d^{3} x^{3}}{3 b^{2}}"," ",0,"x*(-2*a*d**3/b**3 + 3*c*d**2/b**2) + x*(-a**3*d**3 + 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + b**3*c**3)/(2*a**2*b**3 + 2*a*b**4*x**2) - sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)*log(-a**2*b**3*sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)/(5*a**3*d**3 - 9*a**2*b*c*d**2 + 3*a*b**2*c**2*d + b**3*c**3) + x)/4 + sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)*log(a**2*b**3*sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)/(5*a**3*d**3 - 9*a**2*b*c*d**2 + 3*a*b**2*c**2*d + b**3*c**3) + x)/4 + d**3*x**3/(3*b**2)","B",0
285,1,110,0,2.328757," ","integrate((d*x**2+c)**3/x/(b*x**2+a)**2,x)","\frac{- a^{3} d^{3} + 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + b^{3} c^{3}}{2 a^{2} b^{3} + 2 a b^{4} x^{2}} + \frac{d^{3} x^{2}}{2 b^{2}} + \frac{c^{3} \log{\left(x \right)}}{a^{2}} - \frac{\left(a d - b c\right)^{2} \left(2 a d + b c\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{2} b^{3}}"," ",0,"(-a**3*d**3 + 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + b**3*c**3)/(2*a**2*b**3 + 2*a*b**4*x**2) + d**3*x**2/(2*b**2) + c**3*log(x)/a**2 - (a*d - b*c)**2*(2*a*d + b*c)*log(a/b + x**2)/(2*a**2*b**3)","A",0
286,1,309,0,1.537896," ","integrate((d*x**2+c)**3/x**2/(b*x**2+a)**2,x)","\frac{3 \sqrt{- \frac{1}{a^{5} b^{5}}} \left(a d - b c\right)^{2} \left(a d + b c\right) \log{\left(- \frac{3 a^{3} b^{2} \sqrt{- \frac{1}{a^{5} b^{5}}} \left(a d - b c\right)^{2} \left(a d + b c\right)}{3 a^{3} d^{3} - 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + 3 b^{3} c^{3}} + x \right)}}{4} - \frac{3 \sqrt{- \frac{1}{a^{5} b^{5}}} \left(a d - b c\right)^{2} \left(a d + b c\right) \log{\left(\frac{3 a^{3} b^{2} \sqrt{- \frac{1}{a^{5} b^{5}}} \left(a d - b c\right)^{2} \left(a d + b c\right)}{3 a^{3} d^{3} - 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + 3 b^{3} c^{3}} + x \right)}}{4} + \frac{- 2 a b^{2} c^{3} + x^{2} \left(a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - 3 b^{3} c^{3}\right)}{2 a^{3} b^{2} x + 2 a^{2} b^{3} x^{3}} + \frac{d^{3} x}{b^{2}}"," ",0,"3*sqrt(-1/(a**5*b**5))*(a*d - b*c)**2*(a*d + b*c)*log(-3*a**3*b**2*sqrt(-1/(a**5*b**5))*(a*d - b*c)**2*(a*d + b*c)/(3*a**3*d**3 - 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + 3*b**3*c**3) + x)/4 - 3*sqrt(-1/(a**5*b**5))*(a*d - b*c)**2*(a*d + b*c)*log(3*a**3*b**2*sqrt(-1/(a**5*b**5))*(a*d - b*c)**2*(a*d + b*c)/(3*a**3*d**3 - 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + 3*b**3*c**3) + x)/4 + (-2*a*b**2*c**3 + x**2*(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - 3*b**3*c**3))/(2*a**3*b**2*x + 2*a**2*b**3*x**3) + d**3*x/b**2","B",0
287,1,128,0,3.179678," ","integrate((d*x**2+c)**3/x**3/(b*x**2+a)**2,x)","\frac{- a b^{2} c^{3} + x^{2} \left(a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - 2 b^{3} c^{3}\right)}{2 a^{3} b^{2} x^{2} + 2 a^{2} b^{3} x^{4}} + \frac{c^{2} \left(3 a d - 2 b c\right) \log{\left(x \right)}}{a^{3}} + \frac{\left(a d - b c\right)^{2} \left(a d + 2 b c\right) \log{\left(\frac{a}{b} + x^{2} \right)}}{2 a^{3} b^{2}}"," ",0,"(-a*b**2*c**3 + x**2*(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - 2*b**3*c**3))/(2*a**3*b**2*x**2 + 2*a**2*b**3*x**4) + c**2*(3*a*d - 2*b*c)*log(x)/a**3 + (a*d - b*c)**2*(a*d + 2*b*c)*log(a/b + x**2)/(2*a**3*b**2)","A",0
288,1,321,0,1.893248," ","integrate((d*x**2+c)**3/x**4/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{7} b^{3}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right) \log{\left(- \frac{a^{4} b \sqrt{- \frac{1}{a^{7} b^{3}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right)}{a^{3} d^{3} + 3 a^{2} b c d^{2} - 9 a b^{2} c^{2} d + 5 b^{3} c^{3}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{7} b^{3}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right) \log{\left(\frac{a^{4} b \sqrt{- \frac{1}{a^{7} b^{3}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right)}{a^{3} d^{3} + 3 a^{2} b c d^{2} - 9 a b^{2} c^{2} d + 5 b^{3} c^{3}} + x \right)}}{4} + \frac{- 2 a^{2} b c^{3} + x^{4} \left(- 3 a^{3} d^{3} + 9 a^{2} b c d^{2} - 27 a b^{2} c^{2} d + 15 b^{3} c^{3}\right) + x^{2} \left(- 18 a^{2} b c^{2} d + 10 a b^{2} c^{3}\right)}{6 a^{4} b x^{3} + 6 a^{3} b^{2} x^{5}}"," ",0,"-sqrt(-1/(a**7*b**3))*(a*d - b*c)**2*(a*d + 5*b*c)*log(-a**4*b*sqrt(-1/(a**7*b**3))*(a*d - b*c)**2*(a*d + 5*b*c)/(a**3*d**3 + 3*a**2*b*c*d**2 - 9*a*b**2*c**2*d + 5*b**3*c**3) + x)/4 + sqrt(-1/(a**7*b**3))*(a*d - b*c)**2*(a*d + 5*b*c)*log(a**4*b*sqrt(-1/(a**7*b**3))*(a*d - b*c)**2*(a*d + 5*b*c)/(a**3*d**3 + 3*a**2*b*c*d**2 - 9*a*b**2*c**2*d + 5*b**3*c**3) + x)/4 + (-2*a**2*b*c**3 + x**4*(-3*a**3*d**3 + 9*a**2*b*c*d**2 - 27*a*b**2*c**2*d + 15*b**3*c**3) + x**2*(-18*a**2*b*c**2*d + 10*a*b**2*c**3))/(6*a**4*b*x**3 + 6*a**3*b**2*x**5)","B",0
289,-1,0,0,0.000000," ","integrate(x**4/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,1,253,0,1.905826," ","integrate(x**3/(b*x**2+a)**2/(d*x**2+c),x)","- \frac{a}{2 a^{2} b d - 2 a b^{2} c + x^{2} \left(2 a b^{2} d - 2 b^{3} c\right)} - \frac{c \log{\left(x^{2} + \frac{- \frac{a^{3} c d^{3}}{\left(a d - b c\right)^{2}} + \frac{3 a^{2} b c^{2} d^{2}}{\left(a d - b c\right)^{2}} - \frac{3 a b^{2} c^{3} d}{\left(a d - b c\right)^{2}} + a c d + \frac{b^{3} c^{4}}{\left(a d - b c\right)^{2}} + b c^{2}}{2 b c d} \right)}}{2 \left(a d - b c\right)^{2}} + \frac{c \log{\left(x^{2} + \frac{\frac{a^{3} c d^{3}}{\left(a d - b c\right)^{2}} - \frac{3 a^{2} b c^{2} d^{2}}{\left(a d - b c\right)^{2}} + \frac{3 a b^{2} c^{3} d}{\left(a d - b c\right)^{2}} + a c d - \frac{b^{3} c^{4}}{\left(a d - b c\right)^{2}} + b c^{2}}{2 b c d} \right)}}{2 \left(a d - b c\right)^{2}}"," ",0,"-a/(2*a**2*b*d - 2*a*b**2*c + x**2*(2*a*b**2*d - 2*b**3*c)) - c*log(x**2 + (-a**3*c*d**3/(a*d - b*c)**2 + 3*a**2*b*c**2*d**2/(a*d - b*c)**2 - 3*a*b**2*c**3*d/(a*d - b*c)**2 + a*c*d + b**3*c**4/(a*d - b*c)**2 + b*c**2)/(2*b*c*d))/(2*(a*d - b*c)**2) + c*log(x**2 + (a**3*c*d**3/(a*d - b*c)**2 - 3*a**2*b*c**2*d**2/(a*d - b*c)**2 + 3*a*b**2*c**3*d/(a*d - b*c)**2 + a*c*d - b**3*c**4/(a*d - b*c)**2 + b*c**2)/(2*b*c*d))/(2*(a*d - b*c)**2)","B",0
291,-1,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,1,248,0,1.807368," ","integrate(x/(b*x**2+a)**2/(d*x**2+c),x)","\frac{d \log{\left(x^{2} + \frac{- \frac{a^{3} d^{4}}{\left(a d - b c\right)^{2}} + \frac{3 a^{2} b c d^{3}}{\left(a d - b c\right)^{2}} - \frac{3 a b^{2} c^{2} d^{2}}{\left(a d - b c\right)^{2}} + a d^{2} + \frac{b^{3} c^{3} d}{\left(a d - b c\right)^{2}} + b c d}{2 b d^{2}} \right)}}{2 \left(a d - b c\right)^{2}} - \frac{d \log{\left(x^{2} + \frac{\frac{a^{3} d^{4}}{\left(a d - b c\right)^{2}} - \frac{3 a^{2} b c d^{3}}{\left(a d - b c\right)^{2}} + \frac{3 a b^{2} c^{2} d^{2}}{\left(a d - b c\right)^{2}} + a d^{2} - \frac{b^{3} c^{3} d}{\left(a d - b c\right)^{2}} + b c d}{2 b d^{2}} \right)}}{2 \left(a d - b c\right)^{2}} + \frac{1}{2 a^{2} d - 2 a b c + x^{2} \left(2 a b d - 2 b^{2} c\right)}"," ",0,"d*log(x**2 + (-a**3*d**4/(a*d - b*c)**2 + 3*a**2*b*c*d**3/(a*d - b*c)**2 - 3*a*b**2*c**2*d**2/(a*d - b*c)**2 + a*d**2 + b**3*c**3*d/(a*d - b*c)**2 + b*c*d)/(2*b*d**2))/(2*(a*d - b*c)**2) - d*log(x**2 + (a**3*d**4/(a*d - b*c)**2 - 3*a**2*b*c*d**3/(a*d - b*c)**2 + 3*a*b**2*c**2*d**2/(a*d - b*c)**2 + a*d**2 - b**3*c**3*d/(a*d - b*c)**2 + b*c*d)/(2*b*d**2))/(2*(a*d - b*c)**2) + 1/(2*a**2*d - 2*a*b*c + x**2*(2*a*b*d - 2*b**2*c))","B",0
293,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate(1/x/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,-1,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate(1/x**5/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate(1/x**6/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate(1/x**7/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(x**4/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,1,507,0,4.030588," ","integrate(x**3/(b*x**2+a)**2/(d*x**2+c)**2,x)","\frac{2 a c + x^{2} \left(a d + b c\right)}{2 a^{3} c d^{2} - 4 a^{2} b c^{2} d + 2 a b^{2} c^{3} + x^{4} \left(2 a^{2} b d^{3} - 4 a b^{2} c d^{2} + 2 b^{3} c^{2} d\right) + x^{2} \left(2 a^{3} d^{3} - 2 a^{2} b c d^{2} - 2 a b^{2} c^{2} d + 2 b^{3} c^{3}\right)} + \frac{\left(a d + b c\right) \log{\left(x^{2} + \frac{- \frac{a^{4} d^{4} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + \frac{4 a^{3} b c d^{3} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} - \frac{6 a^{2} b^{2} c^{2} d^{2} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + a^{2} d^{2} + \frac{4 a b^{3} c^{3} d \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + 2 a b c d - \frac{b^{4} c^{4} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + b^{2} c^{2}}{2 a b d^{2} + 2 b^{2} c d} \right)}}{2 \left(a d - b c\right)^{3}} - \frac{\left(a d + b c\right) \log{\left(x^{2} + \frac{\frac{a^{4} d^{4} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} - \frac{4 a^{3} b c d^{3} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + \frac{6 a^{2} b^{2} c^{2} d^{2} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + a^{2} d^{2} - \frac{4 a b^{3} c^{3} d \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + 2 a b c d + \frac{b^{4} c^{4} \left(a d + b c\right)}{\left(a d - b c\right)^{3}} + b^{2} c^{2}}{2 a b d^{2} + 2 b^{2} c d} \right)}}{2 \left(a d - b c\right)^{3}}"," ",0,"(2*a*c + x**2*(a*d + b*c))/(2*a**3*c*d**2 - 4*a**2*b*c**2*d + 2*a*b**2*c**3 + x**4*(2*a**2*b*d**3 - 4*a*b**2*c*d**2 + 2*b**3*c**2*d) + x**2*(2*a**3*d**3 - 2*a**2*b*c*d**2 - 2*a*b**2*c**2*d + 2*b**3*c**3)) + (a*d + b*c)*log(x**2 + (-a**4*d**4*(a*d + b*c)/(a*d - b*c)**3 + 4*a**3*b*c*d**3*(a*d + b*c)/(a*d - b*c)**3 - 6*a**2*b**2*c**2*d**2*(a*d + b*c)/(a*d - b*c)**3 + a**2*d**2 + 4*a*b**3*c**3*d*(a*d + b*c)/(a*d - b*c)**3 + 2*a*b*c*d - b**4*c**4*(a*d + b*c)/(a*d - b*c)**3 + b**2*c**2)/(2*a*b*d**2 + 2*b**2*c*d))/(2*(a*d - b*c)**3) - (a*d + b*c)*log(x**2 + (a**4*d**4*(a*d + b*c)/(a*d - b*c)**3 - 4*a**3*b*c*d**3*(a*d + b*c)/(a*d - b*c)**3 + 6*a**2*b**2*c**2*d**2*(a*d + b*c)/(a*d - b*c)**3 + a**2*d**2 - 4*a*b**3*c**3*d*(a*d + b*c)/(a*d - b*c)**3 + 2*a*b*c*d + b**4*c**4*(a*d + b*c)/(a*d - b*c)**3 + b**2*c**2)/(2*a*b*d**2 + 2*b**2*c*d))/(2*(a*d - b*c)**3)","B",0
303,-1,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,1,410,0,2.759676," ","integrate(x/(b*x**2+a)**2/(d*x**2+c)**2,x)","- \frac{b d \log{\left(x^{2} + \frac{- \frac{a^{4} b d^{5}}{\left(a d - b c\right)^{3}} + \frac{4 a^{3} b^{2} c d^{4}}{\left(a d - b c\right)^{3}} - \frac{6 a^{2} b^{3} c^{2} d^{3}}{\left(a d - b c\right)^{3}} + \frac{4 a b^{4} c^{3} d^{2}}{\left(a d - b c\right)^{3}} + a b d^{2} - \frac{b^{5} c^{4} d}{\left(a d - b c\right)^{3}} + b^{2} c d}{2 b^{2} d^{2}} \right)}}{\left(a d - b c\right)^{3}} + \frac{b d \log{\left(x^{2} + \frac{\frac{a^{4} b d^{5}}{\left(a d - b c\right)^{3}} - \frac{4 a^{3} b^{2} c d^{4}}{\left(a d - b c\right)^{3}} + \frac{6 a^{2} b^{3} c^{2} d^{3}}{\left(a d - b c\right)^{3}} - \frac{4 a b^{4} c^{3} d^{2}}{\left(a d - b c\right)^{3}} + a b d^{2} + \frac{b^{5} c^{4} d}{\left(a d - b c\right)^{3}} + b^{2} c d}{2 b^{2} d^{2}} \right)}}{\left(a d - b c\right)^{3}} + \frac{- a d - b c - 2 b d x^{2}}{2 a^{3} c d^{2} - 4 a^{2} b c^{2} d + 2 a b^{2} c^{3} + x^{4} \left(2 a^{2} b d^{3} - 4 a b^{2} c d^{2} + 2 b^{3} c^{2} d\right) + x^{2} \left(2 a^{3} d^{3} - 2 a^{2} b c d^{2} - 2 a b^{2} c^{2} d + 2 b^{3} c^{3}\right)}"," ",0,"-b*d*log(x**2 + (-a**4*b*d**5/(a*d - b*c)**3 + 4*a**3*b**2*c*d**4/(a*d - b*c)**3 - 6*a**2*b**3*c**2*d**3/(a*d - b*c)**3 + 4*a*b**4*c**3*d**2/(a*d - b*c)**3 + a*b*d**2 - b**5*c**4*d/(a*d - b*c)**3 + b**2*c*d)/(2*b**2*d**2))/(a*d - b*c)**3 + b*d*log(x**2 + (a**4*b*d**5/(a*d - b*c)**3 - 4*a**3*b**2*c*d**4/(a*d - b*c)**3 + 6*a**2*b**3*c**2*d**3/(a*d - b*c)**3 - 4*a*b**4*c**3*d**2/(a*d - b*c)**3 + a*b*d**2 + b**5*c**4*d/(a*d - b*c)**3 + b**2*c*d)/(2*b**2*d**2))/(a*d - b*c)**3 + (-a*d - b*c - 2*b*d*x**2)/(2*a**3*c*d**2 - 4*a**2*b*c**2*d + 2*a*b**2*c**3 + x**4*(2*a**2*b*d**3 - 4*a*b**2*c*d**2 + 2*b**3*c**2*d) + x**2*(2*a**3*d**3 - 2*a**2*b*c*d**2 - 2*a*b**2*c**2*d + 2*b**3*c**3))","B",0
305,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate(1/x/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate(x**4/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,1,784,0,7.954531," ","integrate(x**3/(b*x**2+a)**2/(d*x**2+c)**3,x)","- \frac{b \left(2 a d + b c\right) \log{\left(x^{2} + \frac{- \frac{a^{5} b d^{5} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + \frac{5 a^{4} b^{2} c d^{4} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} - \frac{10 a^{3} b^{3} c^{2} d^{3} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + \frac{10 a^{2} b^{4} c^{3} d^{2} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + 2 a^{2} b d^{2} - \frac{5 a b^{5} c^{4} d \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + 3 a b^{2} c d + \frac{b^{6} c^{5} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + b^{3} c^{2}}{4 a b^{2} d^{2} + 2 b^{3} c d} \right)}}{2 \left(a d - b c\right)^{4}} + \frac{b \left(2 a d + b c\right) \log{\left(x^{2} + \frac{\frac{a^{5} b d^{5} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} - \frac{5 a^{4} b^{2} c d^{4} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + \frac{10 a^{3} b^{3} c^{2} d^{3} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} - \frac{10 a^{2} b^{4} c^{3} d^{2} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + 2 a^{2} b d^{2} + \frac{5 a b^{5} c^{4} d \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + 3 a b^{2} c d - \frac{b^{6} c^{5} \left(2 a d + b c\right)}{\left(a d - b c\right)^{4}} + b^{3} c^{2}}{4 a b^{2} d^{2} + 2 b^{3} c d} \right)}}{2 \left(a d - b c\right)^{4}} + \frac{- a^{2} c d - 5 a b c^{2} + x^{4} \left(- 4 a b d^{2} - 2 b^{2} c d\right) + x^{2} \left(- 2 a^{2} d^{2} - 7 a b c d - 3 b^{2} c^{2}\right)}{4 a^{4} c^{2} d^{3} - 12 a^{3} b c^{3} d^{2} + 12 a^{2} b^{2} c^{4} d - 4 a b^{3} c^{5} + x^{6} \left(4 a^{3} b d^{5} - 12 a^{2} b^{2} c d^{4} + 12 a b^{3} c^{2} d^{3} - 4 b^{4} c^{3} d^{2}\right) + x^{4} \left(4 a^{4} d^{5} - 4 a^{3} b c d^{4} - 12 a^{2} b^{2} c^{2} d^{3} + 20 a b^{3} c^{3} d^{2} - 8 b^{4} c^{4} d\right) + x^{2} \left(8 a^{4} c d^{4} - 20 a^{3} b c^{2} d^{3} + 12 a^{2} b^{2} c^{3} d^{2} + 4 a b^{3} c^{4} d - 4 b^{4} c^{5}\right)}"," ",0,"-b*(2*a*d + b*c)*log(x**2 + (-a**5*b*d**5*(2*a*d + b*c)/(a*d - b*c)**4 + 5*a**4*b**2*c*d**4*(2*a*d + b*c)/(a*d - b*c)**4 - 10*a**3*b**3*c**2*d**3*(2*a*d + b*c)/(a*d - b*c)**4 + 10*a**2*b**4*c**3*d**2*(2*a*d + b*c)/(a*d - b*c)**4 + 2*a**2*b*d**2 - 5*a*b**5*c**4*d*(2*a*d + b*c)/(a*d - b*c)**4 + 3*a*b**2*c*d + b**6*c**5*(2*a*d + b*c)/(a*d - b*c)**4 + b**3*c**2)/(4*a*b**2*d**2 + 2*b**3*c*d))/(2*(a*d - b*c)**4) + b*(2*a*d + b*c)*log(x**2 + (a**5*b*d**5*(2*a*d + b*c)/(a*d - b*c)**4 - 5*a**4*b**2*c*d**4*(2*a*d + b*c)/(a*d - b*c)**4 + 10*a**3*b**3*c**2*d**3*(2*a*d + b*c)/(a*d - b*c)**4 - 10*a**2*b**4*c**3*d**2*(2*a*d + b*c)/(a*d - b*c)**4 + 2*a**2*b*d**2 + 5*a*b**5*c**4*d*(2*a*d + b*c)/(a*d - b*c)**4 + 3*a*b**2*c*d - b**6*c**5*(2*a*d + b*c)/(a*d - b*c)**4 + b**3*c**2)/(4*a*b**2*d**2 + 2*b**3*c*d))/(2*(a*d - b*c)**4) + (-a**2*c*d - 5*a*b*c**2 + x**4*(-4*a*b*d**2 - 2*b**2*c*d) + x**2*(-2*a**2*d**2 - 7*a*b*c*d - 3*b**2*c**2))/(4*a**4*c**2*d**3 - 12*a**3*b*c**3*d**2 + 12*a**2*b**2*c**4*d - 4*a*b**3*c**5 + x**6*(4*a**3*b*d**5 - 12*a**2*b**2*c*d**4 + 12*a*b**3*c**2*d**3 - 4*b**4*c**3*d**2) + x**4*(4*a**4*d**5 - 4*a**3*b*c*d**4 - 12*a**2*b**2*c**2*d**3 + 20*a*b**3*c**3*d**2 - 8*b**4*c**4*d) + x**2*(8*a**4*c*d**4 - 20*a**3*b*c**2*d**3 + 12*a**2*b**2*c**3*d**2 + 4*a*b**3*c**4*d - 4*b**4*c**5))","B",0
312,-1,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,1,643,0,10.063001," ","integrate(x/(b*x**2+a)**2/(d*x**2+c)**3,x)","\frac{3 b^{2} d \log{\left(x^{2} + \frac{- \frac{3 a^{5} b^{2} d^{6}}{\left(a d - b c\right)^{4}} + \frac{15 a^{4} b^{3} c d^{5}}{\left(a d - b c\right)^{4}} - \frac{30 a^{3} b^{4} c^{2} d^{4}}{\left(a d - b c\right)^{4}} + \frac{30 a^{2} b^{5} c^{3} d^{3}}{\left(a d - b c\right)^{4}} - \frac{15 a b^{6} c^{4} d^{2}}{\left(a d - b c\right)^{4}} + 3 a b^{2} d^{2} + \frac{3 b^{7} c^{5} d}{\left(a d - b c\right)^{4}} + 3 b^{3} c d}{6 b^{3} d^{2}} \right)}}{2 \left(a d - b c\right)^{4}} - \frac{3 b^{2} d \log{\left(x^{2} + \frac{\frac{3 a^{5} b^{2} d^{6}}{\left(a d - b c\right)^{4}} - \frac{15 a^{4} b^{3} c d^{5}}{\left(a d - b c\right)^{4}} + \frac{30 a^{3} b^{4} c^{2} d^{4}}{\left(a d - b c\right)^{4}} - \frac{30 a^{2} b^{5} c^{3} d^{3}}{\left(a d - b c\right)^{4}} + \frac{15 a b^{6} c^{4} d^{2}}{\left(a d - b c\right)^{4}} + 3 a b^{2} d^{2} - \frac{3 b^{7} c^{5} d}{\left(a d - b c\right)^{4}} + 3 b^{3} c d}{6 b^{3} d^{2}} \right)}}{2 \left(a d - b c\right)^{4}} + \frac{- a^{2} d^{2} + 5 a b c d + 2 b^{2} c^{2} + 6 b^{2} d^{2} x^{4} + x^{2} \left(3 a b d^{2} + 9 b^{2} c d\right)}{4 a^{4} c^{2} d^{3} - 12 a^{3} b c^{3} d^{2} + 12 a^{2} b^{2} c^{4} d - 4 a b^{3} c^{5} + x^{6} \left(4 a^{3} b d^{5} - 12 a^{2} b^{2} c d^{4} + 12 a b^{3} c^{2} d^{3} - 4 b^{4} c^{3} d^{2}\right) + x^{4} \left(4 a^{4} d^{5} - 4 a^{3} b c d^{4} - 12 a^{2} b^{2} c^{2} d^{3} + 20 a b^{3} c^{3} d^{2} - 8 b^{4} c^{4} d\right) + x^{2} \left(8 a^{4} c d^{4} - 20 a^{3} b c^{2} d^{3} + 12 a^{2} b^{2} c^{3} d^{2} + 4 a b^{3} c^{4} d - 4 b^{4} c^{5}\right)}"," ",0,"3*b**2*d*log(x**2 + (-3*a**5*b**2*d**6/(a*d - b*c)**4 + 15*a**4*b**3*c*d**5/(a*d - b*c)**4 - 30*a**3*b**4*c**2*d**4/(a*d - b*c)**4 + 30*a**2*b**5*c**3*d**3/(a*d - b*c)**4 - 15*a*b**6*c**4*d**2/(a*d - b*c)**4 + 3*a*b**2*d**2 + 3*b**7*c**5*d/(a*d - b*c)**4 + 3*b**3*c*d)/(6*b**3*d**2))/(2*(a*d - b*c)**4) - 3*b**2*d*log(x**2 + (3*a**5*b**2*d**6/(a*d - b*c)**4 - 15*a**4*b**3*c*d**5/(a*d - b*c)**4 + 30*a**3*b**4*c**2*d**4/(a*d - b*c)**4 - 30*a**2*b**5*c**3*d**3/(a*d - b*c)**4 + 15*a*b**6*c**4*d**2/(a*d - b*c)**4 + 3*a*b**2*d**2 - 3*b**7*c**5*d/(a*d - b*c)**4 + 3*b**3*c*d)/(6*b**3*d**2))/(2*(a*d - b*c)**4) + (-a**2*d**2 + 5*a*b*c*d + 2*b**2*c**2 + 6*b**2*d**2*x**4 + x**2*(3*a*b*d**2 + 9*b**2*c*d))/(4*a**4*c**2*d**3 - 12*a**3*b*c**3*d**2 + 12*a**2*b**2*c**4*d - 4*a*b**3*c**5 + x**6*(4*a**3*b*d**5 - 12*a**2*b**2*c*d**4 + 12*a*b**3*c**2*d**3 - 4*b**4*c**3*d**2) + x**4*(4*a**4*d**5 - 4*a**3*b*c*d**4 - 12*a**2*b**2*c**2*d**3 + 20*a*b**3*c**3*d**2 - 8*b**4*c**4*d) + x**2*(8*a**4*c*d**4 - 20*a**3*b*c**2*d**3 + 12*a**2*b**2*c**3*d**2 + 4*a*b**3*c**4*d - 4*b**4*c**5))","B",0
314,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate(1/x/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,1,2069,0,3.077394," ","integrate(x**m*(b*x**2+a)**3*(B*x**2+A),x)","\begin{cases} - \frac{A a^{3}}{8 x^{8}} - \frac{A a^{2} b}{2 x^{6}} - \frac{3 A a b^{2}}{4 x^{4}} - \frac{A b^{3}}{2 x^{2}} - \frac{B a^{3}}{6 x^{6}} - \frac{3 B a^{2} b}{4 x^{4}} - \frac{3 B a b^{2}}{2 x^{2}} + B b^{3} \log{\left(x \right)} & \text{for}\: m = -9 \\- \frac{A a^{3}}{6 x^{6}} - \frac{3 A a^{2} b}{4 x^{4}} - \frac{3 A a b^{2}}{2 x^{2}} + A b^{3} \log{\left(x \right)} - \frac{B a^{3}}{4 x^{4}} - \frac{3 B a^{2} b}{2 x^{2}} + 3 B a b^{2} \log{\left(x \right)} + \frac{B b^{3} x^{2}}{2} & \text{for}\: m = -7 \\- \frac{A a^{3}}{4 x^{4}} - \frac{3 A a^{2} b}{2 x^{2}} + 3 A a b^{2} \log{\left(x \right)} + \frac{A b^{3} x^{2}}{2} - \frac{B a^{3}}{2 x^{2}} + 3 B a^{2} b \log{\left(x \right)} + \frac{3 B a b^{2} x^{2}}{2} + \frac{B b^{3} x^{4}}{4} & \text{for}\: m = -5 \\- \frac{A a^{3}}{2 x^{2}} + 3 A a^{2} b \log{\left(x \right)} + \frac{3 A a b^{2} x^{2}}{2} + \frac{A b^{3} x^{4}}{4} + B a^{3} \log{\left(x \right)} + \frac{3 B a^{2} b x^{2}}{2} + \frac{3 B a b^{2} x^{4}}{4} + \frac{B b^{3} x^{6}}{6} & \text{for}\: m = -3 \\A a^{3} \log{\left(x \right)} + \frac{3 A a^{2} b x^{2}}{2} + \frac{3 A a b^{2} x^{4}}{4} + \frac{A b^{3} x^{6}}{6} + \frac{B a^{3} x^{2}}{2} + \frac{3 B a^{2} b x^{4}}{4} + \frac{B a b^{2} x^{6}}{2} + \frac{B b^{3} x^{8}}{8} & \text{for}\: m = -1 \\\frac{A a^{3} m^{4} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{24 A a^{3} m^{3} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{206 A a^{3} m^{2} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{744 A a^{3} m x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{945 A a^{3} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{3 A a^{2} b m^{4} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{66 A a^{2} b m^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{492 A a^{2} b m^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1374 A a^{2} b m x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{945 A a^{2} b x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{3 A a b^{2} m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{60 A a b^{2} m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{390 A a b^{2} m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{900 A a b^{2} m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{567 A a b^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{A b^{3} m^{4} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{18 A b^{3} m^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{104 A b^{3} m^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{222 A b^{3} m x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{135 A b^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{B a^{3} m^{4} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{22 B a^{3} m^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{164 B a^{3} m^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{458 B a^{3} m x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{315 B a^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{3 B a^{2} b m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{60 B a^{2} b m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{390 B a^{2} b m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{900 B a^{2} b m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{567 B a^{2} b x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{3 B a b^{2} m^{4} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{54 B a b^{2} m^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{312 B a b^{2} m^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{666 B a b^{2} m x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{405 B a b^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{B b^{3} m^{4} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{16 B b^{3} m^{3} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{86 B b^{3} m^{2} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{176 B b^{3} m x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{105 B b^{3} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**3/(8*x**8) - A*a**2*b/(2*x**6) - 3*A*a*b**2/(4*x**4) - A*b**3/(2*x**2) - B*a**3/(6*x**6) - 3*B*a**2*b/(4*x**4) - 3*B*a*b**2/(2*x**2) + B*b**3*log(x), Eq(m, -9)), (-A*a**3/(6*x**6) - 3*A*a**2*b/(4*x**4) - 3*A*a*b**2/(2*x**2) + A*b**3*log(x) - B*a**3/(4*x**4) - 3*B*a**2*b/(2*x**2) + 3*B*a*b**2*log(x) + B*b**3*x**2/2, Eq(m, -7)), (-A*a**3/(4*x**4) - 3*A*a**2*b/(2*x**2) + 3*A*a*b**2*log(x) + A*b**3*x**2/2 - B*a**3/(2*x**2) + 3*B*a**2*b*log(x) + 3*B*a*b**2*x**2/2 + B*b**3*x**4/4, Eq(m, -5)), (-A*a**3/(2*x**2) + 3*A*a**2*b*log(x) + 3*A*a*b**2*x**2/2 + A*b**3*x**4/4 + B*a**3*log(x) + 3*B*a**2*b*x**2/2 + 3*B*a*b**2*x**4/4 + B*b**3*x**6/6, Eq(m, -3)), (A*a**3*log(x) + 3*A*a**2*b*x**2/2 + 3*A*a*b**2*x**4/4 + A*b**3*x**6/6 + B*a**3*x**2/2 + 3*B*a**2*b*x**4/4 + B*a*b**2*x**6/2 + B*b**3*x**8/8, Eq(m, -1)), (A*a**3*m**4*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 24*A*a**3*m**3*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 206*A*a**3*m**2*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 744*A*a**3*m*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 945*A*a**3*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 3*A*a**2*b*m**4*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 66*A*a**2*b*m**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 492*A*a**2*b*m**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1374*A*a**2*b*m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 945*A*a**2*b*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 3*A*a*b**2*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 60*A*a*b**2*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 390*A*a*b**2*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 900*A*a*b**2*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 567*A*a*b**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + A*b**3*m**4*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 18*A*b**3*m**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 104*A*b**3*m**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 222*A*b**3*m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 135*A*b**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + B*a**3*m**4*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 22*B*a**3*m**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 164*B*a**3*m**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 458*B*a**3*m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 315*B*a**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 3*B*a**2*b*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 60*B*a**2*b*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 390*B*a**2*b*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 900*B*a**2*b*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 567*B*a**2*b*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 3*B*a*b**2*m**4*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 54*B*a*b**2*m**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 312*B*a*b**2*m**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 666*B*a*b**2*m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 405*B*a*b**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + B*b**3*m**4*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 16*B*b**3*m**3*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 86*B*b**3*m**2*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 176*B*b**3*m*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 105*B*b**3*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945), True))","A",0
320,1,1044,0,1.792197," ","integrate(x**m*(b*x**2+a)**2*(B*x**2+A),x)","\begin{cases} - \frac{A a^{2}}{6 x^{6}} - \frac{A a b}{2 x^{4}} - \frac{A b^{2}}{2 x^{2}} - \frac{B a^{2}}{4 x^{4}} - \frac{B a b}{x^{2}} + B b^{2} \log{\left(x \right)} & \text{for}\: m = -7 \\- \frac{A a^{2}}{4 x^{4}} - \frac{A a b}{x^{2}} + A b^{2} \log{\left(x \right)} - \frac{B a^{2}}{2 x^{2}} + 2 B a b \log{\left(x \right)} + \frac{B b^{2} x^{2}}{2} & \text{for}\: m = -5 \\- \frac{A a^{2}}{2 x^{2}} + 2 A a b \log{\left(x \right)} + \frac{A b^{2} x^{2}}{2} + B a^{2} \log{\left(x \right)} + B a b x^{2} + \frac{B b^{2} x^{4}}{4} & \text{for}\: m = -3 \\A a^{2} \log{\left(x \right)} + A a b x^{2} + \frac{A b^{2} x^{4}}{4} + \frac{B a^{2} x^{2}}{2} + \frac{B a b x^{4}}{2} + \frac{B b^{2} x^{6}}{6} & \text{for}\: m = -1 \\\frac{A a^{2} m^{3} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{15 A a^{2} m^{2} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{71 A a^{2} m x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{105 A a^{2} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{2 A a b m^{3} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{26 A a b m^{2} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{94 A a b m x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{70 A a b x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{A b^{2} m^{3} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{11 A b^{2} m^{2} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{31 A b^{2} m x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{21 A b^{2} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{B a^{2} m^{3} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{13 B a^{2} m^{2} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{47 B a^{2} m x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{35 B a^{2} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{2 B a b m^{3} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{22 B a b m^{2} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{62 B a b m x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{42 B a b x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{B b^{2} m^{3} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{9 B b^{2} m^{2} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{23 B b^{2} m x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{15 B b^{2} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**2/(6*x**6) - A*a*b/(2*x**4) - A*b**2/(2*x**2) - B*a**2/(4*x**4) - B*a*b/x**2 + B*b**2*log(x), Eq(m, -7)), (-A*a**2/(4*x**4) - A*a*b/x**2 + A*b**2*log(x) - B*a**2/(2*x**2) + 2*B*a*b*log(x) + B*b**2*x**2/2, Eq(m, -5)), (-A*a**2/(2*x**2) + 2*A*a*b*log(x) + A*b**2*x**2/2 + B*a**2*log(x) + B*a*b*x**2 + B*b**2*x**4/4, Eq(m, -3)), (A*a**2*log(x) + A*a*b*x**2 + A*b**2*x**4/4 + B*a**2*x**2/2 + B*a*b*x**4/2 + B*b**2*x**6/6, Eq(m, -1)), (A*a**2*m**3*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 15*A*a**2*m**2*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 71*A*a**2*m*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 105*A*a**2*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 2*A*a*b*m**3*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 26*A*a*b*m**2*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 94*A*a*b*m*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 70*A*a*b*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + A*b**2*m**3*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 11*A*b**2*m**2*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 31*A*b**2*m*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 21*A*b**2*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + B*a**2*m**3*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 13*B*a**2*m**2*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 47*B*a**2*m*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 35*B*a**2*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 2*B*a*b*m**3*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 22*B*a*b*m**2*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 62*B*a*b*m*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 42*B*a*b*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + B*b**2*m**3*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 9*B*b**2*m**2*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 23*B*b**2*m*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 15*B*b**2*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105), True))","A",0
321,1,410,0,0.943429," ","integrate(x**m*(b*x**2+a)*(B*x**2+A),x)","\begin{cases} - \frac{A a}{4 x^{4}} - \frac{A b}{2 x^{2}} - \frac{B a}{2 x^{2}} + B b \log{\left(x \right)} & \text{for}\: m = -5 \\- \frac{A a}{2 x^{2}} + A b \log{\left(x \right)} + B a \log{\left(x \right)} + \frac{B b x^{2}}{2} & \text{for}\: m = -3 \\A a \log{\left(x \right)} + \frac{A b x^{2}}{2} + \frac{B a x^{2}}{2} + \frac{B b x^{4}}{4} & \text{for}\: m = -1 \\\frac{A a m^{2} x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{8 A a m x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{15 A a x x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{A b m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{6 A b m x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{5 A b x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{B a m^{2} x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{6 B a m x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{5 B a x^{3} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{B b m^{2} x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{4 B b m x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} + \frac{3 B b x^{5} x^{m}}{m^{3} + 9 m^{2} + 23 m + 15} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a/(4*x**4) - A*b/(2*x**2) - B*a/(2*x**2) + B*b*log(x), Eq(m, -5)), (-A*a/(2*x**2) + A*b*log(x) + B*a*log(x) + B*b*x**2/2, Eq(m, -3)), (A*a*log(x) + A*b*x**2/2 + B*a*x**2/2 + B*b*x**4/4, Eq(m, -1)), (A*a*m**2*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 8*A*a*m*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + 15*A*a*x*x**m/(m**3 + 9*m**2 + 23*m + 15) + A*b*m**2*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 6*A*b*m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 5*A*b*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + B*a*m**2*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 6*B*a*m*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + 5*B*a*x**3*x**m/(m**3 + 9*m**2 + 23*m + 15) + B*b*m**2*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 4*B*b*m*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15) + 3*B*b*x**5*x**m/(m**3 + 9*m**2 + 23*m + 15), True))","A",0
322,1,190,0,4.171164," ","integrate(x**m*(B*x**2+A)/(b*x**2+a),x)","\frac{A m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{A x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{B m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 B x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}"," ",0,"A*m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + A*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + B*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*a*gamma(m/2 + 5/2)) + 3*B*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*a*gamma(m/2 + 5/2))","C",0
323,1,906,0,30.216370," ","integrate(x**m*(B*x**2+A)/(b*x**2+a)**2,x)","A \left(- \frac{a m^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{b m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{b x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}\right) + B \left(- \frac{a m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{4 a m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{2 a m x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{3 a x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{6 a x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{b m^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{4 b m x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{3 b x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}\right)"," ",0,"A*(-a*m**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + 2*a*m*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + a*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + 2*a*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) - b*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + b*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2))) + B*(-a*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 4*a*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) + 2*a*m*x**3*x**m*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 3*a*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) + 6*a*x**3*x**m*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - b*m**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 4*b*m*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 3*b*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)))","C",0
324,1,3053,0,100.060158," ","integrate(x**m*(B*x**2+A)/(b*x**2+a)**3,x)","A \left(\frac{a^{2} m^{3} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{3 a^{2} m^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a^{2} m^{2} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{a^{2} m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{8 a^{2} m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 a^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{10 a^{2} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a b m^{3} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{6 a b m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a b m^{2} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{2 a b m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{4 a b m x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{6 a b x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{6 a b x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{b^{2} m^{3} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{3 b^{2} m^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{b^{2} m x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 b^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}\right) + B \left(\frac{a^{2} m^{3} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 a^{2} m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{2 a^{2} m^{2} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{a^{2} m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{3 a^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{18 a^{2} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{2 a b m^{3} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{6 a b m^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{2 a b m^{2} x^{5} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{2 a b m x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{4 a b m x^{5} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{6 a b x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{6 a b x^{5} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{b^{2} m^{3} x^{7} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 b^{2} m^{2} x^{7} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{b^{2} m x^{7} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{3 b^{2} x^{7} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{32 a^{5} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 64 a^{4} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 32 a^{3} b^{2} x^{4} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}\right)"," ",0,"A*(a**2*m**3*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 3*a**2*m**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 2*a**2*m**2*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - a**2*m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 8*a**2*m*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 3*a**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 10*a**2*x*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 2*a*b*m**3*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 6*a*b*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 2*a*b*m**2*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 2*a*b*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 4*a*b*m*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 6*a*b*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 6*a*b*x**3*x**m*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + b**2*m**3*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - 3*b**2*m**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) - b**2*m*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2)) + 3*b**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(32*a**5*gamma(m/2 + 3/2) + 64*a**4*b*x**2*gamma(m/2 + 3/2) + 32*a**3*b**2*x**4*gamma(m/2 + 3/2))) + B*(a**2*m**3*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) + 3*a**2*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - 2*a**2*m**2*x**3*x**m*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - a**2*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - 3*a**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) + 18*a**2*x**3*x**m*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) + 2*a*b*m**3*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) + 6*a*b*m**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - 2*a*b*m**2*x**5*x**m*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - 2*a*b*m*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - 4*a*b*m*x**5*x**m*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - 6*a*b*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) + 6*a*b*x**5*x**m*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) + b**2*m**3*x**7*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) + 3*b**2*m**2*x**7*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - b**2*m*x**7*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)) - 3*b**2*x**7*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(32*a**5*gamma(m/2 + 5/2) + 64*a**4*b*x**2*gamma(m/2 + 5/2) + 32*a**3*b**2*x**4*gamma(m/2 + 5/2)))","C",0
325,1,4345,0,5.319847," ","integrate(x**m*(b*x**2+a)**2*(d*x**2+c)**3,x)","\begin{cases} - \frac{a^{2} c^{3}}{10 x^{10}} - \frac{3 a^{2} c^{2} d}{8 x^{8}} - \frac{a^{2} c d^{2}}{2 x^{6}} - \frac{a^{2} d^{3}}{4 x^{4}} - \frac{a b c^{3}}{4 x^{8}} - \frac{a b c^{2} d}{x^{6}} - \frac{3 a b c d^{2}}{2 x^{4}} - \frac{a b d^{3}}{x^{2}} - \frac{b^{2} c^{3}}{6 x^{6}} - \frac{3 b^{2} c^{2} d}{4 x^{4}} - \frac{3 b^{2} c d^{2}}{2 x^{2}} + b^{2} d^{3} \log{\left(x \right)} & \text{for}\: m = -11 \\- \frac{a^{2} c^{3}}{8 x^{8}} - \frac{a^{2} c^{2} d}{2 x^{6}} - \frac{3 a^{2} c d^{2}}{4 x^{4}} - \frac{a^{2} d^{3}}{2 x^{2}} - \frac{a b c^{3}}{3 x^{6}} - \frac{3 a b c^{2} d}{2 x^{4}} - \frac{3 a b c d^{2}}{x^{2}} + 2 a b d^{3} \log{\left(x \right)} - \frac{b^{2} c^{3}}{4 x^{4}} - \frac{3 b^{2} c^{2} d}{2 x^{2}} + 3 b^{2} c d^{2} \log{\left(x \right)} + \frac{b^{2} d^{3} x^{2}}{2} & \text{for}\: m = -9 \\- \frac{a^{2} c^{3}}{6 x^{6}} - \frac{3 a^{2} c^{2} d}{4 x^{4}} - \frac{3 a^{2} c d^{2}}{2 x^{2}} + a^{2} d^{3} \log{\left(x \right)} - \frac{a b c^{3}}{2 x^{4}} - \frac{3 a b c^{2} d}{x^{2}} + 6 a b c d^{2} \log{\left(x \right)} + a b d^{3} x^{2} - \frac{b^{2} c^{3}}{2 x^{2}} + 3 b^{2} c^{2} d \log{\left(x \right)} + \frac{3 b^{2} c d^{2} x^{2}}{2} + \frac{b^{2} d^{3} x^{4}}{4} & \text{for}\: m = -7 \\- \frac{a^{2} c^{3}}{4 x^{4}} - \frac{3 a^{2} c^{2} d}{2 x^{2}} + 3 a^{2} c d^{2} \log{\left(x \right)} + \frac{a^{2} d^{3} x^{2}}{2} - \frac{a b c^{3}}{x^{2}} + 6 a b c^{2} d \log{\left(x \right)} + 3 a b c d^{2} x^{2} + \frac{a b d^{3} x^{4}}{2} + b^{2} c^{3} \log{\left(x \right)} + \frac{3 b^{2} c^{2} d x^{2}}{2} + \frac{3 b^{2} c d^{2} x^{4}}{4} + \frac{b^{2} d^{3} x^{6}}{6} & \text{for}\: m = -5 \\- \frac{a^{2} c^{3}}{2 x^{2}} + 3 a^{2} c^{2} d \log{\left(x \right)} + \frac{3 a^{2} c d^{2} x^{2}}{2} + \frac{a^{2} d^{3} x^{4}}{4} + 2 a b c^{3} \log{\left(x \right)} + 3 a b c^{2} d x^{2} + \frac{3 a b c d^{2} x^{4}}{2} + \frac{a b d^{3} x^{6}}{3} + \frac{b^{2} c^{3} x^{2}}{2} + \frac{3 b^{2} c^{2} d x^{4}}{4} + \frac{b^{2} c d^{2} x^{6}}{2} + \frac{b^{2} d^{3} x^{8}}{8} & \text{for}\: m = -3 \\a^{2} c^{3} \log{\left(x \right)} + \frac{3 a^{2} c^{2} d x^{2}}{2} + \frac{3 a^{2} c d^{2} x^{4}}{4} + \frac{a^{2} d^{3} x^{6}}{6} + a b c^{3} x^{2} + \frac{3 a b c^{2} d x^{4}}{2} + a b c d^{2} x^{6} + \frac{a b d^{3} x^{8}}{4} + \frac{b^{2} c^{3} x^{4}}{4} + \frac{b^{2} c^{2} d x^{6}}{2} + \frac{3 b^{2} c d^{2} x^{8}}{8} + \frac{b^{2} d^{3} x^{10}}{10} & \text{for}\: m = -1 \\\frac{a^{2} c^{3} m^{5} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{35 a^{2} c^{3} m^{4} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{470 a^{2} c^{3} m^{3} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3010 a^{2} c^{3} m^{2} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{9129 a^{2} c^{3} m x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10395 a^{2} c^{3} x x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3 a^{2} c^{2} d m^{5} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{99 a^{2} c^{2} d m^{4} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1218 a^{2} c^{2} d m^{3} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{6786 a^{2} c^{2} d m^{2} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{16059 a^{2} c^{2} d m x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10395 a^{2} c^{2} d x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3 a^{2} c d^{2} m^{5} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{93 a^{2} c d^{2} m^{4} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1050 a^{2} c d^{2} m^{3} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{5190 a^{2} c d^{2} m^{2} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10467 a^{2} c d^{2} m x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{6237 a^{2} c d^{2} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{a^{2} d^{3} m^{5} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{29 a^{2} d^{3} m^{4} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{302 a^{2} d^{3} m^{3} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1366 a^{2} d^{3} m^{2} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2577 a^{2} d^{3} m x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1485 a^{2} d^{3} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2 a b c^{3} m^{5} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{66 a b c^{3} m^{4} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{812 a b c^{3} m^{3} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{4524 a b c^{3} m^{2} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10706 a b c^{3} m x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{6930 a b c^{3} x^{3} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{6 a b c^{2} d m^{5} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{186 a b c^{2} d m^{4} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2100 a b c^{2} d m^{3} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{10380 a b c^{2} d m^{2} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{20934 a b c^{2} d m x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{12474 a b c^{2} d x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{6 a b c d^{2} m^{5} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{174 a b c d^{2} m^{4} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1812 a b c d^{2} m^{3} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{8196 a b c d^{2} m^{2} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{15462 a b c d^{2} m x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{8910 a b c d^{2} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2 a b d^{3} m^{5} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{54 a b d^{3} m^{4} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{524 a b d^{3} m^{3} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2244 a b d^{3} m^{2} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{4082 a b d^{3} m x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2310 a b d^{3} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{b^{2} c^{3} m^{5} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{31 b^{2} c^{3} m^{4} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{350 b^{2} c^{3} m^{3} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1730 b^{2} c^{3} m^{2} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3489 b^{2} c^{3} m x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{2079 b^{2} c^{3} x^{5} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3 b^{2} c^{2} d m^{5} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{87 b^{2} c^{2} d m^{4} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{906 b^{2} c^{2} d m^{3} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{4098 b^{2} c^{2} d m^{2} x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{7731 b^{2} c^{2} d m x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{4455 b^{2} c^{2} d x^{7} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3 b^{2} c d^{2} m^{5} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{81 b^{2} c d^{2} m^{4} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{786 b^{2} c d^{2} m^{3} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3366 b^{2} c d^{2} m^{2} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{6123 b^{2} c d^{2} m x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{3465 b^{2} c d^{2} x^{9} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{b^{2} d^{3} m^{5} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{25 b^{2} d^{3} m^{4} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{230 b^{2} d^{3} m^{3} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{950 b^{2} d^{3} m^{2} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{1689 b^{2} d^{3} m x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} + \frac{945 b^{2} d^{3} x^{11} x^{m}}{m^{6} + 36 m^{5} + 505 m^{4} + 3480 m^{3} + 12139 m^{2} + 19524 m + 10395} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*c**3/(10*x**10) - 3*a**2*c**2*d/(8*x**8) - a**2*c*d**2/(2*x**6) - a**2*d**3/(4*x**4) - a*b*c**3/(4*x**8) - a*b*c**2*d/x**6 - 3*a*b*c*d**2/(2*x**4) - a*b*d**3/x**2 - b**2*c**3/(6*x**6) - 3*b**2*c**2*d/(4*x**4) - 3*b**2*c*d**2/(2*x**2) + b**2*d**3*log(x), Eq(m, -11)), (-a**2*c**3/(8*x**8) - a**2*c**2*d/(2*x**6) - 3*a**2*c*d**2/(4*x**4) - a**2*d**3/(2*x**2) - a*b*c**3/(3*x**6) - 3*a*b*c**2*d/(2*x**4) - 3*a*b*c*d**2/x**2 + 2*a*b*d**3*log(x) - b**2*c**3/(4*x**4) - 3*b**2*c**2*d/(2*x**2) + 3*b**2*c*d**2*log(x) + b**2*d**3*x**2/2, Eq(m, -9)), (-a**2*c**3/(6*x**6) - 3*a**2*c**2*d/(4*x**4) - 3*a**2*c*d**2/(2*x**2) + a**2*d**3*log(x) - a*b*c**3/(2*x**4) - 3*a*b*c**2*d/x**2 + 6*a*b*c*d**2*log(x) + a*b*d**3*x**2 - b**2*c**3/(2*x**2) + 3*b**2*c**2*d*log(x) + 3*b**2*c*d**2*x**2/2 + b**2*d**3*x**4/4, Eq(m, -7)), (-a**2*c**3/(4*x**4) - 3*a**2*c**2*d/(2*x**2) + 3*a**2*c*d**2*log(x) + a**2*d**3*x**2/2 - a*b*c**3/x**2 + 6*a*b*c**2*d*log(x) + 3*a*b*c*d**2*x**2 + a*b*d**3*x**4/2 + b**2*c**3*log(x) + 3*b**2*c**2*d*x**2/2 + 3*b**2*c*d**2*x**4/4 + b**2*d**3*x**6/6, Eq(m, -5)), (-a**2*c**3/(2*x**2) + 3*a**2*c**2*d*log(x) + 3*a**2*c*d**2*x**2/2 + a**2*d**3*x**4/4 + 2*a*b*c**3*log(x) + 3*a*b*c**2*d*x**2 + 3*a*b*c*d**2*x**4/2 + a*b*d**3*x**6/3 + b**2*c**3*x**2/2 + 3*b**2*c**2*d*x**4/4 + b**2*c*d**2*x**6/2 + b**2*d**3*x**8/8, Eq(m, -3)), (a**2*c**3*log(x) + 3*a**2*c**2*d*x**2/2 + 3*a**2*c*d**2*x**4/4 + a**2*d**3*x**6/6 + a*b*c**3*x**2 + 3*a*b*c**2*d*x**4/2 + a*b*c*d**2*x**6 + a*b*d**3*x**8/4 + b**2*c**3*x**4/4 + b**2*c**2*d*x**6/2 + 3*b**2*c*d**2*x**8/8 + b**2*d**3*x**10/10, Eq(m, -1)), (a**2*c**3*m**5*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 35*a**2*c**3*m**4*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 470*a**2*c**3*m**3*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3010*a**2*c**3*m**2*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 9129*a**2*c**3*m*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10395*a**2*c**3*x*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3*a**2*c**2*d*m**5*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 99*a**2*c**2*d*m**4*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1218*a**2*c**2*d*m**3*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 6786*a**2*c**2*d*m**2*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 16059*a**2*c**2*d*m*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10395*a**2*c**2*d*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3*a**2*c*d**2*m**5*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 93*a**2*c*d**2*m**4*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1050*a**2*c*d**2*m**3*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 5190*a**2*c*d**2*m**2*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10467*a**2*c*d**2*m*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 6237*a**2*c*d**2*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + a**2*d**3*m**5*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 29*a**2*d**3*m**4*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 302*a**2*d**3*m**3*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1366*a**2*d**3*m**2*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2577*a**2*d**3*m*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1485*a**2*d**3*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2*a*b*c**3*m**5*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 66*a*b*c**3*m**4*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 812*a*b*c**3*m**3*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 4524*a*b*c**3*m**2*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10706*a*b*c**3*m*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 6930*a*b*c**3*x**3*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 6*a*b*c**2*d*m**5*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 186*a*b*c**2*d*m**4*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2100*a*b*c**2*d*m**3*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 10380*a*b*c**2*d*m**2*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 20934*a*b*c**2*d*m*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 12474*a*b*c**2*d*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 6*a*b*c*d**2*m**5*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 174*a*b*c*d**2*m**4*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1812*a*b*c*d**2*m**3*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 8196*a*b*c*d**2*m**2*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 15462*a*b*c*d**2*m*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 8910*a*b*c*d**2*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2*a*b*d**3*m**5*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 54*a*b*d**3*m**4*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 524*a*b*d**3*m**3*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2244*a*b*d**3*m**2*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 4082*a*b*d**3*m*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2310*a*b*d**3*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + b**2*c**3*m**5*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 31*b**2*c**3*m**4*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 350*b**2*c**3*m**3*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1730*b**2*c**3*m**2*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3489*b**2*c**3*m*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 2079*b**2*c**3*x**5*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3*b**2*c**2*d*m**5*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 87*b**2*c**2*d*m**4*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 906*b**2*c**2*d*m**3*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 4098*b**2*c**2*d*m**2*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 7731*b**2*c**2*d*m*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 4455*b**2*c**2*d*x**7*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3*b**2*c*d**2*m**5*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 81*b**2*c*d**2*m**4*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 786*b**2*c*d**2*m**3*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3366*b**2*c*d**2*m**2*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 6123*b**2*c*d**2*m*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 3465*b**2*c*d**2*x**9*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + b**2*d**3*m**5*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 25*b**2*d**3*m**4*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 230*b**2*d**3*m**3*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 950*b**2*d**3*m**2*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 1689*b**2*d**3*m*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395) + 945*b**2*d**3*x**11*x**m/(m**6 + 36*m**5 + 505*m**4 + 3480*m**3 + 12139*m**2 + 19524*m + 10395), True))","A",0
326,1,2363,0,3.185250," ","integrate(x**m*(b*x**2+a)**2*(d*x**2+c)**2,x)","\begin{cases} - \frac{a^{2} c^{2}}{8 x^{8}} - \frac{a^{2} c d}{3 x^{6}} - \frac{a^{2} d^{2}}{4 x^{4}} - \frac{a b c^{2}}{3 x^{6}} - \frac{a b c d}{x^{4}} - \frac{a b d^{2}}{x^{2}} - \frac{b^{2} c^{2}}{4 x^{4}} - \frac{b^{2} c d}{x^{2}} + b^{2} d^{2} \log{\left(x \right)} & \text{for}\: m = -9 \\- \frac{a^{2} c^{2}}{6 x^{6}} - \frac{a^{2} c d}{2 x^{4}} - \frac{a^{2} d^{2}}{2 x^{2}} - \frac{a b c^{2}}{2 x^{4}} - \frac{2 a b c d}{x^{2}} + 2 a b d^{2} \log{\left(x \right)} - \frac{b^{2} c^{2}}{2 x^{2}} + 2 b^{2} c d \log{\left(x \right)} + \frac{b^{2} d^{2} x^{2}}{2} & \text{for}\: m = -7 \\- \frac{a^{2} c^{2}}{4 x^{4}} - \frac{a^{2} c d}{x^{2}} + a^{2} d^{2} \log{\left(x \right)} - \frac{a b c^{2}}{x^{2}} + 4 a b c d \log{\left(x \right)} + a b d^{2} x^{2} + b^{2} c^{2} \log{\left(x \right)} + b^{2} c d x^{2} + \frac{b^{2} d^{2} x^{4}}{4} & \text{for}\: m = -5 \\- \frac{a^{2} c^{2}}{2 x^{2}} + 2 a^{2} c d \log{\left(x \right)} + \frac{a^{2} d^{2} x^{2}}{2} + 2 a b c^{2} \log{\left(x \right)} + 2 a b c d x^{2} + \frac{a b d^{2} x^{4}}{2} + \frac{b^{2} c^{2} x^{2}}{2} + \frac{b^{2} c d x^{4}}{2} + \frac{b^{2} d^{2} x^{6}}{6} & \text{for}\: m = -3 \\a^{2} c^{2} \log{\left(x \right)} + a^{2} c d x^{2} + \frac{a^{2} d^{2} x^{4}}{4} + a b c^{2} x^{2} + a b c d x^{4} + \frac{a b d^{2} x^{6}}{3} + \frac{b^{2} c^{2} x^{4}}{4} + \frac{b^{2} c d x^{6}}{3} + \frac{b^{2} d^{2} x^{8}}{8} & \text{for}\: m = -1 \\\frac{a^{2} c^{2} m^{4} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{24 a^{2} c^{2} m^{3} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{206 a^{2} c^{2} m^{2} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{744 a^{2} c^{2} m x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{945 a^{2} c^{2} x x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{2 a^{2} c d m^{4} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{44 a^{2} c d m^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{328 a^{2} c d m^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{916 a^{2} c d m x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{630 a^{2} c d x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{a^{2} d^{2} m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{20 a^{2} d^{2} m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{130 a^{2} d^{2} m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{300 a^{2} d^{2} m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{189 a^{2} d^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{2 a b c^{2} m^{4} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{44 a b c^{2} m^{3} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{328 a b c^{2} m^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{916 a b c^{2} m x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{630 a b c^{2} x^{3} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{4 a b c d m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{80 a b c d m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{520 a b c d m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{1200 a b c d m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{756 a b c d x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{2 a b d^{2} m^{4} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{36 a b d^{2} m^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{208 a b d^{2} m^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{444 a b d^{2} m x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{270 a b d^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{b^{2} c^{2} m^{4} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{20 b^{2} c^{2} m^{3} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{130 b^{2} c^{2} m^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{300 b^{2} c^{2} m x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{189 b^{2} c^{2} x^{5} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{2 b^{2} c d m^{4} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{36 b^{2} c d m^{3} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{208 b^{2} c d m^{2} x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{444 b^{2} c d m x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{270 b^{2} c d x^{7} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{b^{2} d^{2} m^{4} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{16 b^{2} d^{2} m^{3} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{86 b^{2} d^{2} m^{2} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{176 b^{2} d^{2} m x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} + \frac{105 b^{2} d^{2} x^{9} x^{m}}{m^{5} + 25 m^{4} + 230 m^{3} + 950 m^{2} + 1689 m + 945} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*c**2/(8*x**8) - a**2*c*d/(3*x**6) - a**2*d**2/(4*x**4) - a*b*c**2/(3*x**6) - a*b*c*d/x**4 - a*b*d**2/x**2 - b**2*c**2/(4*x**4) - b**2*c*d/x**2 + b**2*d**2*log(x), Eq(m, -9)), (-a**2*c**2/(6*x**6) - a**2*c*d/(2*x**4) - a**2*d**2/(2*x**2) - a*b*c**2/(2*x**4) - 2*a*b*c*d/x**2 + 2*a*b*d**2*log(x) - b**2*c**2/(2*x**2) + 2*b**2*c*d*log(x) + b**2*d**2*x**2/2, Eq(m, -7)), (-a**2*c**2/(4*x**4) - a**2*c*d/x**2 + a**2*d**2*log(x) - a*b*c**2/x**2 + 4*a*b*c*d*log(x) + a*b*d**2*x**2 + b**2*c**2*log(x) + b**2*c*d*x**2 + b**2*d**2*x**4/4, Eq(m, -5)), (-a**2*c**2/(2*x**2) + 2*a**2*c*d*log(x) + a**2*d**2*x**2/2 + 2*a*b*c**2*log(x) + 2*a*b*c*d*x**2 + a*b*d**2*x**4/2 + b**2*c**2*x**2/2 + b**2*c*d*x**4/2 + b**2*d**2*x**6/6, Eq(m, -3)), (a**2*c**2*log(x) + a**2*c*d*x**2 + a**2*d**2*x**4/4 + a*b*c**2*x**2 + a*b*c*d*x**4 + a*b*d**2*x**6/3 + b**2*c**2*x**4/4 + b**2*c*d*x**6/3 + b**2*d**2*x**8/8, Eq(m, -1)), (a**2*c**2*m**4*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 24*a**2*c**2*m**3*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 206*a**2*c**2*m**2*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 744*a**2*c**2*m*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 945*a**2*c**2*x*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 2*a**2*c*d*m**4*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 44*a**2*c*d*m**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 328*a**2*c*d*m**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 916*a**2*c*d*m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 630*a**2*c*d*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + a**2*d**2*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 20*a**2*d**2*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 130*a**2*d**2*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 300*a**2*d**2*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 189*a**2*d**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 2*a*b*c**2*m**4*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 44*a*b*c**2*m**3*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 328*a*b*c**2*m**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 916*a*b*c**2*m*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 630*a*b*c**2*x**3*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 4*a*b*c*d*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 80*a*b*c*d*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 520*a*b*c*d*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 1200*a*b*c*d*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 756*a*b*c*d*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 2*a*b*d**2*m**4*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 36*a*b*d**2*m**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 208*a*b*d**2*m**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 444*a*b*d**2*m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 270*a*b*d**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + b**2*c**2*m**4*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 20*b**2*c**2*m**3*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 130*b**2*c**2*m**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 300*b**2*c**2*m*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 189*b**2*c**2*x**5*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 2*b**2*c*d*m**4*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 36*b**2*c*d*m**3*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 208*b**2*c*d*m**2*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 444*b**2*c*d*m*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 270*b**2*c*d*x**7*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + b**2*d**2*m**4*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 16*b**2*d**2*m**3*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 86*b**2*d**2*m**2*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 176*b**2*d**2*m*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945) + 105*b**2*d**2*x**9*x**m/(m**5 + 25*m**4 + 230*m**3 + 950*m**2 + 1689*m + 945), True))","A",0
327,1,1044,0,1.758412," ","integrate(x**m*(b*x**2+a)**2*(d*x**2+c),x)","\begin{cases} - \frac{a^{2} c}{6 x^{6}} - \frac{a^{2} d}{4 x^{4}} - \frac{a b c}{2 x^{4}} - \frac{a b d}{x^{2}} - \frac{b^{2} c}{2 x^{2}} + b^{2} d \log{\left(x \right)} & \text{for}\: m = -7 \\- \frac{a^{2} c}{4 x^{4}} - \frac{a^{2} d}{2 x^{2}} - \frac{a b c}{x^{2}} + 2 a b d \log{\left(x \right)} + b^{2} c \log{\left(x \right)} + \frac{b^{2} d x^{2}}{2} & \text{for}\: m = -5 \\- \frac{a^{2} c}{2 x^{2}} + a^{2} d \log{\left(x \right)} + 2 a b c \log{\left(x \right)} + a b d x^{2} + \frac{b^{2} c x^{2}}{2} + \frac{b^{2} d x^{4}}{4} & \text{for}\: m = -3 \\a^{2} c \log{\left(x \right)} + \frac{a^{2} d x^{2}}{2} + a b c x^{2} + \frac{a b d x^{4}}{2} + \frac{b^{2} c x^{4}}{4} + \frac{b^{2} d x^{6}}{6} & \text{for}\: m = -1 \\\frac{a^{2} c m^{3} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{15 a^{2} c m^{2} x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{71 a^{2} c m x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{105 a^{2} c x x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{a^{2} d m^{3} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{13 a^{2} d m^{2} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{47 a^{2} d m x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{35 a^{2} d x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{2 a b c m^{3} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{26 a b c m^{2} x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{94 a b c m x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{70 a b c x^{3} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{2 a b d m^{3} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{22 a b d m^{2} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{62 a b d m x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{42 a b d x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{b^{2} c m^{3} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{11 b^{2} c m^{2} x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{31 b^{2} c m x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{21 b^{2} c x^{5} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{b^{2} d m^{3} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{9 b^{2} d m^{2} x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{23 b^{2} d m x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} + \frac{15 b^{2} d x^{7} x^{m}}{m^{4} + 16 m^{3} + 86 m^{2} + 176 m + 105} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*c/(6*x**6) - a**2*d/(4*x**4) - a*b*c/(2*x**4) - a*b*d/x**2 - b**2*c/(2*x**2) + b**2*d*log(x), Eq(m, -7)), (-a**2*c/(4*x**4) - a**2*d/(2*x**2) - a*b*c/x**2 + 2*a*b*d*log(x) + b**2*c*log(x) + b**2*d*x**2/2, Eq(m, -5)), (-a**2*c/(2*x**2) + a**2*d*log(x) + 2*a*b*c*log(x) + a*b*d*x**2 + b**2*c*x**2/2 + b**2*d*x**4/4, Eq(m, -3)), (a**2*c*log(x) + a**2*d*x**2/2 + a*b*c*x**2 + a*b*d*x**4/2 + b**2*c*x**4/4 + b**2*d*x**6/6, Eq(m, -1)), (a**2*c*m**3*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 15*a**2*c*m**2*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 71*a**2*c*m*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 105*a**2*c*x*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + a**2*d*m**3*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 13*a**2*d*m**2*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 47*a**2*d*m*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 35*a**2*d*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 2*a*b*c*m**3*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 26*a*b*c*m**2*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 94*a*b*c*m*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 70*a*b*c*x**3*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 2*a*b*d*m**3*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 22*a*b*d*m**2*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 62*a*b*d*m*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 42*a*b*d*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + b**2*c*m**3*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 11*b**2*c*m**2*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 31*b**2*c*m*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 21*b**2*c*x**5*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + b**2*d*m**3*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 9*b**2*d*m**2*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 23*b**2*d*m*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105) + 15*b**2*d*x**7*x**m/(m**4 + 16*m**3 + 86*m**2 + 176*m + 105), True))","A",0
328,1,299,0,6.616066," ","integrate(x**m*(b*x**2+a)**2/(d*x**2+c),x)","\frac{a^{2} m x x^{m} \Phi\left(\frac{d x^{2} e^{i \pi}}{c}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 c \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a^{2} x x^{m} \Phi\left(\frac{d x^{2} e^{i \pi}}{c}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 c \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a b m x^{3} x^{m} \Phi\left(\frac{d x^{2} e^{i \pi}}{c}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{2 c \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 a b x^{3} x^{m} \Phi\left(\frac{d x^{2} e^{i \pi}}{c}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{2 c \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{b^{2} m x^{5} x^{m} \Phi\left(\frac{d x^{2} e^{i \pi}}{c}, 1, \frac{m}{2} + \frac{5}{2}\right) \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}{4 c \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{5 b^{2} x^{5} x^{m} \Phi\left(\frac{d x^{2} e^{i \pi}}{c}, 1, \frac{m}{2} + \frac{5}{2}\right) \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}{4 c \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)}"," ",0,"a**2*m*x*x**m*lerchphi(d*x**2*exp_polar(I*pi)/c, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*c*gamma(m/2 + 3/2)) + a**2*x*x**m*lerchphi(d*x**2*exp_polar(I*pi)/c, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*c*gamma(m/2 + 3/2)) + a*b*m*x**3*x**m*lerchphi(d*x**2*exp_polar(I*pi)/c, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(2*c*gamma(m/2 + 5/2)) + 3*a*b*x**3*x**m*lerchphi(d*x**2*exp_polar(I*pi)/c, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(2*c*gamma(m/2 + 5/2)) + b**2*m*x**5*x**m*lerchphi(d*x**2*exp_polar(I*pi)/c, 1, m/2 + 5/2)*gamma(m/2 + 5/2)/(4*c*gamma(m/2 + 7/2)) + 5*b**2*x**5*x**m*lerchphi(d*x**2*exp_polar(I*pi)/c, 1, m/2 + 5/2)*gamma(m/2 + 5/2)/(4*c*gamma(m/2 + 7/2))","C",0
329,0,0,0,0.000000," ","integrate(x**m*(b*x**2+a)**2/(d*x**2+c)**2,x)","\int \frac{x^{m} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**m*(a + b*x**2)**2/(c + d*x**2)**2, x)","F",0
330,0,0,0,0.000000," ","integrate(x**m*(b*x**2+a)**2/(d*x**2+c)**3,x)","\int \frac{x^{m} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{3}}\, dx"," ",0,"Integral(x**m*(a + b*x**2)**2/(c + d*x**2)**3, x)","F",0
331,1,411,0,10.073049," ","integrate(x**m*(d*x**2+c)**3/(b*x**2+a),x)","\frac{c^{3} m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{c^{3} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 c^{2} d m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{9 c^{2} d x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 c d^{2} m x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{5}{2}\right) \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{15 c d^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{5}{2}\right) \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{d^{3} m x^{7} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{7}{2}\right) \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{9}{2}\right)} + \frac{7 d^{3} x^{7} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{7}{2}\right) \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{9}{2}\right)}"," ",0,"c**3*m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + c**3*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + 3*c**2*d*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*a*gamma(m/2 + 5/2)) + 9*c**2*d*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*a*gamma(m/2 + 5/2)) + 3*c*d**2*m*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 5/2)*gamma(m/2 + 5/2)/(4*a*gamma(m/2 + 7/2)) + 15*c*d**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 5/2)*gamma(m/2 + 5/2)/(4*a*gamma(m/2 + 7/2)) + d**3*m*x**7*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 7/2)*gamma(m/2 + 7/2)/(4*a*gamma(m/2 + 9/2)) + 7*d**3*x**7*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 7/2)*gamma(m/2 + 7/2)/(4*a*gamma(m/2 + 9/2))","C",0
332,1,299,0,6.574815," ","integrate(x**m*(d*x**2+c)**2/(b*x**2+a),x)","\frac{c^{2} m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{c^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{c d m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{2 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 c d x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{2 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{d^{2} m x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{5}{2}\right) \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{5 d^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{5}{2}\right) \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)}"," ",0,"c**2*m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + c**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + c*d*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(2*a*gamma(m/2 + 5/2)) + 3*c*d*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(2*a*gamma(m/2 + 5/2)) + d**2*m*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 5/2)*gamma(m/2 + 5/2)/(4*a*gamma(m/2 + 7/2)) + 5*d**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 5/2)*gamma(m/2 + 5/2)/(4*a*gamma(m/2 + 7/2))","C",0
333,1,190,0,4.135602," ","integrate(x**m*(d*x**2+c)/(b*x**2+a),x)","\frac{c m x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{c x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{d m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{3 d x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{4 a \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}"," ",0,"c*m*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + c*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(4*a*gamma(m/2 + 3/2)) + d*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*a*gamma(m/2 + 5/2)) + 3*d*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(4*a*gamma(m/2 + 5/2))","C",0
334,1,354,0,7.021363," ","integrate(x**m/(b*x**2+a)/(d*x**2+c),x)","\frac{a m x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{3}{2} - \frac{m}{2}\right) \Gamma^{2}\left(\frac{3}{2} - \frac{m}{2}\right)}{x^{3} \left(4 a b d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right) - 4 b^{2} c \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right)\right)} - \frac{3 a x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{3}{2} - \frac{m}{2}\right) \Gamma^{2}\left(\frac{3}{2} - \frac{m}{2}\right)}{x^{3} \left(4 a b d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right) - 4 b^{2} c \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right)\right)} + \frac{b m x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right)}{x \left(4 a b d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right) - 4 b^{2} c \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right)\right)} - \frac{b x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right)}{x \left(4 a b d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right) - 4 b^{2} c \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) \Gamma\left(\frac{5}{2} - \frac{m}{2}\right)\right)}"," ",0,"a*m*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 3/2 - m/2)*gamma(3/2 - m/2)**2/(x**3*(4*a*b*d*gamma(3/2 - m/2)*gamma(5/2 - m/2) - 4*b**2*c*gamma(3/2 - m/2)*gamma(5/2 - m/2))) - 3*a*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 3/2 - m/2)*gamma(3/2 - m/2)**2/(x**3*(4*a*b*d*gamma(3/2 - m/2)*gamma(5/2 - m/2) - 4*b**2*c*gamma(3/2 - m/2)*gamma(5/2 - m/2))) + b*m*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)*gamma(5/2 - m/2)/(x*(4*a*b*d*gamma(3/2 - m/2)*gamma(5/2 - m/2) - 4*b**2*c*gamma(3/2 - m/2)*gamma(5/2 - m/2))) - b*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)*gamma(5/2 - m/2)/(x*(4*a*b*d*gamma(3/2 - m/2)*gamma(5/2 - m/2) - 4*b**2*c*gamma(3/2 - m/2)*gamma(5/2 - m/2)))","C",0
335,1,7446,0,74.333790," ","integrate(x**m/(b*x**2+a)**2/(d*x**2+c),x)","\frac{a^{3} d m^{2} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{4 a^{3} d m x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{2 a^{3} d m x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{3 a^{3} d x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{2 a^{3} d x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{a^{2} b c m^{2} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{2 a^{2} b c m x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{a^{2} b c x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{2 a^{2} b d m^{2} x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{8 a^{2} b d m x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{4 a^{2} b d m x x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a^{2} b d m x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{6 a^{2} b d x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{4 a^{2} b d x x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a^{2} b d x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} c m^{2} x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{4 a b^{2} c m x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} c m x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} c x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a b^{2} c x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{a b^{2} d m^{2} x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{4 a b^{2} d m x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a b^{2} d m x^{3} x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a b^{2} d m x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{3 a b^{2} d x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} d x^{3} x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} d x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{b^{3} c m^{2} x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 b^{3} c m x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 b^{3} c m x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{b^{3} c x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 b^{3} c x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)}"," ",0,"a**3*d*m**2*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - 4*a**3*d*m*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 2*a**3*d*m*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 3*a**3*d*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - 2*a**3*d*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - a**2*b*c*m**2*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 2*a**2*b*c*m*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - a**2*b*c*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 2*a**2*b*d*m**2*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 8*a**2*b*d*m*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 4*a**2*b*d*m*x*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a**2*b*d*m*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 6*a**2*b*d*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 4*a**2*b*d*x*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a**2*b*d*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*c*m**2*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 4*a*b**2*c*m*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*c*m*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*c*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a*b**2*c*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + a*b**2*d*m**2*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 4*a*b**2*d*m*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a*b**2*d*m*x**3*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a*b**2*d*m*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 3*a*b**2*d*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*d*x**3*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*d*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - b**3*c*m**2*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*b**3*c*m*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*b**3*c*m*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - b**3*c*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*b**3*c*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))","C",0
336,-1,0,0,0.000000," ","integrate(x**m/(b*x**2+a)**3/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,0,0,0,0.000000," ","integrate(x**m*(d*x**2+c)**3/(b*x**2+a)**2,x)","\int \frac{x^{m} \left(c + d x^{2}\right)^{3}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**m*(c + d*x**2)**3/(a + b*x**2)**2, x)","F",0
338,0,0,0,0.000000," ","integrate(x**m*(d*x**2+c)**2/(b*x**2+a)**2,x)","\int \frac{x^{m} \left(c + d x^{2}\right)^{2}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**m*(c + d*x**2)**2/(a + b*x**2)**2, x)","F",0
339,1,906,0,31.636736," ","integrate(x**m*(d*x**2+c)/(b*x**2+a)**2,x)","c \left(- \frac{a m^{2} x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a m x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a x x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{2 a x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{b m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{b x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{1}{2}\right) \Gamma\left(\frac{m}{2} + \frac{1}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}\right) + d \left(- \frac{a m^{2} x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{4 a m x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{2 a m x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{3 a x^{3} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{6 a x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{b m^{2} x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{4 b m x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{3 b x^{5} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + \frac{3}{2}\right) \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}{8 a^{3} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) + 8 a^{2} b x^{2} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}\right)"," ",0,"c*(-a*m**2*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + 2*a*m*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + a*x*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + 2*a*x*x**m*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) - b*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2)) + b*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1/2)*gamma(m/2 + 1/2)/(8*a**3*gamma(m/2 + 3/2) + 8*a**2*b*x**2*gamma(m/2 + 3/2))) + d*(-a*m**2*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 4*a*m*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) + 2*a*m*x**3*x**m*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 3*a*x**3*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) + 6*a*x**3*x**m*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - b*m**2*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 4*b*m*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)) - 3*b*x**5*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 3/2)*gamma(m/2 + 3/2)/(8*a**3*gamma(m/2 + 5/2) + 8*a**2*b*x**2*gamma(m/2 + 5/2)))","C",0
340,1,7446,0,77.484927," ","integrate(x**m/(b*x**2+a)**2/(d*x**2+c),x)","\frac{a^{3} d m^{2} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{4 a^{3} d m x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{2 a^{3} d m x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{3 a^{3} d x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{2 a^{3} d x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{a^{2} b c m^{2} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{2 a^{2} b c m x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} - \frac{a^{2} b c x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{x \left(8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)\right)} + \frac{2 a^{2} b d m^{2} x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{8 a^{2} b d m x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{4 a^{2} b d m x x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a^{2} b d m x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{6 a^{2} b d x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{4 a^{2} b d x x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a^{2} b d x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} c m^{2} x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{4 a b^{2} c m x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} c m x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} c x x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a b^{2} c x x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{a b^{2} d m^{2} x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{4 a b^{2} d m x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a b^{2} d m x^{3} x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 a b^{2} d m x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{3 a b^{2} d x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} d x^{3} x^{m} \Phi\left(\frac{c e^{i \pi}}{d x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 a b^{2} d x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{b^{3} c m^{2} x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 b^{3} c m x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{2 b^{3} c m x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{b^{3} c x^{3} x^{m} \Phi\left(\frac{a e^{i \pi}}{b x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{2 b^{3} c x^{3} x^{m} \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{8 a^{5} d^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{4} b c d \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{4} b d^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} c^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 32 a^{3} b^{2} c d x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a^{3} b^{2} d^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 16 a^{2} b^{3} c^{2} x^{2} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) - 16 a^{2} b^{3} c d x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right) + 8 a b^{4} c^{2} x^{4} \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)}"," ",0,"a**3*d*m**2*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - 4*a**3*d*m*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 2*a**3*d*m*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 3*a**3*d*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - 2*a**3*d*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - a**2*b*c*m**2*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 2*a**2*b*c*m*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) - a**2*b*c*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(x*(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))) + 2*a**2*b*d*m**2*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 8*a**2*b*d*m*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 4*a**2*b*d*m*x*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a**2*b*d*m*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 6*a**2*b*d*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 4*a**2*b*d*x*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a**2*b*d*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*c*m**2*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 4*a*b**2*c*m*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*c*m*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*c*x*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a*b**2*c*x*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + a*b**2*d*m**2*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 4*a*b**2*d*m*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a*b**2*d*m*x**3*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*a*b**2*d*m*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 3*a*b**2*d*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*d*x**3*x**m*lerchphi(c*exp_polar(I*pi)/(d*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*a*b**2*d*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - b**3*c*m**2*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*b**3*c*m*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - 2*b**3*c*m*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) - b**3*c*x**3*x**m*lerchphi(a*exp_polar(I*pi)/(b*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2)) + 2*b**3*c*x**3*x**m*gamma(1/2 - m/2)/(8*a**5*d**2*gamma(3/2 - m/2) - 16*a**4*b*c*d*gamma(3/2 - m/2) + 16*a**4*b*d**2*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*c**2*gamma(3/2 - m/2) - 32*a**3*b**2*c*d*x**2*gamma(3/2 - m/2) + 8*a**3*b**2*d**2*x**4*gamma(3/2 - m/2) + 16*a**2*b**3*c**2*x**2*gamma(3/2 - m/2) - 16*a**2*b**3*c*d*x**4*gamma(3/2 - m/2) + 8*a*b**4*c**2*x**4*gamma(3/2 - m/2))","C",0
341,-1,0,0,0.000000," ","integrate(x**m/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate(x**m/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,1,46,0,10.206259," ","integrate(x**(7/2)*(b*x**2+a)*(B*x**2+A),x)","\frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A b x^{\frac{13}{2}}}{13} + \frac{2 B a x^{\frac{13}{2}}}{13} + \frac{2 B b x^{\frac{17}{2}}}{17}"," ",0,"2*A*a*x**(9/2)/9 + 2*A*b*x**(13/2)/13 + 2*B*a*x**(13/2)/13 + 2*B*b*x**(17/2)/17","A",0
344,1,46,0,5.302620," ","integrate(x**(5/2)*(b*x**2+a)*(B*x**2+A),x)","\frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A b x^{\frac{11}{2}}}{11} + \frac{2 B a x^{\frac{11}{2}}}{11} + \frac{2 B b x^{\frac{15}{2}}}{15}"," ",0,"2*A*a*x**(7/2)/7 + 2*A*b*x**(11/2)/11 + 2*B*a*x**(11/2)/11 + 2*B*b*x**(15/2)/15","A",0
345,1,46,0,2.412452," ","integrate(x**(3/2)*(b*x**2+a)*(B*x**2+A),x)","\frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 A b x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{13}{2}}}{13}"," ",0,"2*A*a*x**(5/2)/5 + 2*A*b*x**(9/2)/9 + 2*B*a*x**(9/2)/9 + 2*B*b*x**(13/2)/13","A",0
346,1,37,0,1.990347," ","integrate((b*x**2+a)*(B*x**2+A)*x**(1/2),x)","\frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{11}{2}}}{11} + \frac{2 x^{\frac{7}{2}} \left(A b + B a\right)}{7}"," ",0,"2*A*a*x**(3/2)/3 + 2*B*b*x**(11/2)/11 + 2*x**(7/2)*(A*b + B*a)/7","A",0
347,1,44,0,0.777935," ","integrate((b*x**2+a)*(B*x**2+A)/x**(1/2),x)","2 A a \sqrt{x} + \frac{2 A b x^{\frac{5}{2}}}{5} + \frac{2 B a x^{\frac{5}{2}}}{5} + \frac{2 B b x^{\frac{9}{2}}}{9}"," ",0,"2*A*a*sqrt(x) + 2*A*b*x**(5/2)/5 + 2*B*a*x**(5/2)/5 + 2*B*b*x**(9/2)/9","A",0
348,1,44,0,0.994303," ","integrate((b*x**2+a)*(B*x**2+A)/x**(3/2),x)","- \frac{2 A a}{\sqrt{x}} + \frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 B a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a/sqrt(x) + 2*A*b*x**(3/2)/3 + 2*B*a*x**(3/2)/3 + 2*B*b*x**(7/2)/7","A",0
349,1,42,0,1.193924," ","integrate((b*x**2+a)*(B*x**2+A)/x**(5/2),x)","- \frac{2 A a}{3 x^{\frac{3}{2}}} + 2 A b \sqrt{x} + 2 B a \sqrt{x} + \frac{2 B b x^{\frac{5}{2}}}{5}"," ",0,"-2*A*a/(3*x**(3/2)) + 2*A*b*sqrt(x) + 2*B*a*sqrt(x) + 2*B*b*x**(5/2)/5","A",0
350,1,42,0,1.761363," ","integrate((b*x**2+a)*(B*x**2+A)/x**(7/2),x)","- \frac{2 A a}{5 x^{\frac{5}{2}}} - \frac{2 A b}{\sqrt{x}} - \frac{2 B a}{\sqrt{x}} + \frac{2 B b x^{\frac{3}{2}}}{3}"," ",0,"-2*A*a/(5*x**(5/2)) - 2*A*b/sqrt(x) - 2*B*a/sqrt(x) + 2*B*b*x**(3/2)/3","A",0
351,1,80,0,19.432113," ","integrate(x**(7/2)*(b*x**2+a)**2*(B*x**2+A),x)","\frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a b x^{\frac{13}{2}}}{13} + \frac{2 A b^{2} x^{\frac{17}{2}}}{17} + \frac{2 B a^{2} x^{\frac{13}{2}}}{13} + \frac{4 B a b x^{\frac{17}{2}}}{17} + \frac{2 B b^{2} x^{\frac{21}{2}}}{21}"," ",0,"2*A*a**2*x**(9/2)/9 + 4*A*a*b*x**(13/2)/13 + 2*A*b**2*x**(17/2)/17 + 2*B*a**2*x**(13/2)/13 + 4*B*a*b*x**(17/2)/17 + 2*B*b**2*x**(21/2)/21","A",0
352,1,80,0,10.848904," ","integrate(x**(5/2)*(b*x**2+a)**2*(B*x**2+A),x)","\frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{4 A a b x^{\frac{11}{2}}}{11} + \frac{2 A b^{2} x^{\frac{15}{2}}}{15} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a b x^{\frac{15}{2}}}{15} + \frac{2 B b^{2} x^{\frac{19}{2}}}{19}"," ",0,"2*A*a**2*x**(7/2)/7 + 4*A*a*b*x**(11/2)/11 + 2*A*b**2*x**(15/2)/15 + 2*B*a**2*x**(11/2)/11 + 4*B*a*b*x**(15/2)/15 + 2*B*b**2*x**(19/2)/19","A",0
353,1,80,0,5.710744," ","integrate(x**(3/2)*(b*x**2+a)**2*(B*x**2+A),x)","\frac{2 A a^{2} x^{\frac{5}{2}}}{5} + \frac{4 A a b x^{\frac{9}{2}}}{9} + \frac{2 A b^{2} x^{\frac{13}{2}}}{13} + \frac{2 B a^{2} x^{\frac{9}{2}}}{9} + \frac{4 B a b x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*A*a**2*x**(5/2)/5 + 4*A*a*b*x**(9/2)/9 + 2*A*b**2*x**(13/2)/13 + 2*B*a**2*x**(9/2)/9 + 4*B*a*b*x**(13/2)/13 + 2*B*b**2*x**(17/2)/17","A",0
354,1,66,0,2.531103," ","integrate((b*x**2+a)**2*(B*x**2+A)*x**(1/2),x)","\frac{2 A a^{2} x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15} + \frac{2 x^{\frac{11}{2}} \left(A b^{2} + 2 B a b\right)}{11} + \frac{2 x^{\frac{7}{2}} \left(2 A a b + B a^{2}\right)}{7}"," ",0,"2*A*a**2*x**(3/2)/3 + 2*B*b**2*x**(15/2)/15 + 2*x**(11/2)*(A*b**2 + 2*B*a*b)/11 + 2*x**(7/2)*(2*A*a*b + B*a**2)/7","A",0
355,1,78,0,2.108396," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**(1/2),x)","2 A a^{2} \sqrt{x} + \frac{4 A a b x^{\frac{5}{2}}}{5} + \frac{2 A b^{2} x^{\frac{9}{2}}}{9} + \frac{2 B a^{2} x^{\frac{5}{2}}}{5} + \frac{4 B a b x^{\frac{9}{2}}}{9} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13}"," ",0,"2*A*a**2*sqrt(x) + 4*A*a*b*x**(5/2)/5 + 2*A*b**2*x**(9/2)/9 + 2*B*a**2*x**(5/2)/5 + 4*B*a*b*x**(9/2)/9 + 2*B*b**2*x**(13/2)/13","A",0
356,1,78,0,2.417997," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**(3/2),x)","- \frac{2 A a^{2}}{\sqrt{x}} + \frac{4 A a b x^{\frac{3}{2}}}{3} + \frac{2 A b^{2} x^{\frac{7}{2}}}{7} + \frac{2 B a^{2} x^{\frac{3}{2}}}{3} + \frac{4 B a b x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} x^{\frac{11}{2}}}{11}"," ",0,"-2*A*a**2/sqrt(x) + 4*A*a*b*x**(3/2)/3 + 2*A*b**2*x**(7/2)/7 + 2*B*a**2*x**(3/2)/3 + 4*B*a*b*x**(7/2)/7 + 2*B*b**2*x**(11/2)/11","A",0
357,1,76,0,2.955852," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**(5/2),x)","- \frac{2 A a^{2}}{3 x^{\frac{3}{2}}} + 4 A a b \sqrt{x} + \frac{2 A b^{2} x^{\frac{5}{2}}}{5} + 2 B a^{2} \sqrt{x} + \frac{4 B a b x^{\frac{5}{2}}}{5} + \frac{2 B b^{2} x^{\frac{9}{2}}}{9}"," ",0,"-2*A*a**2/(3*x**(3/2)) + 4*A*a*b*sqrt(x) + 2*A*b**2*x**(5/2)/5 + 2*B*a**2*sqrt(x) + 4*B*a*b*x**(5/2)/5 + 2*B*b**2*x**(9/2)/9","A",0
358,1,76,0,4.014006," ","integrate((b*x**2+a)**2*(B*x**2+A)/x**(7/2),x)","- \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a b}{\sqrt{x}} + \frac{2 A b^{2} x^{\frac{3}{2}}}{3} - \frac{2 B a^{2}}{\sqrt{x}} + \frac{4 B a b x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{7}{2}}}{7}"," ",0,"-2*A*a**2/(5*x**(5/2)) - 4*A*a*b/sqrt(x) + 2*A*b**2*x**(3/2)/3 - 2*B*a**2/sqrt(x) + 4*B*a*b*x**(3/2)/3 + 2*B*b**2*x**(7/2)/7","A",0
359,1,114,0,34.247749," ","integrate(x**(7/2)*(b*x**2+a)**3*(B*x**2+A),x)","\frac{2 A a^{3} x^{\frac{9}{2}}}{9} + \frac{6 A a^{2} b x^{\frac{13}{2}}}{13} + \frac{6 A a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 A b^{3} x^{\frac{21}{2}}}{21} + \frac{2 B a^{3} x^{\frac{13}{2}}}{13} + \frac{6 B a^{2} b x^{\frac{17}{2}}}{17} + \frac{2 B a b^{2} x^{\frac{21}{2}}}{7} + \frac{2 B b^{3} x^{\frac{25}{2}}}{25}"," ",0,"2*A*a**3*x**(9/2)/9 + 6*A*a**2*b*x**(13/2)/13 + 6*A*a*b**2*x**(17/2)/17 + 2*A*b**3*x**(21/2)/21 + 2*B*a**3*x**(13/2)/13 + 6*B*a**2*b*x**(17/2)/17 + 2*B*a*b**2*x**(21/2)/7 + 2*B*b**3*x**(25/2)/25","A",0
360,1,114,0,20.627878," ","integrate(x**(5/2)*(b*x**2+a)**3*(B*x**2+A),x)","\frac{2 A a^{3} x^{\frac{7}{2}}}{7} + \frac{6 A a^{2} b x^{\frac{11}{2}}}{11} + \frac{2 A a b^{2} x^{\frac{15}{2}}}{5} + \frac{2 A b^{3} x^{\frac{19}{2}}}{19} + \frac{2 B a^{3} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} b x^{\frac{15}{2}}}{5} + \frac{6 B a b^{2} x^{\frac{19}{2}}}{19} + \frac{2 B b^{3} x^{\frac{23}{2}}}{23}"," ",0,"2*A*a**3*x**(7/2)/7 + 6*A*a**2*b*x**(11/2)/11 + 2*A*a*b**2*x**(15/2)/5 + 2*A*b**3*x**(19/2)/19 + 2*B*a**3*x**(11/2)/11 + 2*B*a**2*b*x**(15/2)/5 + 6*B*a*b**2*x**(19/2)/19 + 2*B*b**3*x**(23/2)/23","A",0
361,1,114,0,11.403689," ","integrate(x**(3/2)*(b*x**2+a)**3*(B*x**2+A),x)","\frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{2 A a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 A a b^{2} x^{\frac{13}{2}}}{13} + \frac{2 A b^{3} x^{\frac{17}{2}}}{17} + \frac{2 B a^{3} x^{\frac{9}{2}}}{9} + \frac{6 B a^{2} b x^{\frac{13}{2}}}{13} + \frac{6 B a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 B b^{3} x^{\frac{21}{2}}}{21}"," ",0,"2*A*a**3*x**(5/2)/5 + 2*A*a**2*b*x**(9/2)/3 + 6*A*a*b**2*x**(13/2)/13 + 2*A*b**3*x**(17/2)/17 + 2*B*a**3*x**(9/2)/9 + 6*B*a**2*b*x**(13/2)/13 + 6*B*a*b**2*x**(17/2)/17 + 2*B*b**3*x**(21/2)/21","A",0
362,1,95,0,3.337984," ","integrate((b*x**2+a)**3*(B*x**2+A)*x**(1/2),x)","\frac{2 A a^{3} x^{\frac{3}{2}}}{3} + \frac{2 B b^{3} x^{\frac{19}{2}}}{19} + \frac{2 x^{\frac{15}{2}} \left(A b^{3} + 3 B a b^{2}\right)}{15} + \frac{2 x^{\frac{11}{2}} \left(3 A a b^{2} + 3 B a^{2} b\right)}{11} + \frac{2 x^{\frac{7}{2}} \left(3 A a^{2} b + B a^{3}\right)}{7}"," ",0,"2*A*a**3*x**(3/2)/3 + 2*B*b**3*x**(19/2)/19 + 2*x**(15/2)*(A*b**3 + 3*B*a*b**2)/15 + 2*x**(11/2)*(3*A*a*b**2 + 3*B*a**2*b)/11 + 2*x**(7/2)*(3*A*a**2*b + B*a**3)/7","A",0
363,1,112,0,4.824733," ","integrate((b*x**2+a)**3*(B*x**2+A)/x**(1/2),x)","2 A a^{3} \sqrt{x} + \frac{6 A a^{2} b x^{\frac{5}{2}}}{5} + \frac{2 A a b^{2} x^{\frac{9}{2}}}{3} + \frac{2 A b^{3} x^{\frac{13}{2}}}{13} + \frac{2 B a^{3} x^{\frac{5}{2}}}{5} + \frac{2 B a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 B a b^{2} x^{\frac{13}{2}}}{13} + \frac{2 B b^{3} x^{\frac{17}{2}}}{17}"," ",0,"2*A*a**3*sqrt(x) + 6*A*a**2*b*x**(5/2)/5 + 2*A*a*b**2*x**(9/2)/3 + 2*A*b**3*x**(13/2)/13 + 2*B*a**3*x**(5/2)/5 + 2*B*a**2*b*x**(9/2)/3 + 6*B*a*b**2*x**(13/2)/13 + 2*B*b**3*x**(17/2)/17","A",0
364,1,110,0,5.325715," ","integrate((b*x**2+a)**3*(B*x**2+A)/x**(3/2),x)","- \frac{2 A a^{3}}{\sqrt{x}} + 2 A a^{2} b x^{\frac{3}{2}} + \frac{6 A a b^{2} x^{\frac{7}{2}}}{7} + \frac{2 A b^{3} x^{\frac{11}{2}}}{11} + \frac{2 B a^{3} x^{\frac{3}{2}}}{3} + \frac{6 B a^{2} b x^{\frac{7}{2}}}{7} + \frac{6 B a b^{2} x^{\frac{11}{2}}}{11} + \frac{2 B b^{3} x^{\frac{15}{2}}}{15}"," ",0,"-2*A*a**3/sqrt(x) + 2*A*a**2*b*x**(3/2) + 6*A*a*b**2*x**(7/2)/7 + 2*A*b**3*x**(11/2)/11 + 2*B*a**3*x**(3/2)/3 + 6*B*a**2*b*x**(7/2)/7 + 6*B*a*b**2*x**(11/2)/11 + 2*B*b**3*x**(15/2)/15","A",0
365,1,110,0,6.056719," ","integrate((b*x**2+a)**3*(B*x**2+A)/x**(5/2),x)","- \frac{2 A a^{3}}{3 x^{\frac{3}{2}}} + 6 A a^{2} b \sqrt{x} + \frac{6 A a b^{2} x^{\frac{5}{2}}}{5} + \frac{2 A b^{3} x^{\frac{9}{2}}}{9} + 2 B a^{3} \sqrt{x} + \frac{6 B a^{2} b x^{\frac{5}{2}}}{5} + \frac{2 B a b^{2} x^{\frac{9}{2}}}{3} + \frac{2 B b^{3} x^{\frac{13}{2}}}{13}"," ",0,"-2*A*a**3/(3*x**(3/2)) + 6*A*a**2*b*sqrt(x) + 6*A*a*b**2*x**(5/2)/5 + 2*A*b**3*x**(9/2)/9 + 2*B*a**3*sqrt(x) + 6*B*a**2*b*x**(5/2)/5 + 2*B*a*b**2*x**(9/2)/3 + 2*B*b**3*x**(13/2)/13","A",0
366,1,107,0,8.684350," ","integrate((b*x**2+a)**3*(B*x**2+A)/x**(7/2),x)","- \frac{2 A a^{3}}{5 x^{\frac{5}{2}}} - \frac{6 A a^{2} b}{\sqrt{x}} + 2 A a b^{2} x^{\frac{3}{2}} + \frac{2 A b^{3} x^{\frac{7}{2}}}{7} - \frac{2 B a^{3}}{\sqrt{x}} + 2 B a^{2} b x^{\frac{3}{2}} + \frac{6 B a b^{2} x^{\frac{7}{2}}}{7} + \frac{2 B b^{3} x^{\frac{11}{2}}}{11}"," ",0,"-2*A*a**3/(5*x**(5/2)) - 6*A*a**2*b/sqrt(x) + 2*A*a*b**2*x**(3/2) + 2*A*b**3*x**(7/2)/7 - 2*B*a**3/sqrt(x) + 2*B*a**2*b*x**(3/2) + 6*B*a*b**2*x**(7/2)/7 + 2*B*b**3*x**(11/2)/11","A",0
367,1,434,0,127.296933," ","integrate(x**(7/2)*(B*x**2+A)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \left(\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{9}{2}}}{9}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{9}{2}}}{9} + \frac{2 B x^{\frac{13}{2}}}{13}}{a} & \text{for}\: b = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{9}{2}}}{9}}{b} & \text{for}\: a = 0 \\- \frac{\sqrt[4]{-1} A a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{\sqrt[4]{-1} A a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} - \frac{\sqrt[4]{-1} A a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2}} - \frac{2 A a \sqrt{x}}{b^{2}} + \frac{2 A x^{\frac{5}{2}}}{5 b} + \frac{\sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3}} - \frac{\sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3}} + \frac{\sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{3}} + \frac{2 B a^{2} \sqrt{x}}{b^{3}} - \frac{2 B a x^{\frac{5}{2}}}{5 b^{2}} + \frac{2 B x^{\frac{9}{2}}}{9 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*x**(5/2)/5 + 2*B*x**(9/2)/9), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(9/2)/9 + 2*B*x**(13/2)/13)/a, Eq(b, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(9/2)/9)/b, Eq(a, 0)), (-(-1)**(1/4)*A*a**(5/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + (-1)**(1/4)*A*a**(5/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) - (-1)**(1/4)*A*a**(5/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**2 - 2*A*a*sqrt(x)/b**2 + 2*A*x**(5/2)/(5*b) + (-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3) - (-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3) + (-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**3 + 2*B*a**2*sqrt(x)/b**3 - 2*B*a*x**(5/2)/(5*b**2) + 2*B*x**(9/2)/(9*b), True))","A",0
368,1,502,0,54.692555," ","integrate(x**(5/2)*(B*x**2+A)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \left(\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{7}{2}}}{7}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{7}{2}}}{7} + \frac{2 B x^{\frac{11}{2}}}{11}}{a} & \text{for}\: b = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{7}{2}}}{7}}{b} & \text{for}\: a = 0 \\\frac{\left(-1\right)^{\frac{3}{4}} A a^{\frac{3}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{\left(-1\right)^{\frac{3}{4}} A a^{\frac{3}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} + \frac{\left(-1\right)^{\frac{3}{4}} A a^{\frac{3}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} - \frac{2 \left(-1\right)^{\frac{3}{4}} A a^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2} \sqrt[4]{\frac{1}{b}}} + \frac{2 A x^{\frac{3}{2}}}{3 b} - \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{7}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{7}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} - \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{7}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2}} + \frac{2 \left(-1\right)^{\frac{3}{4}} B a^{\frac{7}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{3} \sqrt[4]{\frac{1}{b}}} - \frac{2 B a x^{\frac{3}{2}}}{3 b^{2}} + \frac{2 B x^{\frac{7}{2}}}{7 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*x**(3/2)/3 + 2*B*x**(7/2)/7), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(7/2)/7 + 2*B*x**(11/2)/11)/a, Eq(b, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(7/2)/7)/b, Eq(a, 0)), ((-1)**(3/4)*A*a**(3/4)*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - (-1)**(3/4)*A*a**(3/4)*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) + (-1)**(3/4)*A*a**(3/4)*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b - 2*(-1)**(3/4)*A*a**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(b**2*(1/b)**(1/4)) + 2*A*x**(3/2)/(3*b) - (-1)**(3/4)*B*a**(7/4)*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + (-1)**(3/4)*B*a**(7/4)*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) - (-1)**(3/4)*B*a**(7/4)*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**2 + 2*(-1)**(3/4)*B*a**(7/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(b**3*(1/b)**(1/4)) - 2*B*a*x**(3/2)/(3*b**2) + 2*B*x**(7/2)/(7*b), True))","A",0
369,1,393,0,16.604593," ","integrate(x**(3/2)*(B*x**2+A)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \left(2 A \sqrt{x} + \frac{2 B x^{\frac{5}{2}}}{5}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{9}{2}}}{9}}{a} & \text{for}\: b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{5}{2}}}{5}}{b} & \text{for}\: a = 0 \\\frac{\sqrt[4]{-1} A \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{\sqrt[4]{-1} A \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} + \frac{\sqrt[4]{-1} A \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} + \frac{2 A \sqrt{x}}{b} - \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} - \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2}} - \frac{2 B a \sqrt{x}}{b^{2}} + \frac{2 B x^{\frac{5}{2}}}{5 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*A*sqrt(x) + 2*B*x**(5/2)/5), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(9/2)/9)/a, Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(5/2)/5)/b, Eq(a, 0)), ((-1)**(1/4)*A*a**(1/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - (-1)**(1/4)*A*a**(1/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) + (-1)**(1/4)*A*a**(1/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b + 2*A*sqrt(x)/b - (-1)**(1/4)*B*a**(5/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + (-1)**(1/4)*B*a**(5/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) - (-1)**(1/4)*B*a**(5/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**2 - 2*B*a*sqrt(x)/b**2 + 2*B*x**(5/2)/(5*b), True))","A",0
370,1,459,0,6.757925," ","integrate((B*x**2+A)*x**(1/2)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{\sqrt{x}} + \frac{2 B x^{\frac{3}{2}}}{3}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 A x^{\frac{3}{2}}}{3} + \frac{2 B x^{\frac{7}{2}}}{7}}{a} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{\sqrt{x}} + \frac{2 B x^{\frac{3}{2}}}{3}}{b} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{3}{4}} A \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a}} + \frac{\left(-1\right)^{\frac{3}{4}} A \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a}} - \frac{\left(-1\right)^{\frac{3}{4}} A \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{\sqrt[4]{a}} + \frac{2 \left(-1\right)^{\frac{3}{4}} A \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{\sqrt[4]{a} b \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{3}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{3}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} + \frac{\left(-1\right)^{\frac{3}{4}} B a^{\frac{3}{4}} \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} - \frac{2 \left(-1\right)^{\frac{3}{4}} B a^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2} \sqrt[4]{\frac{1}{b}}} + \frac{2 B x^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/sqrt(x) + 2*B*x**(3/2)/3), Eq(a, 0) & Eq(b, 0)), ((2*A*x**(3/2)/3 + 2*B*x**(7/2)/7)/a, Eq(b, 0)), ((-2*A/sqrt(x) + 2*B*x**(3/2)/3)/b, Eq(a, 0)), (-(-1)**(3/4)*A*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)) + (-1)**(3/4)*A*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)) - (-1)**(3/4)*A*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(1/4) + 2*(-1)**(3/4)*A*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(1/4)*b*(1/b)**(1/4)) + (-1)**(3/4)*B*a**(3/4)*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - (-1)**(3/4)*B*a**(3/4)*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) + (-1)**(3/4)*B*a**(3/4)*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b - 2*(-1)**(3/4)*B*a**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(b**2*(1/b)**(1/4)) + 2*B*x**(3/2)/(3*b), True))","A",0
371,1,355,0,6.498547," ","integrate((B*x**2+A)/(b*x**2+a)/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} + 2 B \sqrt{x}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{5}{2}}}{5}}{a} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} + 2 B \sqrt{x}}{b} & \text{for}\: a = 0 \\- \frac{\sqrt[4]{-1} A \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} A \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} A \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} B \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{\sqrt[4]{-1} B \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} + \frac{\sqrt[4]{-1} B \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} + \frac{2 B \sqrt{x}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) + 2*B*sqrt(x)), Eq(a, 0) & Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(5/2)/5)/a, Eq(b, 0)), ((-2*A/(3*x**(3/2)) + 2*B*sqrt(x))/b, Eq(a, 0)), (-(-1)**(1/4)*A*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) + (-1)**(1/4)*A*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) - (-1)**(1/4)*A*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(3/4) + (-1)**(1/4)*B*a**(1/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - (-1)**(1/4)*B*a**(1/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) + (-1)**(1/4)*B*a**(1/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b + 2*B*sqrt(x)/b, True))","A",0
372,1,206,0,19.841503," ","integrate((B*x**2+A)/x**(3/2)/(b*x**2+a),x)","A \left(\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{a \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}\right) + 2 B \operatorname{RootSum} {\left(256 t^{4} a b^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} a b^{2} + \sqrt{x} \right)} \right)\right)}"," ",0,"A*Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (-2/(a*sqrt(x)), Eq(b, 0)), (-2/(a*sqrt(x)) + (-1)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(5/4)*(1/b)**(1/4)), True)) + 2*B*RootSum(256*_t**4*a*b**3 + 1, Lambda(_t, _t*log(64*_t**3*a*b**2 + sqrt(x))))","A",0
373,1,364,0,31.263392," ","integrate((B*x**2+A)/x**(5/2)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{b} & \text{for}\: a = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} + 2 B \sqrt{x}}{a} & \text{for}\: b = 0 \\- \frac{2 A}{3 a x^{\frac{3}{2}}} + \frac{\sqrt[4]{-1} A b \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} A b \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} + \frac{\sqrt[4]{-1} A b \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} B \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} B \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} B \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(3*x**(3/2))), Eq(a, 0) & Eq(b, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(3*x**(3/2)))/b, Eq(a, 0)), ((-2*A/(3*x**(3/2)) + 2*B*sqrt(x))/a, Eq(b, 0)), (-2*A/(3*a*x**(3/2)) + (-1)**(1/4)*A*b*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(7/4)) - (-1)**(1/4)*A*b*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(7/4)) + (-1)**(1/4)*A*b*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(7/4) - (-1)**(1/4)*B*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) + (-1)**(1/4)*B*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) - (-1)**(1/4)*B*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(3/4), True))","A",0
374,1,366,0,124.886864," ","integrate((B*x**2+A)/x**(7/2)/(b*x**2+a),x)","A \left(\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{9 b x^{\frac{9}{2}}} & \text{for}\: a = 0 \\- \frac{2}{5 a x^{\frac{5}{2}}} & \text{for}\: b = 0 \\- \frac{2}{5 a x^{\frac{5}{2}}} + \frac{2 b}{a^{2} \sqrt{x}} - \frac{\left(-1\right)^{\frac{3}{4}} b \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} b \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} b \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}\right) + B \left(\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{a \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(b, 0)), (-2/(9*b*x**(9/2)), Eq(a, 0)), (-2/(5*a*x**(5/2)), Eq(b, 0)), (-2/(5*a*x**(5/2)) + 2*b/(a**2*sqrt(x)) - (-1)**(3/4)*b*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(9/4)*(1/b)**(1/4)) + (-1)**(3/4)*b*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(9/4)*(1/b)**(1/4)) + (-1)**(3/4)*b*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(9/4)*(1/b)**(1/4)), True)) + B*Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (-2/(a*sqrt(x)), Eq(b, 0)), (-2/(a*sqrt(x)) + (-1)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(5/4)*(1/b)**(1/4)), True))","A",0
375,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x**2+A)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x**2+A)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,1,984,0,84.943221," ","integrate(x**(3/2)*(B*x**2+A)/(b*x**2+a)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{3 x^{\frac{3}{2}}} + 2 B \sqrt{x}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 A}{3 x^{\frac{3}{2}}} + 2 B \sqrt{x}}{b^{2}} & \text{for}\: a = 0 \\\frac{\frac{2 A x^{\frac{5}{2}}}{5} + \frac{2 B x^{\frac{9}{2}}}{9}}{a^{2}} & \text{for}\: b = 0 \\- \frac{\sqrt[4]{-1} A a^{\frac{5}{4}} b \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{\sqrt[4]{-1} A a^{\frac{5}{4}} b \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} - \frac{2 \sqrt[4]{-1} A a^{\frac{5}{4}} b \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} - \frac{\sqrt[4]{-1} A \sqrt[4]{a} b^{2} x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{\sqrt[4]{-1} A \sqrt[4]{a} b^{2} x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} - \frac{2 \sqrt[4]{-1} A \sqrt[4]{a} b^{2} x^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} - \frac{4 A a b \sqrt{x}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{5 \sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} - \frac{5 \sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{10 \sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{5 \sqrt[4]{-1} B a^{\frac{5}{4}} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} - \frac{5 \sqrt[4]{-1} B a^{\frac{5}{4}} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{10 \sqrt[4]{-1} B a^{\frac{5}{4}} b x^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{20 B a^{2} \sqrt{x}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} + \frac{16 B a b x^{\frac{5}{2}}}{8 a^{2} b^{2} + 8 a b^{3} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(3*x**(3/2)) + 2*B*sqrt(x)), Eq(a, 0) & Eq(b, 0)), ((-2*A/(3*x**(3/2)) + 2*B*sqrt(x))/b**2, Eq(a, 0)), ((2*A*x**(5/2)/5 + 2*B*x**(9/2)/9)/a**2, Eq(b, 0)), (-(-1)**(1/4)*A*a**(5/4)*b*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) + (-1)**(1/4)*A*a**(5/4)*b*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) - 2*(-1)**(1/4)*A*a**(5/4)*b*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**2*b**2 + 8*a*b**3*x**2) - (-1)**(1/4)*A*a**(1/4)*b**2*x**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) + (-1)**(1/4)*A*a**(1/4)*b**2*x**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) - 2*(-1)**(1/4)*A*a**(1/4)*b**2*x**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**2*b**2 + 8*a*b**3*x**2) - 4*A*a*b*sqrt(x)/(8*a**2*b**2 + 8*a*b**3*x**2) + 5*(-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) - 5*(-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) + 10*(-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**2*b**2 + 8*a*b**3*x**2) + 5*(-1)**(1/4)*B*a**(5/4)*b*x**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) - 5*(-1)**(1/4)*B*a**(5/4)*b*x**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**2*b**2 + 8*a*b**3*x**2) + 10*(-1)**(1/4)*B*a**(5/4)*b*x**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**2*b**2 + 8*a*b**3*x**2) + 20*B*a**2*sqrt(x)/(8*a**2*b**2 + 8*a*b**3*x**2) + 16*B*a*b*x**(5/2)/(8*a**2*b**2 + 8*a*b**3*x**2), True))","A",0
378,1,162,0,32.131831," ","integrate((B*x**2+A)*x**(1/2)/(b*x**2+a)**2,x)","\frac{2 A x^{\frac{3}{2}}}{4 a^{2} + 4 a b x^{2}} + 2 A \operatorname{RootSum} {\left(65536 t^{4} a^{5} b^{3} + 1, \left( t \mapsto t \log{\left(4096 t^{3} a^{4} b^{2} + \sqrt{x} \right)} \right)\right)} - \frac{2 B a x^{\frac{3}{2}}}{4 a^{2} b + 4 a b^{2} x^{2}} - \frac{2 B a \operatorname{RootSum} {\left(65536 t^{4} a^{5} b^{3} + 1, \left( t \mapsto t \log{\left(4096 t^{3} a^{4} b^{2} + \sqrt{x} \right)} \right)\right)}}{b} + \frac{2 B \operatorname{RootSum} {\left(256 t^{4} a b^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} a b^{2} + \sqrt{x} \right)} \right)\right)}}{b}"," ",0,"2*A*x**(3/2)/(4*a**2 + 4*a*b*x**2) + 2*A*RootSum(65536*_t**4*a**5*b**3 + 1, Lambda(_t, _t*log(4096*_t**3*a**4*b**2 + sqrt(x)))) - 2*B*a*x**(3/2)/(4*a**2*b + 4*a*b**2*x**2) - 2*B*a*RootSum(65536*_t**4*a**5*b**3 + 1, Lambda(_t, _t*log(4096*_t**3*a**4*b**2 + sqrt(x))))/b + 2*B*RootSum(256*_t**4*a*b**3 + 1, Lambda(_t, _t*log(64*_t**3*a*b**2 + sqrt(x))))/b","A",0
379,1,959,0,78.536146," ","integrate((B*x**2+A)/(b*x**2+a)**2/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 A \sqrt{x} + \frac{2 B x^{\frac{5}{2}}}{5}}{a^{2}} & \text{for}\: b = 0 \\\frac{- \frac{2 A}{7 x^{\frac{7}{2}}} - \frac{2 B}{3 x^{\frac{3}{2}}}}{b^{2}} & \text{for}\: a = 0 \\- \frac{3 \sqrt[4]{-1} A a^{\frac{5}{4}} b \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} + \frac{3 \sqrt[4]{-1} A a^{\frac{5}{4}} b \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{6 \sqrt[4]{-1} A a^{\frac{5}{4}} b \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{3 \sqrt[4]{-1} A \sqrt[4]{a} b^{2} x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} + \frac{3 \sqrt[4]{-1} A \sqrt[4]{a} b^{2} x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{6 \sqrt[4]{-1} A \sqrt[4]{a} b^{2} x^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} + \frac{4 A a b \sqrt{x}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{\sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} + \frac{\sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{2 \sqrt[4]{-1} B a^{\frac{9}{4}} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} + \frac{\sqrt[4]{-1} B a^{\frac{5}{4}} b x^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{2 \sqrt[4]{-1} B a^{\frac{5}{4}} b x^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} - \frac{4 B a^{2} \sqrt{x}}{8 a^{3} b + 8 a^{2} b^{2} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*A/(7*x**(7/2)) - 2*B/(3*x**(3/2))), Eq(a, 0) & Eq(b, 0)), ((2*A*sqrt(x) + 2*B*x**(5/2)/5)/a**2, Eq(b, 0)), ((-2*A/(7*x**(7/2)) - 2*B/(3*x**(3/2)))/b**2, Eq(a, 0)), (-3*(-1)**(1/4)*A*a**(5/4)*b*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) + 3*(-1)**(1/4)*A*a**(5/4)*b*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) - 6*(-1)**(1/4)*A*a**(5/4)*b*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**3*b + 8*a**2*b**2*x**2) - 3*(-1)**(1/4)*A*a**(1/4)*b**2*x**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) + 3*(-1)**(1/4)*A*a**(1/4)*b**2*x**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) - 6*(-1)**(1/4)*A*a**(1/4)*b**2*x**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**3*b + 8*a**2*b**2*x**2) + 4*A*a*b*sqrt(x)/(8*a**3*b + 8*a**2*b**2*x**2) - (-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) + (-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) - 2*(-1)**(1/4)*B*a**(9/4)*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**3*b + 8*a**2*b**2*x**2) - (-1)**(1/4)*B*a**(5/4)*b*x**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) + (-1)**(1/4)*B*a**(5/4)*b*x**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(8*a**3*b + 8*a**2*b**2*x**2) - 2*(-1)**(1/4)*B*a**(5/4)*b*x**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(8*a**3*b + 8*a**2*b**2*x**2) - 4*B*a**2*sqrt(x)/(8*a**3*b + 8*a**2*b**2*x**2), True))","A",0
380,-1,0,0,0.000000," ","integrate((B*x**2+A)/x**(3/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((B*x**2+A)/x**(5/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate((B*x**2+A)/x**(7/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate(x**(7/2)*(B*x**2+A)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate(x**(5/2)*(B*x**2+A)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(x**(3/2)*(B*x**2+A)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,1,299,0,152.839544," ","integrate((B*x**2+A)*x**(1/2)/(b*x**2+a)**3,x)","\frac{18 A a x^{\frac{3}{2}}}{32 a^{4} + 64 a^{3} b x^{2} + 32 a^{2} b^{2} x^{4}} + \frac{10 A b x^{\frac{7}{2}}}{32 a^{4} + 64 a^{3} b x^{2} + 32 a^{2} b^{2} x^{4}} + 2 A \operatorname{RootSum} {\left(268435456 t^{4} a^{9} b^{3} + 625, \left( t \mapsto t \log{\left(\frac{2097152 t^{3} a^{7} b^{2}}{125} + \sqrt{x} \right)} \right)\right)} - \frac{18 B a^{2} x^{\frac{3}{2}}}{32 a^{4} b + 64 a^{3} b^{2} x^{2} + 32 a^{2} b^{3} x^{4}} - \frac{10 B a x^{\frac{7}{2}}}{32 a^{4} + 64 a^{3} b x^{2} + 32 a^{2} b^{2} x^{4}} - \frac{2 B a \operatorname{RootSum} {\left(268435456 t^{4} a^{9} b^{3} + 625, \left( t \mapsto t \log{\left(\frac{2097152 t^{3} a^{7} b^{2}}{125} + \sqrt{x} \right)} \right)\right)}}{b} + \frac{2 B x^{\frac{3}{2}}}{4 a^{2} b + 4 a b^{2} x^{2}} + \frac{2 B \operatorname{RootSum} {\left(65536 t^{4} a^{5} b^{3} + 1, \left( t \mapsto t \log{\left(4096 t^{3} a^{4} b^{2} + \sqrt{x} \right)} \right)\right)}}{b}"," ",0,"18*A*a*x**(3/2)/(32*a**4 + 64*a**3*b*x**2 + 32*a**2*b**2*x**4) + 10*A*b*x**(7/2)/(32*a**4 + 64*a**3*b*x**2 + 32*a**2*b**2*x**4) + 2*A*RootSum(268435456*_t**4*a**9*b**3 + 625, Lambda(_t, _t*log(2097152*_t**3*a**7*b**2/125 + sqrt(x)))) - 18*B*a**2*x**(3/2)/(32*a**4*b + 64*a**3*b**2*x**2 + 32*a**2*b**3*x**4) - 10*B*a*x**(7/2)/(32*a**4 + 64*a**3*b*x**2 + 32*a**2*b**2*x**4) - 2*B*a*RootSum(268435456*_t**4*a**9*b**3 + 625, Lambda(_t, _t*log(2097152*_t**3*a**7*b**2/125 + sqrt(x))))/b + 2*B*x**(3/2)/(4*a**2*b + 4*a*b**2*x**2) + 2*B*RootSum(65536*_t**4*a**5*b**3 + 1, Lambda(_t, _t*log(4096*_t**3*a**4*b**2 + sqrt(x))))/b","A",0
387,-1,0,0,0.000000," ","integrate((B*x**2+A)/(b*x**2+a)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate((B*x**2+A)/x**(3/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate((B*x**2+A)/x**(5/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate((B*x**2+A)/x**(7/2)/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,1,80,0,19.899645," ","integrate(x**(7/2)*(b*x**2+a)**2*(d*x**2+c),x)","\frac{2 a^{2} c x^{\frac{9}{2}}}{9} + \frac{2 a^{2} d x^{\frac{13}{2}}}{13} + \frac{4 a b c x^{\frac{13}{2}}}{13} + \frac{4 a b d x^{\frac{17}{2}}}{17} + \frac{2 b^{2} c x^{\frac{17}{2}}}{17} + \frac{2 b^{2} d x^{\frac{21}{2}}}{21}"," ",0,"2*a**2*c*x**(9/2)/9 + 2*a**2*d*x**(13/2)/13 + 4*a*b*c*x**(13/2)/13 + 4*a*b*d*x**(17/2)/17 + 2*b**2*c*x**(17/2)/17 + 2*b**2*d*x**(21/2)/21","A",0
392,1,80,0,11.154748," ","integrate(x**(5/2)*(b*x**2+a)**2*(d*x**2+c),x)","\frac{2 a^{2} c x^{\frac{7}{2}}}{7} + \frac{2 a^{2} d x^{\frac{11}{2}}}{11} + \frac{4 a b c x^{\frac{11}{2}}}{11} + \frac{4 a b d x^{\frac{15}{2}}}{15} + \frac{2 b^{2} c x^{\frac{15}{2}}}{15} + \frac{2 b^{2} d x^{\frac{19}{2}}}{19}"," ",0,"2*a**2*c*x**(7/2)/7 + 2*a**2*d*x**(11/2)/11 + 4*a*b*c*x**(11/2)/11 + 4*a*b*d*x**(15/2)/15 + 2*b**2*c*x**(15/2)/15 + 2*b**2*d*x**(19/2)/19","A",0
393,1,80,0,5.888250," ","integrate(x**(3/2)*(b*x**2+a)**2*(d*x**2+c),x)","\frac{2 a^{2} c x^{\frac{5}{2}}}{5} + \frac{2 a^{2} d x^{\frac{9}{2}}}{9} + \frac{4 a b c x^{\frac{9}{2}}}{9} + \frac{4 a b d x^{\frac{13}{2}}}{13} + \frac{2 b^{2} c x^{\frac{13}{2}}}{13} + \frac{2 b^{2} d x^{\frac{17}{2}}}{17}"," ",0,"2*a**2*c*x**(5/2)/5 + 2*a**2*d*x**(9/2)/9 + 4*a*b*c*x**(9/2)/9 + 4*a*b*d*x**(13/2)/13 + 2*b**2*c*x**(13/2)/13 + 2*b**2*d*x**(17/2)/17","A",0
394,1,66,0,2.569638," ","integrate((b*x**2+a)**2*(d*x**2+c)*x**(1/2),x)","\frac{2 a^{2} c x^{\frac{3}{2}}}{3} + \frac{2 b^{2} d x^{\frac{15}{2}}}{15} + \frac{2 x^{\frac{11}{2}} \left(2 a b d + b^{2} c\right)}{11} + \frac{2 x^{\frac{7}{2}} \left(a^{2} d + 2 a b c\right)}{7}"," ",0,"2*a**2*c*x**(3/2)/3 + 2*b**2*d*x**(15/2)/15 + 2*x**(11/2)*(2*a*b*d + b**2*c)/11 + 2*x**(7/2)*(a**2*d + 2*a*b*c)/7","A",0
395,1,78,0,2.117452," ","integrate((b*x**2+a)**2*(d*x**2+c)/x**(1/2),x)","2 a^{2} c \sqrt{x} + \frac{2 a^{2} d x^{\frac{5}{2}}}{5} + \frac{4 a b c x^{\frac{5}{2}}}{5} + \frac{4 a b d x^{\frac{9}{2}}}{9} + \frac{2 b^{2} c x^{\frac{9}{2}}}{9} + \frac{2 b^{2} d x^{\frac{13}{2}}}{13}"," ",0,"2*a**2*c*sqrt(x) + 2*a**2*d*x**(5/2)/5 + 4*a*b*c*x**(5/2)/5 + 4*a*b*d*x**(9/2)/9 + 2*b**2*c*x**(9/2)/9 + 2*b**2*d*x**(13/2)/13","A",0
396,1,78,0,2.314232," ","integrate((b*x**2+a)**2*(d*x**2+c)/x**(3/2),x)","- \frac{2 a^{2} c}{\sqrt{x}} + \frac{2 a^{2} d x^{\frac{3}{2}}}{3} + \frac{4 a b c x^{\frac{3}{2}}}{3} + \frac{4 a b d x^{\frac{7}{2}}}{7} + \frac{2 b^{2} c x^{\frac{7}{2}}}{7} + \frac{2 b^{2} d x^{\frac{11}{2}}}{11}"," ",0,"-2*a**2*c/sqrt(x) + 2*a**2*d*x**(3/2)/3 + 4*a*b*c*x**(3/2)/3 + 4*a*b*d*x**(7/2)/7 + 2*b**2*c*x**(7/2)/7 + 2*b**2*d*x**(11/2)/11","A",0
397,1,76,0,2.762079," ","integrate((b*x**2+a)**2*(d*x**2+c)/x**(5/2),x)","- \frac{2 a^{2} c}{3 x^{\frac{3}{2}}} + 2 a^{2} d \sqrt{x} + 4 a b c \sqrt{x} + \frac{4 a b d x^{\frac{5}{2}}}{5} + \frac{2 b^{2} c x^{\frac{5}{2}}}{5} + \frac{2 b^{2} d x^{\frac{9}{2}}}{9}"," ",0,"-2*a**2*c/(3*x**(3/2)) + 2*a**2*d*sqrt(x) + 4*a*b*c*sqrt(x) + 4*a*b*d*x**(5/2)/5 + 2*b**2*c*x**(5/2)/5 + 2*b**2*d*x**(9/2)/9","A",0
398,1,76,0,3.831163," ","integrate((b*x**2+a)**2*(d*x**2+c)/x**(7/2),x)","- \frac{2 a^{2} c}{5 x^{\frac{5}{2}}} - \frac{2 a^{2} d}{\sqrt{x}} - \frac{4 a b c}{\sqrt{x}} + \frac{4 a b d x^{\frac{3}{2}}}{3} + \frac{2 b^{2} c x^{\frac{3}{2}}}{3} + \frac{2 b^{2} d x^{\frac{7}{2}}}{7}"," ",0,"-2*a**2*c/(5*x**(5/2)) - 2*a**2*d/sqrt(x) - 4*a*b*c/sqrt(x) + 4*a*b*d*x**(3/2)/3 + 2*b**2*c*x**(3/2)/3 + 2*b**2*d*x**(7/2)/7","A",0
399,1,136,0,31.908853," ","integrate(x**(7/2)*(b*x**2+a)**2*(d*x**2+c)**2,x)","\frac{2 a^{2} c^{2} x^{\frac{9}{2}}}{9} + \frac{4 a^{2} c d x^{\frac{13}{2}}}{13} + \frac{2 a^{2} d^{2} x^{\frac{17}{2}}}{17} + \frac{4 a b c^{2} x^{\frac{13}{2}}}{13} + \frac{8 a b c d x^{\frac{17}{2}}}{17} + \frac{4 a b d^{2} x^{\frac{21}{2}}}{21} + \frac{2 b^{2} c^{2} x^{\frac{17}{2}}}{17} + \frac{4 b^{2} c d x^{\frac{21}{2}}}{21} + \frac{2 b^{2} d^{2} x^{\frac{25}{2}}}{25}"," ",0,"2*a**2*c**2*x**(9/2)/9 + 4*a**2*c*d*x**(13/2)/13 + 2*a**2*d**2*x**(17/2)/17 + 4*a*b*c**2*x**(13/2)/13 + 8*a*b*c*d*x**(17/2)/17 + 4*a*b*d**2*x**(21/2)/21 + 2*b**2*c**2*x**(17/2)/17 + 4*b**2*c*d*x**(21/2)/21 + 2*b**2*d**2*x**(25/2)/25","A",0
400,1,136,0,20.275713," ","integrate(x**(5/2)*(b*x**2+a)**2*(d*x**2+c)**2,x)","\frac{2 a^{2} c^{2} x^{\frac{7}{2}}}{7} + \frac{4 a^{2} c d x^{\frac{11}{2}}}{11} + \frac{2 a^{2} d^{2} x^{\frac{15}{2}}}{15} + \frac{4 a b c^{2} x^{\frac{11}{2}}}{11} + \frac{8 a b c d x^{\frac{15}{2}}}{15} + \frac{4 a b d^{2} x^{\frac{19}{2}}}{19} + \frac{2 b^{2} c^{2} x^{\frac{15}{2}}}{15} + \frac{4 b^{2} c d x^{\frac{19}{2}}}{19} + \frac{2 b^{2} d^{2} x^{\frac{23}{2}}}{23}"," ",0,"2*a**2*c**2*x**(7/2)/7 + 4*a**2*c*d*x**(11/2)/11 + 2*a**2*d**2*x**(15/2)/15 + 4*a*b*c**2*x**(11/2)/11 + 8*a*b*c*d*x**(15/2)/15 + 4*a*b*d**2*x**(19/2)/19 + 2*b**2*c**2*x**(15/2)/15 + 4*b**2*c*d*x**(19/2)/19 + 2*b**2*d**2*x**(23/2)/23","A",0
401,1,136,0,10.865631," ","integrate(x**(3/2)*(b*x**2+a)**2*(d*x**2+c)**2,x)","\frac{2 a^{2} c^{2} x^{\frac{5}{2}}}{5} + \frac{4 a^{2} c d x^{\frac{9}{2}}}{9} + \frac{2 a^{2} d^{2} x^{\frac{13}{2}}}{13} + \frac{4 a b c^{2} x^{\frac{9}{2}}}{9} + \frac{8 a b c d x^{\frac{13}{2}}}{13} + \frac{4 a b d^{2} x^{\frac{17}{2}}}{17} + \frac{2 b^{2} c^{2} x^{\frac{13}{2}}}{13} + \frac{4 b^{2} c d x^{\frac{17}{2}}}{17} + \frac{2 b^{2} d^{2} x^{\frac{21}{2}}}{21}"," ",0,"2*a**2*c**2*x**(5/2)/5 + 4*a**2*c*d*x**(9/2)/9 + 2*a**2*d**2*x**(13/2)/13 + 4*a*b*c**2*x**(9/2)/9 + 8*a*b*c*d*x**(13/2)/13 + 4*a*b*d**2*x**(17/2)/17 + 2*b**2*c**2*x**(13/2)/13 + 4*b**2*c*d*x**(17/2)/17 + 2*b**2*d**2*x**(21/2)/21","A",0
402,1,110,0,3.380165," ","integrate((b*x**2+a)**2*(d*x**2+c)**2*x**(1/2),x)","\frac{2 a^{2} c^{2} x^{\frac{3}{2}}}{3} + \frac{2 b^{2} d^{2} x^{\frac{19}{2}}}{19} + \frac{2 x^{\frac{15}{2}} \left(2 a b d^{2} + 2 b^{2} c d\right)}{15} + \frac{2 x^{\frac{11}{2}} \left(a^{2} d^{2} + 4 a b c d + b^{2} c^{2}\right)}{11} + \frac{2 x^{\frac{7}{2}} \left(2 a^{2} c d + 2 a b c^{2}\right)}{7}"," ",0,"2*a**2*c**2*x**(3/2)/3 + 2*b**2*d**2*x**(19/2)/19 + 2*x**(15/2)*(2*a*b*d**2 + 2*b**2*c*d)/15 + 2*x**(11/2)*(a**2*d**2 + 4*a*b*c*d + b**2*c**2)/11 + 2*x**(7/2)*(2*a**2*c*d + 2*a*b*c**2)/7","A",0
403,1,134,0,4.776476," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x**(1/2),x)","2 a^{2} c^{2} \sqrt{x} + \frac{4 a^{2} c d x^{\frac{5}{2}}}{5} + \frac{2 a^{2} d^{2} x^{\frac{9}{2}}}{9} + \frac{4 a b c^{2} x^{\frac{5}{2}}}{5} + \frac{8 a b c d x^{\frac{9}{2}}}{9} + \frac{4 a b d^{2} x^{\frac{13}{2}}}{13} + \frac{2 b^{2} c^{2} x^{\frac{9}{2}}}{9} + \frac{4 b^{2} c d x^{\frac{13}{2}}}{13} + \frac{2 b^{2} d^{2} x^{\frac{17}{2}}}{17}"," ",0,"2*a**2*c**2*sqrt(x) + 4*a**2*c*d*x**(5/2)/5 + 2*a**2*d**2*x**(9/2)/9 + 4*a*b*c**2*x**(5/2)/5 + 8*a*b*c*d*x**(9/2)/9 + 4*a*b*d**2*x**(13/2)/13 + 2*b**2*c**2*x**(9/2)/9 + 4*b**2*c*d*x**(13/2)/13 + 2*b**2*d**2*x**(17/2)/17","A",0
404,1,134,0,5.255297," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x**(3/2),x)","- \frac{2 a^{2} c^{2}}{\sqrt{x}} + \frac{4 a^{2} c d x^{\frac{3}{2}}}{3} + \frac{2 a^{2} d^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b c^{2} x^{\frac{3}{2}}}{3} + \frac{8 a b c d x^{\frac{7}{2}}}{7} + \frac{4 a b d^{2} x^{\frac{11}{2}}}{11} + \frac{2 b^{2} c^{2} x^{\frac{7}{2}}}{7} + \frac{4 b^{2} c d x^{\frac{11}{2}}}{11} + \frac{2 b^{2} d^{2} x^{\frac{15}{2}}}{15}"," ",0,"-2*a**2*c**2/sqrt(x) + 4*a**2*c*d*x**(3/2)/3 + 2*a**2*d**2*x**(7/2)/7 + 4*a*b*c**2*x**(3/2)/3 + 8*a*b*c*d*x**(7/2)/7 + 4*a*b*d**2*x**(11/2)/11 + 2*b**2*c**2*x**(7/2)/7 + 4*b**2*c*d*x**(11/2)/11 + 2*b**2*d**2*x**(15/2)/15","A",0
405,1,133,0,6.067827," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x**(5/2),x)","- \frac{2 a^{2} c^{2}}{3 x^{\frac{3}{2}}} + 4 a^{2} c d \sqrt{x} + \frac{2 a^{2} d^{2} x^{\frac{5}{2}}}{5} + 4 a b c^{2} \sqrt{x} + \frac{8 a b c d x^{\frac{5}{2}}}{5} + \frac{4 a b d^{2} x^{\frac{9}{2}}}{9} + \frac{2 b^{2} c^{2} x^{\frac{5}{2}}}{5} + \frac{4 b^{2} c d x^{\frac{9}{2}}}{9} + \frac{2 b^{2} d^{2} x^{\frac{13}{2}}}{13}"," ",0,"-2*a**2*c**2/(3*x**(3/2)) + 4*a**2*c*d*sqrt(x) + 2*a**2*d**2*x**(5/2)/5 + 4*a*b*c**2*sqrt(x) + 8*a*b*c*d*x**(5/2)/5 + 4*a*b*d**2*x**(9/2)/9 + 2*b**2*c**2*x**(5/2)/5 + 4*b**2*c*d*x**(9/2)/9 + 2*b**2*d**2*x**(13/2)/13","A",0
406,1,133,0,8.043576," ","integrate((b*x**2+a)**2*(d*x**2+c)**2/x**(7/2),x)","- \frac{2 a^{2} c^{2}}{5 x^{\frac{5}{2}}} - \frac{4 a^{2} c d}{\sqrt{x}} + \frac{2 a^{2} d^{2} x^{\frac{3}{2}}}{3} - \frac{4 a b c^{2}}{\sqrt{x}} + \frac{8 a b c d x^{\frac{3}{2}}}{3} + \frac{4 a b d^{2} x^{\frac{7}{2}}}{7} + \frac{2 b^{2} c^{2} x^{\frac{3}{2}}}{3} + \frac{4 b^{2} c d x^{\frac{7}{2}}}{7} + \frac{2 b^{2} d^{2} x^{\frac{11}{2}}}{11}"," ",0,"-2*a**2*c**2/(5*x**(5/2)) - 4*a**2*c*d/sqrt(x) + 2*a**2*d**2*x**(3/2)/3 - 4*a*b*c**2/sqrt(x) + 8*a*b*c*d*x**(3/2)/3 + 4*a*b*d**2*x**(7/2)/7 + 2*b**2*c**2*x**(3/2)/3 + 4*b**2*c*d*x**(7/2)/7 + 2*b**2*d**2*x**(11/2)/11","A",0
407,1,192,0,53.081510," ","integrate(x**(7/2)*(b*x**2+a)**2*(d*x**2+c)**3,x)","\frac{2 a^{2} c^{3} x^{\frac{9}{2}}}{9} + \frac{6 a^{2} c^{2} d x^{\frac{13}{2}}}{13} + \frac{6 a^{2} c d^{2} x^{\frac{17}{2}}}{17} + \frac{2 a^{2} d^{3} x^{\frac{21}{2}}}{21} + \frac{4 a b c^{3} x^{\frac{13}{2}}}{13} + \frac{12 a b c^{2} d x^{\frac{17}{2}}}{17} + \frac{4 a b c d^{2} x^{\frac{21}{2}}}{7} + \frac{4 a b d^{3} x^{\frac{25}{2}}}{25} + \frac{2 b^{2} c^{3} x^{\frac{17}{2}}}{17} + \frac{2 b^{2} c^{2} d x^{\frac{21}{2}}}{7} + \frac{6 b^{2} c d^{2} x^{\frac{25}{2}}}{25} + \frac{2 b^{2} d^{3} x^{\frac{29}{2}}}{29}"," ",0,"2*a**2*c**3*x**(9/2)/9 + 6*a**2*c**2*d*x**(13/2)/13 + 6*a**2*c*d**2*x**(17/2)/17 + 2*a**2*d**3*x**(21/2)/21 + 4*a*b*c**3*x**(13/2)/13 + 12*a*b*c**2*d*x**(17/2)/17 + 4*a*b*c*d**2*x**(21/2)/7 + 4*a*b*d**3*x**(25/2)/25 + 2*b**2*c**3*x**(17/2)/17 + 2*b**2*c**2*d*x**(21/2)/7 + 6*b**2*c*d**2*x**(25/2)/25 + 2*b**2*d**3*x**(29/2)/29","A",0
408,1,192,0,33.451836," ","integrate(x**(5/2)*(b*x**2+a)**2*(d*x**2+c)**3,x)","\frac{2 a^{2} c^{3} x^{\frac{7}{2}}}{7} + \frac{6 a^{2} c^{2} d x^{\frac{11}{2}}}{11} + \frac{2 a^{2} c d^{2} x^{\frac{15}{2}}}{5} + \frac{2 a^{2} d^{3} x^{\frac{19}{2}}}{19} + \frac{4 a b c^{3} x^{\frac{11}{2}}}{11} + \frac{4 a b c^{2} d x^{\frac{15}{2}}}{5} + \frac{12 a b c d^{2} x^{\frac{19}{2}}}{19} + \frac{4 a b d^{3} x^{\frac{23}{2}}}{23} + \frac{2 b^{2} c^{3} x^{\frac{15}{2}}}{15} + \frac{6 b^{2} c^{2} d x^{\frac{19}{2}}}{19} + \frac{6 b^{2} c d^{2} x^{\frac{23}{2}}}{23} + \frac{2 b^{2} d^{3} x^{\frac{27}{2}}}{27}"," ",0,"2*a**2*c**3*x**(7/2)/7 + 6*a**2*c**2*d*x**(11/2)/11 + 2*a**2*c*d**2*x**(15/2)/5 + 2*a**2*d**3*x**(19/2)/19 + 4*a*b*c**3*x**(11/2)/11 + 4*a*b*c**2*d*x**(15/2)/5 + 12*a*b*c*d**2*x**(19/2)/19 + 4*a*b*d**3*x**(23/2)/23 + 2*b**2*c**3*x**(15/2)/15 + 6*b**2*c**2*d*x**(19/2)/19 + 6*b**2*c*d**2*x**(23/2)/23 + 2*b**2*d**3*x**(27/2)/27","A",0
409,1,192,0,19.975284," ","integrate(x**(3/2)*(b*x**2+a)**2*(d*x**2+c)**3,x)","\frac{2 a^{2} c^{3} x^{\frac{5}{2}}}{5} + \frac{2 a^{2} c^{2} d x^{\frac{9}{2}}}{3} + \frac{6 a^{2} c d^{2} x^{\frac{13}{2}}}{13} + \frac{2 a^{2} d^{3} x^{\frac{17}{2}}}{17} + \frac{4 a b c^{3} x^{\frac{9}{2}}}{9} + \frac{12 a b c^{2} d x^{\frac{13}{2}}}{13} + \frac{12 a b c d^{2} x^{\frac{17}{2}}}{17} + \frac{4 a b d^{3} x^{\frac{21}{2}}}{21} + \frac{2 b^{2} c^{3} x^{\frac{13}{2}}}{13} + \frac{6 b^{2} c^{2} d x^{\frac{17}{2}}}{17} + \frac{2 b^{2} c d^{2} x^{\frac{21}{2}}}{7} + \frac{2 b^{2} d^{3} x^{\frac{25}{2}}}{25}"," ",0,"2*a**2*c**3*x**(5/2)/5 + 2*a**2*c**2*d*x**(9/2)/3 + 6*a**2*c*d**2*x**(13/2)/13 + 2*a**2*d**3*x**(17/2)/17 + 4*a*b*c**3*x**(9/2)/9 + 12*a*b*c**2*d*x**(13/2)/13 + 12*a*b*c*d**2*x**(17/2)/17 + 4*a*b*d**3*x**(21/2)/21 + 2*b**2*c**3*x**(13/2)/13 + 6*b**2*c**2*d*x**(17/2)/17 + 2*b**2*c*d**2*x**(21/2)/7 + 2*b**2*d**3*x**(25/2)/25","A",0
410,1,155,0,4.364231," ","integrate((b*x**2+a)**2*(d*x**2+c)**3*x**(1/2),x)","\frac{2 a^{2} c^{3} x^{\frac{3}{2}}}{3} + \frac{2 b^{2} d^{3} x^{\frac{23}{2}}}{23} + \frac{2 x^{\frac{19}{2}} \left(2 a b d^{3} + 3 b^{2} c d^{2}\right)}{19} + \frac{2 x^{\frac{15}{2}} \left(a^{2} d^{3} + 6 a b c d^{2} + 3 b^{2} c^{2} d\right)}{15} + \frac{2 x^{\frac{11}{2}} \left(3 a^{2} c d^{2} + 6 a b c^{2} d + b^{2} c^{3}\right)}{11} + \frac{2 x^{\frac{7}{2}} \left(3 a^{2} c^{2} d + 2 a b c^{3}\right)}{7}"," ",0,"2*a**2*c**3*x**(3/2)/3 + 2*b**2*d**3*x**(23/2)/23 + 2*x**(19/2)*(2*a*b*d**3 + 3*b**2*c*d**2)/19 + 2*x**(15/2)*(a**2*d**3 + 6*a*b*c*d**2 + 3*b**2*c**2*d)/15 + 2*x**(11/2)*(3*a**2*c*d**2 + 6*a*b*c**2*d + b**2*c**3)/11 + 2*x**(7/2)*(3*a**2*c**2*d + 2*a*b*c**3)/7","A",0
411,1,190,0,9.681981," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x**(1/2),x)","2 a^{2} c^{3} \sqrt{x} + \frac{6 a^{2} c^{2} d x^{\frac{5}{2}}}{5} + \frac{2 a^{2} c d^{2} x^{\frac{9}{2}}}{3} + \frac{2 a^{2} d^{3} x^{\frac{13}{2}}}{13} + \frac{4 a b c^{3} x^{\frac{5}{2}}}{5} + \frac{4 a b c^{2} d x^{\frac{9}{2}}}{3} + \frac{12 a b c d^{2} x^{\frac{13}{2}}}{13} + \frac{4 a b d^{3} x^{\frac{17}{2}}}{17} + \frac{2 b^{2} c^{3} x^{\frac{9}{2}}}{9} + \frac{6 b^{2} c^{2} d x^{\frac{13}{2}}}{13} + \frac{6 b^{2} c d^{2} x^{\frac{17}{2}}}{17} + \frac{2 b^{2} d^{3} x^{\frac{21}{2}}}{21}"," ",0,"2*a**2*c**3*sqrt(x) + 6*a**2*c**2*d*x**(5/2)/5 + 2*a**2*c*d**2*x**(9/2)/3 + 2*a**2*d**3*x**(13/2)/13 + 4*a*b*c**3*x**(5/2)/5 + 4*a*b*c**2*d*x**(9/2)/3 + 12*a*b*c*d**2*x**(13/2)/13 + 4*a*b*d**3*x**(17/2)/17 + 2*b**2*c**3*x**(9/2)/9 + 6*b**2*c**2*d*x**(13/2)/13 + 6*b**2*c*d**2*x**(17/2)/17 + 2*b**2*d**3*x**(21/2)/21","A",0
412,1,189,0,10.560946," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x**(3/2),x)","- \frac{2 a^{2} c^{3}}{\sqrt{x}} + 2 a^{2} c^{2} d x^{\frac{3}{2}} + \frac{6 a^{2} c d^{2} x^{\frac{7}{2}}}{7} + \frac{2 a^{2} d^{3} x^{\frac{11}{2}}}{11} + \frac{4 a b c^{3} x^{\frac{3}{2}}}{3} + \frac{12 a b c^{2} d x^{\frac{7}{2}}}{7} + \frac{12 a b c d^{2} x^{\frac{11}{2}}}{11} + \frac{4 a b d^{3} x^{\frac{15}{2}}}{15} + \frac{2 b^{2} c^{3} x^{\frac{7}{2}}}{7} + \frac{6 b^{2} c^{2} d x^{\frac{11}{2}}}{11} + \frac{2 b^{2} c d^{2} x^{\frac{15}{2}}}{5} + \frac{2 b^{2} d^{3} x^{\frac{19}{2}}}{19}"," ",0,"-2*a**2*c**3/sqrt(x) + 2*a**2*c**2*d*x**(3/2) + 6*a**2*c*d**2*x**(7/2)/7 + 2*a**2*d**3*x**(11/2)/11 + 4*a*b*c**3*x**(3/2)/3 + 12*a*b*c**2*d*x**(7/2)/7 + 12*a*b*c*d**2*x**(11/2)/11 + 4*a*b*d**3*x**(15/2)/15 + 2*b**2*c**3*x**(7/2)/7 + 6*b**2*c**2*d*x**(11/2)/11 + 2*b**2*c*d**2*x**(15/2)/5 + 2*b**2*d**3*x**(19/2)/19","A",0
413,1,189,0,12.050257," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x**(5/2),x)","- \frac{2 a^{2} c^{3}}{3 x^{\frac{3}{2}}} + 6 a^{2} c^{2} d \sqrt{x} + \frac{6 a^{2} c d^{2} x^{\frac{5}{2}}}{5} + \frac{2 a^{2} d^{3} x^{\frac{9}{2}}}{9} + 4 a b c^{3} \sqrt{x} + \frac{12 a b c^{2} d x^{\frac{5}{2}}}{5} + \frac{4 a b c d^{2} x^{\frac{9}{2}}}{3} + \frac{4 a b d^{3} x^{\frac{13}{2}}}{13} + \frac{2 b^{2} c^{3} x^{\frac{5}{2}}}{5} + \frac{2 b^{2} c^{2} d x^{\frac{9}{2}}}{3} + \frac{6 b^{2} c d^{2} x^{\frac{13}{2}}}{13} + \frac{2 b^{2} d^{3} x^{\frac{17}{2}}}{17}"," ",0,"-2*a**2*c**3/(3*x**(3/2)) + 6*a**2*c**2*d*sqrt(x) + 6*a**2*c*d**2*x**(5/2)/5 + 2*a**2*d**3*x**(9/2)/9 + 4*a*b*c**3*sqrt(x) + 12*a*b*c**2*d*x**(5/2)/5 + 4*a*b*c*d**2*x**(9/2)/3 + 4*a*b*d**3*x**(13/2)/13 + 2*b**2*c**3*x**(5/2)/5 + 2*b**2*c**2*d*x**(9/2)/3 + 6*b**2*c*d**2*x**(13/2)/13 + 2*b**2*d**3*x**(17/2)/17","A",0
414,1,185,0,15.274439," ","integrate((b*x**2+a)**2*(d*x**2+c)**3/x**(7/2),x)","- \frac{2 a^{2} c^{3}}{5 x^{\frac{5}{2}}} - \frac{6 a^{2} c^{2} d}{\sqrt{x}} + 2 a^{2} c d^{2} x^{\frac{3}{2}} + \frac{2 a^{2} d^{3} x^{\frac{7}{2}}}{7} - \frac{4 a b c^{3}}{\sqrt{x}} + 4 a b c^{2} d x^{\frac{3}{2}} + \frac{12 a b c d^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b d^{3} x^{\frac{11}{2}}}{11} + \frac{2 b^{2} c^{3} x^{\frac{3}{2}}}{3} + \frac{6 b^{2} c^{2} d x^{\frac{7}{2}}}{7} + \frac{6 b^{2} c d^{2} x^{\frac{11}{2}}}{11} + \frac{2 b^{2} d^{3} x^{\frac{15}{2}}}{15}"," ",0,"-2*a**2*c**3/(5*x**(5/2)) - 6*a**2*c**2*d/sqrt(x) + 2*a**2*c*d**2*x**(3/2) + 2*a**2*d**3*x**(7/2)/7 - 4*a*b*c**3/sqrt(x) + 4*a*b*c**2*d*x**(3/2) + 12*a*b*c*d**2*x**(7/2)/7 + 4*a*b*d**3*x**(11/2)/11 + 2*b**2*c**3*x**(3/2)/3 + 6*b**2*c**2*d*x**(7/2)/7 + 6*b**2*c*d**2*x**(11/2)/11 + 2*b**2*d**3*x**(15/2)/15","A",0
415,-1,0,0,0.000000," ","integrate(x**(7/2)*(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate(x**(5/2)*(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,1,656,0,53.529225," ","integrate(x**(3/2)*(b*x**2+a)**2/(d*x**2+c),x)","\begin{cases} \tilde{\infty} \left(2 a^{2} \sqrt{x} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{9}{2}}}{9}\right) & \text{for}\: c = 0 \wedge d = 0 \\\frac{\frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b x^{\frac{9}{2}}}{9} + \frac{2 b^{2} x^{\frac{13}{2}}}{13}}{c} & \text{for}\: d = 0 \\\frac{2 a^{2} \sqrt{x} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{9}{2}}}{9}}{d} & \text{for}\: c = 0 \\\frac{\sqrt[4]{-1} a^{2} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d} - \frac{\sqrt[4]{-1} a^{2} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d} + \frac{\sqrt[4]{-1} a^{2} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{d} + \frac{2 a^{2} \sqrt{x}}{d} - \frac{\sqrt[4]{-1} a b c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{d^{2}} + \frac{\sqrt[4]{-1} a b c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{d^{2}} - \frac{2 \sqrt[4]{-1} a b c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{d^{2}} - \frac{4 a b c \sqrt{x}}{d^{2}} + \frac{4 a b x^{\frac{5}{2}}}{5 d} + \frac{\sqrt[4]{-1} b^{2} c^{\frac{9}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d^{3}} - \frac{\sqrt[4]{-1} b^{2} c^{\frac{9}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d^{3}} + \frac{\sqrt[4]{-1} b^{2} c^{\frac{9}{4}} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{d^{3}} + \frac{2 b^{2} c^{2} \sqrt{x}}{d^{3}} - \frac{2 b^{2} c x^{\frac{5}{2}}}{5 d^{2}} + \frac{2 b^{2} x^{\frac{9}{2}}}{9 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(2*a**2*sqrt(x) + 4*a*b*x**(5/2)/5 + 2*b**2*x**(9/2)/9), Eq(c, 0) & Eq(d, 0)), ((2*a**2*x**(5/2)/5 + 4*a*b*x**(9/2)/9 + 2*b**2*x**(13/2)/13)/c, Eq(d, 0)), ((2*a**2*sqrt(x) + 4*a*b*x**(5/2)/5 + 2*b**2*x**(9/2)/9)/d, Eq(c, 0)), ((-1)**(1/4)*a**2*c**(1/4)*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d) - (-1)**(1/4)*a**2*c**(1/4)*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d) + (-1)**(1/4)*a**2*c**(1/4)*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/d + 2*a**2*sqrt(x)/d - (-1)**(1/4)*a*b*c**(5/4)*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/d**2 + (-1)**(1/4)*a*b*c**(5/4)*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/d**2 - 2*(-1)**(1/4)*a*b*c**(5/4)*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/d**2 - 4*a*b*c*sqrt(x)/d**2 + 4*a*b*x**(5/2)/(5*d) + (-1)**(1/4)*b**2*c**(9/4)*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d**3) - (-1)**(1/4)*b**2*c**(9/4)*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d**3) + (-1)**(1/4)*b**2*c**(9/4)*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/d**3 + 2*b**2*c**2*sqrt(x)/d**3 - 2*b**2*c*x**(5/2)/(5*d**2) + 2*b**2*x**(9/2)/(9*d), True))","A",0
418,1,87,0,11.400812," ","integrate((b*x**2+a)**2*x**(1/2)/(d*x**2+c),x)","\frac{4 a b x^{\frac{3}{2}}}{3 d} - \frac{2 b^{2} c x^{\frac{3}{2}}}{3 d^{2}} + \frac{2 b^{2} x^{\frac{7}{2}}}{7 d} + \frac{2 \left(a d - b c\right)^{2} \operatorname{RootSum} {\left(256 t^{4} c d^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} c d^{2} + \sqrt{x} \right)} \right)\right)}}{d^{2}}"," ",0,"4*a*b*x**(3/2)/(3*d) - 2*b**2*c*x**(3/2)/(3*d**2) + 2*b**2*x**(7/2)/(7*d) + 2*(a*d - b*c)**2*RootSum(256*_t**4*c*d**3 + 1, Lambda(_t, _t*log(64*_t**3*c*d**2 + sqrt(x))))/d**2","A",0
419,1,597,0,16.757670," ","integrate((b*x**2+a)**2/(d*x**2+c)/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + 4 a b \sqrt{x} + \frac{2 b^{2} x^{\frac{5}{2}}}{5}\right) & \text{for}\: c = 0 \wedge d = 0 \\\frac{- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + 4 a b \sqrt{x} + \frac{2 b^{2} x^{\frac{5}{2}}}{5}}{d} & \text{for}\: c = 0 \\\frac{2 a^{2} \sqrt{x} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{9}{2}}}{9}}{c} & \text{for}\: d = 0 \\- \frac{\sqrt[4]{-1} a^{2} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} a^{2} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} a^{2} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{c^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} a b \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{d} - \frac{\sqrt[4]{-1} a b \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{d} + \frac{2 \sqrt[4]{-1} a b \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{d} + \frac{4 a b \sqrt{x}}{d} - \frac{\sqrt[4]{-1} b^{2} c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d^{2}} + \frac{\sqrt[4]{-1} b^{2} c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d^{2}} - \frac{\sqrt[4]{-1} b^{2} c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{d^{2}} - \frac{2 b^{2} c \sqrt{x}}{d^{2}} + \frac{2 b^{2} x^{\frac{5}{2}}}{5 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*a**2/(3*x**(3/2)) + 4*a*b*sqrt(x) + 2*b**2*x**(5/2)/5), Eq(c, 0) & Eq(d, 0)), ((-2*a**2/(3*x**(3/2)) + 4*a*b*sqrt(x) + 2*b**2*x**(5/2)/5)/d, Eq(c, 0)), ((2*a**2*sqrt(x) + 4*a*b*x**(5/2)/5 + 2*b**2*x**(9/2)/9)/c, Eq(d, 0)), (-(-1)**(1/4)*a**2*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(3/4)) + (-1)**(1/4)*a**2*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(3/4)) - (-1)**(1/4)*a**2*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/c**(3/4) + (-1)**(1/4)*a*b*c**(1/4)*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/d - (-1)**(1/4)*a*b*c**(1/4)*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/d + 2*(-1)**(1/4)*a*b*c**(1/4)*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/d + 4*a*b*sqrt(x)/d - (-1)**(1/4)*b**2*c**(5/4)*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d**2) + (-1)**(1/4)*b**2*c**(5/4)*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d**2) - (-1)**(1/4)*b**2*c**(5/4)*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/d**2 - 2*b**2*c*sqrt(x)/d**2 + 2*b**2*x**(5/2)/(5*d), True))","A",0
420,1,394,0,36.721546," ","integrate((b*x**2+a)**2/x**(3/2)/(d*x**2+c),x)","a^{2} \left(\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: c = 0 \wedge d = 0 \\- \frac{2}{c \sqrt{x}} & \text{for}\: d = 0 \\- \frac{2}{5 d x^{\frac{5}{2}}} & \text{for}\: c = 0 \\- \frac{2}{c \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}}} & \text{otherwise} \end{cases}\right) + 4 a b \operatorname{RootSum} {\left(256 t^{4} c d^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} c d^{2} + \sqrt{x} \right)} \right)\right)} + b^{2} \left(\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: c = 0 \wedge d = 0 \\\frac{2 x^{\frac{7}{2}}}{7 c} & \text{for}\: d = 0 \\\frac{2 x^{\frac{3}{2}}}{3 d} & \text{for}\: c = 0 \\\frac{\left(-1\right)^{\frac{3}{4}} c^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d^{2} \sqrt[4]{\frac{1}{d}}} - \frac{\left(-1\right)^{\frac{3}{4}} c^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d^{2} \sqrt[4]{\frac{1}{d}}} - \frac{\left(-1\right)^{\frac{3}{4}} c^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{d^{2} \sqrt[4]{\frac{1}{d}}} + \frac{2 x^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right)"," ",0,"a**2*Piecewise((zoo/x**(5/2), Eq(c, 0) & Eq(d, 0)), (-2/(c*sqrt(x)), Eq(d, 0)), (-2/(5*d*x**(5/2)), Eq(c, 0)), (-2/(c*sqrt(x)) + (-1)**(3/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(5/4)*(1/d)**(1/4)) - (-1)**(3/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(5/4)*(1/d)**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(c**(5/4)*(1/d)**(1/4)), True)) + 4*a*b*RootSum(256*_t**4*c*d**3 + 1, Lambda(_t, _t*log(64*_t**3*c*d**2 + sqrt(x)))) + b**2*Piecewise((zoo*x**(3/2), Eq(c, 0) & Eq(d, 0)), (2*x**(7/2)/(7*c), Eq(d, 0)), (2*x**(3/2)/(3*d), Eq(c, 0)), ((-1)**(3/4)*c**(3/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d**2*(1/d)**(1/4)) - (-1)**(3/4)*c**(3/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d**2*(1/d)**(1/4)) - (-1)**(3/4)*c**(3/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(d**2*(1/d)**(1/4)) + 2*x**(3/2)/(3*d), True))","A",0
421,1,576,0,31.822175," ","integrate((b*x**2+a)**2/x**(5/2)/(d*x**2+c),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 a^{2}}{7 x^{\frac{7}{2}}} - \frac{4 a b}{3 x^{\frac{3}{2}}} + 2 b^{2} \sqrt{x}\right) & \text{for}\: c = 0 \wedge d = 0 \\\frac{- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} + 4 a b \sqrt{x} + \frac{2 b^{2} x^{\frac{5}{2}}}{5}}{c} & \text{for}\: d = 0 \\\frac{- \frac{2 a^{2}}{7 x^{\frac{7}{2}}} - \frac{4 a b}{3 x^{\frac{3}{2}}} + 2 b^{2} \sqrt{x}}{d} & \text{for}\: c = 0 \\- \frac{2 a^{2}}{3 c x^{\frac{3}{2}}} + \frac{\sqrt[4]{-1} a^{2} d \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} a^{2} d \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{7}{4}}} + \frac{\sqrt[4]{-1} a^{2} d \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{c^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} a b \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{c^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} a b \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{c^{\frac{3}{4}}} - \frac{2 \sqrt[4]{-1} a b \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{c^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} b^{2} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d} - \frac{\sqrt[4]{-1} b^{2} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 d} + \frac{\sqrt[4]{-1} b^{2} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{d} + \frac{2 b^{2} \sqrt{x}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*a**2/(7*x**(7/2)) - 4*a*b/(3*x**(3/2)) + 2*b**2*sqrt(x)), Eq(c, 0) & Eq(d, 0)), ((-2*a**2/(3*x**(3/2)) + 4*a*b*sqrt(x) + 2*b**2*x**(5/2)/5)/c, Eq(d, 0)), ((-2*a**2/(7*x**(7/2)) - 4*a*b/(3*x**(3/2)) + 2*b**2*sqrt(x))/d, Eq(c, 0)), (-2*a**2/(3*c*x**(3/2)) + (-1)**(1/4)*a**2*d*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(7/4)) - (-1)**(1/4)*a**2*d*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(7/4)) + (-1)**(1/4)*a**2*d*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/c**(7/4) - (-1)**(1/4)*a*b*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/c**(3/4) + (-1)**(1/4)*a*b*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/c**(3/4) - 2*(-1)**(1/4)*a*b*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/c**(3/4) + (-1)**(1/4)*b**2*c**(1/4)*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d) - (-1)**(1/4)*b**2*c**(1/4)*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*d) + (-1)**(1/4)*b**2*c**(1/4)*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/d + 2*b**2*sqrt(x)/d, True))","A",0
422,1,406,0,125.078979," ","integrate((b*x**2+a)**2/x**(7/2)/(d*x**2+c),x)","a^{2} \left(\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: c = 0 \wedge d = 0 \\- \frac{2}{9 d x^{\frac{9}{2}}} & \text{for}\: c = 0 \\- \frac{2}{5 c x^{\frac{5}{2}}} & \text{for}\: d = 0 \\- \frac{2}{5 c x^{\frac{5}{2}}} + \frac{2 d}{c^{2} \sqrt{x}} - \frac{\left(-1\right)^{\frac{3}{4}} d \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{9}{4}} \sqrt[4]{\frac{1}{d}}} + \frac{\left(-1\right)^{\frac{3}{4}} d \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{9}{4}} \sqrt[4]{\frac{1}{d}}} + \frac{\left(-1\right)^{\frac{3}{4}} d \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{c^{\frac{9}{4}} \sqrt[4]{\frac{1}{d}}} & \text{otherwise} \end{cases}\right) + 2 a b \left(\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: c = 0 \wedge d = 0 \\- \frac{2}{c \sqrt{x}} & \text{for}\: d = 0 \\- \frac{2}{5 d x^{\frac{5}{2}}} & \text{for}\: c = 0 \\- \frac{2}{c \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{2 c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{c^{\frac{5}{4}} \sqrt[4]{\frac{1}{d}}} & \text{otherwise} \end{cases}\right) + 2 b^{2} \operatorname{RootSum} {\left(256 t^{4} c d^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} c d^{2} + \sqrt{x} \right)} \right)\right)}"," ",0,"a**2*Piecewise((zoo/x**(9/2), Eq(c, 0) & Eq(d, 0)), (-2/(9*d*x**(9/2)), Eq(c, 0)), (-2/(5*c*x**(5/2)), Eq(d, 0)), (-2/(5*c*x**(5/2)) + 2*d/(c**2*sqrt(x)) - (-1)**(3/4)*d*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(9/4)*(1/d)**(1/4)) + (-1)**(3/4)*d*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(9/4)*(1/d)**(1/4)) + (-1)**(3/4)*d*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(c**(9/4)*(1/d)**(1/4)), True)) + 2*a*b*Piecewise((zoo/x**(5/2), Eq(c, 0) & Eq(d, 0)), (-2/(c*sqrt(x)), Eq(d, 0)), (-2/(5*d*x**(5/2)), Eq(c, 0)), (-2/(c*sqrt(x)) + (-1)**(3/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(5/4)*(1/d)**(1/4)) - (-1)**(3/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(2*c**(5/4)*(1/d)**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(c**(5/4)*(1/d)**(1/4)), True)) + 2*b**2*RootSum(256*_t**4*c*d**3 + 1, Lambda(_t, _t*log(64*_t**3*c*d**2 + sqrt(x))))","A",0
423,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**(9/2)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate((d*x**2+c)**2/x**(11/2)/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(x**(7/2)*(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(x**(5/2)*(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate(x**(3/2)*(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,1,173,0,42.058332," ","integrate((b*x**2+a)**2*x**(1/2)/(d*x**2+c)**2,x)","\frac{4 a b \operatorname{RootSum} {\left(256 t^{4} c d^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} c d^{2} + \sqrt{x} \right)} \right)\right)}}{d} - \frac{4 b^{2} c \operatorname{RootSum} {\left(256 t^{4} c d^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} c d^{2} + \sqrt{x} \right)} \right)\right)}}{d^{2}} + \frac{2 b^{2} x^{\frac{3}{2}}}{3 d^{2}} + \frac{2 x^{\frac{3}{2}} \left(a d - b c\right)^{2}}{4 c^{2} d^{2} + 4 c d^{3} x^{2}} + \frac{2 \left(a d - b c\right)^{2} \operatorname{RootSum} {\left(65536 t^{4} c^{5} d^{3} + 1, \left( t \mapsto t \log{\left(4096 t^{3} c^{4} d^{2} + \sqrt{x} \right)} \right)\right)}}{d^{2}}"," ",0,"4*a*b*RootSum(256*_t**4*c*d**3 + 1, Lambda(_t, _t*log(64*_t**3*c*d**2 + sqrt(x))))/d - 4*b**2*c*RootSum(256*_t**4*c*d**3 + 1, Lambda(_t, _t*log(64*_t**3*c*d**2 + sqrt(x))))/d**2 + 2*b**2*x**(3/2)/(3*d**2) + 2*x**(3/2)*(a*d - b*c)**2/(4*c**2*d**2 + 4*c*d**3*x**2) + 2*(a*d - b*c)**2*RootSum(65536*_t**4*c**5*d**3 + 1, Lambda(_t, _t*log(4096*_t**3*c**4*d**2 + sqrt(x))))/d**2","A",0
429,1,1574,0,79.525667," ","integrate((b*x**2+a)**2/(d*x**2+c)**2/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 a^{2}}{7 x^{\frac{7}{2}}} - \frac{4 a b}{3 x^{\frac{3}{2}}} + 2 b^{2} \sqrt{x}\right) & \text{for}\: c = 0 \wedge d = 0 \\\frac{- \frac{2 a^{2}}{7 x^{\frac{7}{2}}} - \frac{4 a b}{3 x^{\frac{3}{2}}} + 2 b^{2} \sqrt{x}}{d^{2}} & \text{for}\: c = 0 \\\frac{2 a^{2} \sqrt{x} + \frac{4 a b x^{\frac{5}{2}}}{5} + \frac{2 b^{2} x^{\frac{9}{2}}}{9}}{c^{2}} & \text{for}\: d = 0 \\- \frac{3 \sqrt[4]{-1} a^{2} c^{\frac{5}{4}} d^{2} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{3 \sqrt[4]{-1} a^{2} c^{\frac{5}{4}} d^{2} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{6 \sqrt[4]{-1} a^{2} c^{\frac{5}{4}} d^{2} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{3 \sqrt[4]{-1} a^{2} \sqrt[4]{c} d^{3} x^{2} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{3 \sqrt[4]{-1} a^{2} \sqrt[4]{c} d^{3} x^{2} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{6 \sqrt[4]{-1} a^{2} \sqrt[4]{c} d^{3} x^{2} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{4 a^{2} c d^{2} \sqrt{x}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{2 \sqrt[4]{-1} a b c^{\frac{9}{4}} d \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{2 \sqrt[4]{-1} a b c^{\frac{9}{4}} d \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{4 \sqrt[4]{-1} a b c^{\frac{9}{4}} d \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{2 \sqrt[4]{-1} a b c^{\frac{5}{4}} d^{2} x^{2} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{2 \sqrt[4]{-1} a b c^{\frac{5}{4}} d^{2} x^{2} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{4 \sqrt[4]{-1} a b c^{\frac{5}{4}} d^{2} x^{2} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{8 a b c^{2} d \sqrt{x}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{5 \sqrt[4]{-1} b^{2} c^{\frac{13}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{5 \sqrt[4]{-1} b^{2} c^{\frac{13}{4}} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{10 \sqrt[4]{-1} b^{2} c^{\frac{13}{4}} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{5 \sqrt[4]{-1} b^{2} c^{\frac{9}{4}} d x^{2} \sqrt[4]{\frac{1}{d}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} - \frac{5 \sqrt[4]{-1} b^{2} c^{\frac{9}{4}} d x^{2} \sqrt[4]{\frac{1}{d}} \log{\left(\sqrt[4]{-1} \sqrt[4]{c} \sqrt[4]{\frac{1}{d}} + \sqrt{x} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{10 \sqrt[4]{-1} b^{2} c^{\frac{9}{4}} d x^{2} \sqrt[4]{\frac{1}{d}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{c} \sqrt[4]{\frac{1}{d}}} \right)}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{20 b^{2} c^{3} \sqrt{x}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} + \frac{16 b^{2} c^{2} d x^{\frac{5}{2}}}{8 c^{3} d^{2} + 8 c^{2} d^{3} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*a**2/(7*x**(7/2)) - 4*a*b/(3*x**(3/2)) + 2*b**2*sqrt(x)), Eq(c, 0) & Eq(d, 0)), ((-2*a**2/(7*x**(7/2)) - 4*a*b/(3*x**(3/2)) + 2*b**2*sqrt(x))/d**2, Eq(c, 0)), ((2*a**2*sqrt(x) + 4*a*b*x**(5/2)/5 + 2*b**2*x**(9/2)/9)/c**2, Eq(d, 0)), (-3*(-1)**(1/4)*a**2*c**(5/4)*d**2*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 3*(-1)**(1/4)*a**2*c**(5/4)*d**2*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 6*(-1)**(1/4)*a**2*c**(5/4)*d**2*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 3*(-1)**(1/4)*a**2*c**(1/4)*d**3*x**2*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 3*(-1)**(1/4)*a**2*c**(1/4)*d**3*x**2*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 6*(-1)**(1/4)*a**2*c**(1/4)*d**3*x**2*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 4*a**2*c*d**2*sqrt(x)/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 2*(-1)**(1/4)*a*b*c**(9/4)*d*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 2*(-1)**(1/4)*a*b*c**(9/4)*d*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 4*(-1)**(1/4)*a*b*c**(9/4)*d*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 2*(-1)**(1/4)*a*b*c**(5/4)*d**2*x**2*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 2*(-1)**(1/4)*a*b*c**(5/4)*d**2*x**2*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 4*(-1)**(1/4)*a*b*c**(5/4)*d**2*x**2*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 8*a*b*c**2*d*sqrt(x)/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 5*(-1)**(1/4)*b**2*c**(13/4)*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 5*(-1)**(1/4)*b**2*c**(13/4)*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 10*(-1)**(1/4)*b**2*c**(13/4)*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 5*(-1)**(1/4)*b**2*c**(9/4)*d*x**2*(1/d)**(1/4)*log(-(-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) - 5*(-1)**(1/4)*b**2*c**(9/4)*d*x**2*(1/d)**(1/4)*log((-1)**(1/4)*c**(1/4)*(1/d)**(1/4) + sqrt(x))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 10*(-1)**(1/4)*b**2*c**(9/4)*d*x**2*(1/d)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(c**(1/4)*(1/d)**(1/4)))/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 20*b**2*c**3*sqrt(x)/(8*c**3*d**2 + 8*c**2*d**3*x**2) + 16*b**2*c**2*d*x**(5/2)/(8*c**3*d**2 + 8*c**2*d**3*x**2), True))","A",0
430,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**(3/2)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**(5/2)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**(7/2)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate(x**(7/2)*(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate(x**(5/2)*(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate(x**(3/2)*(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*x**(1/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/(d*x**2+c)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**(3/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**(5/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**(7/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate(x**(5/2)*(d*x**2+c)**3/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate(x**(3/2)*(d*x**2+c)**3/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,1,874,0,93.472347," ","integrate((d*x**2+c)**3*x**(1/2)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 c^{3}}{\sqrt{x}} + 2 c^{2} d x^{\frac{3}{2}} + \frac{6 c d^{2} x^{\frac{7}{2}}}{7} + \frac{2 d^{3} x^{\frac{11}{2}}}{11}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{\frac{2 c^{3} x^{\frac{3}{2}}}{3} + \frac{6 c^{2} d x^{\frac{7}{2}}}{7} + \frac{6 c d^{2} x^{\frac{11}{2}}}{11} + \frac{2 d^{3} x^{\frac{15}{2}}}{15}}{a} & \text{for}\: b = 0 \\\frac{- \frac{2 c^{3}}{\sqrt{x}} + 2 c^{2} d x^{\frac{3}{2}} + \frac{6 c d^{2} x^{\frac{7}{2}}}{7} + \frac{2 d^{3} x^{\frac{11}{2}}}{11}}{b} & \text{for}\: a = 0 \\\frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{11}{4}} d^{3} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3}} - \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{11}{4}} d^{3} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3}} - \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{11}{4}} d^{3} \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{3}} - \frac{3 \left(-1\right)^{\frac{3}{4}} a^{\frac{7}{4}} c d^{2} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{3 \left(-1\right)^{\frac{3}{4}} a^{\frac{7}{4}} c d^{2} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{3 \left(-1\right)^{\frac{3}{4}} a^{\frac{7}{4}} c d^{2} \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2}} + \frac{3 \left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} c^{2} d \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{3 \left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} c^{2} d \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{3 \left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} c^{2} d \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} + \frac{2 a^{2} d^{3} x^{\frac{3}{2}}}{3 b^{3}} - \frac{2 a c d^{2} x^{\frac{3}{2}}}{b^{2}} - \frac{2 a d^{3} x^{\frac{7}{2}}}{7 b^{2}} + \frac{2 c^{2} d x^{\frac{3}{2}}}{b} + \frac{6 c d^{2} x^{\frac{7}{2}}}{7 b} + \frac{2 d^{3} x^{\frac{11}{2}}}{11 b} - \frac{\left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a}} + \frac{\left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{b}\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 \sqrt[4]{a}} + \frac{\left(-1\right)^{\frac{3}{4}} c^{3} \left(\frac{1}{b}\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{\sqrt[4]{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*c**3/sqrt(x) + 2*c**2*d*x**(3/2) + 6*c*d**2*x**(7/2)/7 + 2*d**3*x**(11/2)/11), Eq(a, 0) & Eq(b, 0)), ((2*c**3*x**(3/2)/3 + 6*c**2*d*x**(7/2)/7 + 6*c*d**2*x**(11/2)/11 + 2*d**3*x**(15/2)/15)/a, Eq(b, 0)), ((-2*c**3/sqrt(x) + 2*c**2*d*x**(3/2) + 6*c*d**2*x**(7/2)/7 + 2*d**3*x**(11/2)/11)/b, Eq(a, 0)), ((-1)**(3/4)*a**(11/4)*d**3*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3) - (-1)**(3/4)*a**(11/4)*d**3*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3) - (-1)**(3/4)*a**(11/4)*d**3*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**3 - 3*(-1)**(3/4)*a**(7/4)*c*d**2*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + 3*(-1)**(3/4)*a**(7/4)*c*d**2*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + 3*(-1)**(3/4)*a**(7/4)*c*d**2*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**2 + 3*(-1)**(3/4)*a**(3/4)*c**2*d*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - 3*(-1)**(3/4)*a**(3/4)*c**2*d*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - 3*(-1)**(3/4)*a**(3/4)*c**2*d*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b + 2*a**2*d**3*x**(3/2)/(3*b**3) - 2*a*c*d**2*x**(3/2)/b**2 - 2*a*d**3*x**(7/2)/(7*b**2) + 2*c**2*d*x**(3/2)/b + 6*c*d**2*x**(7/2)/(7*b) + 2*d**3*x**(11/2)/(11*b) - (-1)**(3/4)*c**3*(1/b)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)) + (-1)**(3/4)*c**3*(1/b)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(1/4)) + (-1)**(3/4)*c**3*(1/b)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(1/4), True))","A",0
444,1,874,0,71.753392," ","integrate((d*x**2+c)**3/(b*x**2+a)/x**(1/2),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 c^{3}}{3 x^{\frac{3}{2}}} + 6 c^{2} d \sqrt{x} + \frac{6 c d^{2} x^{\frac{5}{2}}}{5} + \frac{2 d^{3} x^{\frac{9}{2}}}{9}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 c^{3} \sqrt{x} + \frac{6 c^{2} d x^{\frac{5}{2}}}{5} + \frac{2 c d^{2} x^{\frac{9}{2}}}{3} + \frac{2 d^{3} x^{\frac{13}{2}}}{13}}{a} & \text{for}\: b = 0 \\\frac{- \frac{2 c^{3}}{3 x^{\frac{3}{2}}} + 6 c^{2} d \sqrt{x} + \frac{6 c d^{2} x^{\frac{5}{2}}}{5} + \frac{2 d^{3} x^{\frac{9}{2}}}{9}}{b} & \text{for}\: a = 0 \\\frac{\sqrt[4]{-1} a^{\frac{9}{4}} d^{3} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3}} - \frac{\sqrt[4]{-1} a^{\frac{9}{4}} d^{3} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3}} + \frac{\sqrt[4]{-1} a^{\frac{9}{4}} d^{3} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{3}} - \frac{3 \sqrt[4]{-1} a^{\frac{5}{4}} c d^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{3 \sqrt[4]{-1} a^{\frac{5}{4}} c d^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} - \frac{3 \sqrt[4]{-1} a^{\frac{5}{4}} c d^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2}} + \frac{3 \sqrt[4]{-1} \sqrt[4]{a} c^{2} d \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{3 \sqrt[4]{-1} \sqrt[4]{a} c^{2} d \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} + \frac{3 \sqrt[4]{-1} \sqrt[4]{a} c^{2} d \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} + \frac{2 a^{2} d^{3} \sqrt{x}}{b^{3}} - \frac{6 a c d^{2} \sqrt{x}}{b^{2}} - \frac{2 a d^{3} x^{\frac{5}{2}}}{5 b^{2}} + \frac{6 c^{2} d \sqrt{x}}{b} + \frac{6 c d^{2} x^{\frac{5}{2}}}{5 b} + \frac{2 d^{3} x^{\frac{9}{2}}}{9 b} - \frac{\sqrt[4]{-1} c^{3} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} c^{3} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} - \frac{\sqrt[4]{-1} c^{3} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{3}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*c**3/(3*x**(3/2)) + 6*c**2*d*sqrt(x) + 6*c*d**2*x**(5/2)/5 + 2*d**3*x**(9/2)/9), Eq(a, 0) & Eq(b, 0)), ((2*c**3*sqrt(x) + 6*c**2*d*x**(5/2)/5 + 2*c*d**2*x**(9/2)/3 + 2*d**3*x**(13/2)/13)/a, Eq(b, 0)), ((-2*c**3/(3*x**(3/2)) + 6*c**2*d*sqrt(x) + 6*c*d**2*x**(5/2)/5 + 2*d**3*x**(9/2)/9)/b, Eq(a, 0)), ((-1)**(1/4)*a**(9/4)*d**3*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3) - (-1)**(1/4)*a**(9/4)*d**3*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3) + (-1)**(1/4)*a**(9/4)*d**3*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**3 - 3*(-1)**(1/4)*a**(5/4)*c*d**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + 3*(-1)**(1/4)*a**(5/4)*c*d**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) - 3*(-1)**(1/4)*a**(5/4)*c*d**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**2 + 3*(-1)**(1/4)*a**(1/4)*c**2*d*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - 3*(-1)**(1/4)*a**(1/4)*c**2*d*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) + 3*(-1)**(1/4)*a**(1/4)*c**2*d*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b + 2*a**2*d**3*sqrt(x)/b**3 - 6*a*c*d**2*sqrt(x)/b**2 - 2*a*d**3*x**(5/2)/(5*b**2) + 6*c**2*d*sqrt(x)/b + 6*c*d**2*x**(5/2)/(5*b) + 2*d**3*x**(9/2)/(9*b) - (-1)**(1/4)*c**3*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) + (-1)**(1/4)*c**3*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) - (-1)**(1/4)*c**3*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(3/4), True))","A",0
445,1,598,0,161.472936," ","integrate((d*x**2+c)**3/x**(3/2)/(b*x**2+a),x)","c^{3} \left(\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{a \sqrt{x}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{5}{4}} \sqrt[4]{\frac{1}{b}}} & \text{otherwise} \end{cases}\right) + 6 c^{2} d \operatorname{RootSum} {\left(256 t^{4} a b^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} a b^{2} + \sqrt{x} \right)} \right)\right)} + 3 c d^{2} \left(\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{7}{2}}}{7 a} & \text{for}\: b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b} & \text{for}\: a = 0 \\\frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2} \sqrt[4]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2} \sqrt[4]{\frac{1}{b}}} + \frac{2 x^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) + d^{3} \left(\begin{cases} \tilde{\infty} x^{\frac{7}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{11}{2}}}{11 a} & \text{for}\: b = 0 \\\frac{2 x^{\frac{7}{2}}}{7 b} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{7}{4}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3} \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{7}{4}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{3} \sqrt[4]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{3}{4}} a^{\frac{7}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{3} \sqrt[4]{\frac{1}{b}}} - \frac{2 a x^{\frac{3}{2}}}{3 b^{2}} + \frac{2 x^{\frac{7}{2}}}{7 b} & \text{otherwise} \end{cases}\right)"," ",0,"c**3*Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (-2/(a*sqrt(x)), Eq(b, 0)), (-2/(a*sqrt(x)) + (-1)**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(5/4)*(1/b)**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(a**(5/4)*(1/b)**(1/4)), True)) + 6*c**2*d*RootSum(256*_t**4*a*b**3 + 1, Lambda(_t, _t*log(64*_t**3*a*b**2 + sqrt(x)))) + 3*c*d**2*Piecewise((zoo*x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*x**(7/2)/(7*a), Eq(b, 0)), (2*x**(3/2)/(3*b), Eq(a, 0)), ((-1)**(3/4)*a**(3/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2*(1/b)**(1/4)) - (-1)**(3/4)*a**(3/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2*(1/b)**(1/4)) - (-1)**(3/4)*a**(3/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(b**2*(1/b)**(1/4)) + 2*x**(3/2)/(3*b), True)) + d**3*Piecewise((zoo*x**(7/2), Eq(a, 0) & Eq(b, 0)), (2*x**(11/2)/(11*a), Eq(b, 0)), (2*x**(7/2)/(7*b), Eq(a, 0)), (-(-1)**(3/4)*a**(7/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3*(1/b)**(1/4)) + (-1)**(3/4)*a**(7/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**3*(1/b)**(1/4)) + (-1)**(3/4)*a**(7/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/(b**3*(1/b)**(1/4)) - 2*a*x**(3/2)/(3*b**2) + 2*x**(7/2)/(7*b), True))","A",0
446,1,828,0,125.946992," ","integrate((d*x**2+c)**3/x**(5/2)/(b*x**2+a),x)","\begin{cases} \tilde{\infty} \left(- \frac{2 c^{3}}{7 x^{\frac{7}{2}}} - \frac{2 c^{2} d}{x^{\frac{3}{2}}} + 6 c d^{2} \sqrt{x} + \frac{2 d^{3} x^{\frac{5}{2}}}{5}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{- \frac{2 c^{3}}{3 x^{\frac{3}{2}}} + 6 c^{2} d \sqrt{x} + \frac{6 c d^{2} x^{\frac{5}{2}}}{5} + \frac{2 d^{3} x^{\frac{9}{2}}}{9}}{a} & \text{for}\: b = 0 \\\frac{- \frac{2 c^{3}}{7 x^{\frac{7}{2}}} - \frac{2 c^{2} d}{x^{\frac{3}{2}}} + 6 c d^{2} \sqrt{x} + \frac{2 d^{3} x^{\frac{5}{2}}}{5}}{b} & \text{for}\: a = 0 \\- \frac{\sqrt[4]{-1} a^{\frac{5}{4}} d^{3} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} + \frac{\sqrt[4]{-1} a^{\frac{5}{4}} d^{3} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b^{2}} - \frac{\sqrt[4]{-1} a^{\frac{5}{4}} d^{3} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b^{2}} + \frac{3 \sqrt[4]{-1} \sqrt[4]{a} c d^{2} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} - \frac{3 \sqrt[4]{-1} \sqrt[4]{a} c d^{2} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 b} + \frac{3 \sqrt[4]{-1} \sqrt[4]{a} c d^{2} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{b} - \frac{2 a d^{3} \sqrt{x}}{b^{2}} + \frac{6 c d^{2} \sqrt{x}}{b} + \frac{2 d^{3} x^{\frac{5}{2}}}{5 b} - \frac{2 c^{3}}{3 a x^{\frac{3}{2}}} - \frac{3 \sqrt[4]{-1} c^{2} d \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} + \frac{3 \sqrt[4]{-1} c^{2} d \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{3}{4}}} - \frac{3 \sqrt[4]{-1} c^{2} d \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{3}{4}}} + \frac{\sqrt[4]{-1} b c^{3} \sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} - \frac{\sqrt[4]{-1} b c^{3} \sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{-1} \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{4}}} + \frac{\sqrt[4]{-1} b c^{3} \sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{x}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{a^{\frac{7}{4}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-2*c**3/(7*x**(7/2)) - 2*c**2*d/x**(3/2) + 6*c*d**2*sqrt(x) + 2*d**3*x**(5/2)/5), Eq(a, 0) & Eq(b, 0)), ((-2*c**3/(3*x**(3/2)) + 6*c**2*d*sqrt(x) + 6*c*d**2*x**(5/2)/5 + 2*d**3*x**(9/2)/9)/a, Eq(b, 0)), ((-2*c**3/(7*x**(7/2)) - 2*c**2*d/x**(3/2) + 6*c*d**2*sqrt(x) + 2*d**3*x**(5/2)/5)/b, Eq(a, 0)), (-(-1)**(1/4)*a**(5/4)*d**3*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) + (-1)**(1/4)*a**(5/4)*d**3*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b**2) - (-1)**(1/4)*a**(5/4)*d**3*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b**2 + 3*(-1)**(1/4)*a**(1/4)*c*d**2*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) - 3*(-1)**(1/4)*a**(1/4)*c*d**2*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*b) + 3*(-1)**(1/4)*a**(1/4)*c*d**2*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/b - 2*a*d**3*sqrt(x)/b**2 + 6*c*d**2*sqrt(x)/b + 2*d**3*x**(5/2)/(5*b) - 2*c**3/(3*a*x**(3/2)) - 3*(-1)**(1/4)*c**2*d*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) + 3*(-1)**(1/4)*c**2*d*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(3/4)) - 3*(-1)**(1/4)*c**2*d*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(3/4) + (-1)**(1/4)*b*c**3*(1/b)**(1/4)*log(-(-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(7/4)) - (-1)**(1/4)*b*c**3*(1/b)**(1/4)*log((-1)**(1/4)*a**(1/4)*(1/b)**(1/4) + sqrt(x))/(2*a**(7/4)) + (-1)**(1/4)*b*c**3*(1/b)**(1/4)*atan((-1)**(3/4)*sqrt(x)/(a**(1/4)*(1/b)**(1/4)))/a**(7/4), True))","A",0
447,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(7/2)/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(9/2)/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(11/2)/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(13/2)/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(15/2)/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate(x**(7/2)*(d*x**2+c)**3/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,-1,0,0,0.000000," ","integrate(x**(5/2)*(d*x**2+c)**3/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
454,-1,0,0,0.000000," ","integrate(x**(3/2)*(d*x**2+c)**3/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
455,1,173,0,136.463346," ","integrate((d*x**2+c)**3*x**(1/2)/(b*x**2+a)**2,x)","- \frac{4 a d^{3} x^{\frac{3}{2}}}{3 b^{3}} - \frac{2 x^{\frac{3}{2}} \left(a d - b c\right)^{3}}{4 a^{2} b^{3} + 4 a b^{4} x^{2}} + \frac{2 c d^{2} x^{\frac{3}{2}}}{b^{2}} + \frac{2 d^{3} x^{\frac{7}{2}}}{7 b^{2}} + \frac{6 d \left(a d - b c\right)^{2} \operatorname{RootSum} {\left(256 t^{4} a b^{3} + 1, \left( t \mapsto t \log{\left(64 t^{3} a b^{2} + \sqrt{x} \right)} \right)\right)}}{b^{3}} - \frac{2 \left(a d - b c\right)^{3} \operatorname{RootSum} {\left(65536 t^{4} a^{5} b^{3} + 1, \left( t \mapsto t \log{\left(4096 t^{3} a^{4} b^{2} + \sqrt{x} \right)} \right)\right)}}{b^{3}}"," ",0,"-4*a*d**3*x**(3/2)/(3*b**3) - 2*x**(3/2)*(a*d - b*c)**3/(4*a**2*b**3 + 4*a*b**4*x**2) + 2*c*d**2*x**(3/2)/b**2 + 2*d**3*x**(7/2)/(7*b**2) + 6*d*(a*d - b*c)**2*RootSum(256*_t**4*a*b**3 + 1, Lambda(_t, _t*log(64*_t**3*a*b**2 + sqrt(x))))/b**3 - 2*(a*d - b*c)**3*RootSum(65536*_t**4*a**5*b**3 + 1, Lambda(_t, _t*log(4096*_t**3*a**4*b**2 + sqrt(x))))/b**3","A",0
456,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/(b*x**2+a)**2/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(3/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(5/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(7/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate((d*x**2+c)**3/x**(9/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate(x**(9/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate(x**(7/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate(x**(5/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,-1,0,0,0.000000," ","integrate(x**(3/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,-1,0,0,0.000000," ","integrate(x**(1/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(b*x**2+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(x**(11/2)/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
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472,-1,0,0,0.000000," ","integrate(x**(7/2)/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate(x**(5/2)/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate(x**(3/2)/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,-1,0,0,0.000000," ","integrate(x**(1/2)/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**2/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
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479,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate(x**(7/2)/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate(x**(5/2)/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate(x**(3/2)/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate(x**(1/2)/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(x**(7/2)/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate(x**(5/2)/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
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491,-1,0,0,0.000000," ","integrate(x**(1/2)/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**2/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
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495,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate(x**(7/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate(x**(5/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate(x**(3/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate(x**(1/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**3/x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate(1/x**(3/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate(1/x**(5/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(1/x**(7/2)/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,1,212,0,2.216863," ","integrate(x**5*(B*x**2+A)*(b*x**2+a)**(1/2),x)","\begin{cases} \frac{8 A a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 A a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{A a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{A x^{6} \sqrt{a + b x^{2}}}{7} - \frac{16 B a^{4} \sqrt{a + b x^{2}}}{315 b^{4}} + \frac{8 B a^{3} x^{2} \sqrt{a + b x^{2}}}{315 b^{3}} - \frac{2 B a^{2} x^{4} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{B a x^{6} \sqrt{a + b x^{2}}}{63 b} + \frac{B x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\\sqrt{a} \left(\frac{A x^{6}}{6} + \frac{B x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*A*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + A*a*x**4*sqrt(a + b*x**2)/(35*b) + A*x**6*sqrt(a + b*x**2)/7 - 16*B*a**4*sqrt(a + b*x**2)/(315*b**4) + 8*B*a**3*x**2*sqrt(a + b*x**2)/(315*b**3) - 2*B*a**2*x**4*sqrt(a + b*x**2)/(105*b**2) + B*a*x**6*sqrt(a + b*x**2)/(63*b) + B*x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (sqrt(a)*(A*x**6/6 + B*x**8/8), True))","A",0
505,1,286,0,17.645444," ","integrate(x**4*(B*x**2+A)*(b*x**2+a)**(1/2),x)","- \frac{A a^{\frac{5}{2}} x}{16 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a^{\frac{3}{2}} x^{3}}{48 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 A \sqrt{a} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{A a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{5}{2}}} + \frac{A b x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{\frac{7}{2}} x}{128 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{\frac{5}{2}} x^{3}}{384 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{3}{2}} x^{5}}{192 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{7 B \sqrt{a} x^{7}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 B a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{7}{2}}} + \frac{B b x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-A*a**(5/2)*x/(16*b**2*sqrt(1 + b*x**2/a)) - A*a**(3/2)*x**3/(48*b*sqrt(1 + b*x**2/a)) + 5*A*sqrt(a)*x**5/(24*sqrt(1 + b*x**2/a)) + A*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(5/2)) + A*b*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) + 5*B*a**(7/2)*x/(128*b**3*sqrt(1 + b*x**2/a)) + 5*B*a**(5/2)*x**3/(384*b**2*sqrt(1 + b*x**2/a)) - B*a**(3/2)*x**5/(192*b*sqrt(1 + b*x**2/a)) + 7*B*sqrt(a)*x**7/(48*sqrt(1 + b*x**2/a)) - 5*B*a**4*asinh(sqrt(b)*x/sqrt(a))/(128*b**(7/2)) + B*b*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
506,1,162,0,0.949029," ","integrate(x**3*(B*x**2+A)*(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{2 A a^{2} \sqrt{a + b x^{2}}}{15 b^{2}} + \frac{A a x^{2} \sqrt{a + b x^{2}}}{15 b} + \frac{A x^{4} \sqrt{a + b x^{2}}}{5} + \frac{8 B a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 B a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{B a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{B x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\sqrt{a} \left(\frac{A x^{4}}{4} + \frac{B x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a**2*sqrt(a + b*x**2)/(15*b**2) + A*a*x**2*sqrt(a + b*x**2)/(15*b) + A*x**4*sqrt(a + b*x**2)/5 + 8*B*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*B*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + B*a*x**4*sqrt(a + b*x**2)/(35*b) + B*x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*(A*x**4/4 + B*x**6/6), True))","A",0
507,1,226,0,12.085206," ","integrate(x**2*(B*x**2+A)*(b*x**2+a)**(1/2),x)","\frac{A a^{\frac{3}{2}} x}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A \sqrt{a} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{A b x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{5}{2}} x}{16 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{3}{2}} x^{3}}{48 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B \sqrt{a} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{B a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{5}{2}}} + \frac{B b x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*a**(3/2)*x/(8*b*sqrt(1 + b*x**2/a)) + 3*A*sqrt(a)*x**3/(8*sqrt(1 + b*x**2/a)) - A*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(3/2)) + A*b*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) - B*a**(5/2)*x/(16*b**2*sqrt(1 + b*x**2/a)) - B*a**(3/2)*x**3/(48*b*sqrt(1 + b*x**2/a)) + 5*B*sqrt(a)*x**5/(24*sqrt(1 + b*x**2/a)) + B*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(5/2)) + B*b*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
508,1,110,0,0.371280," ","integrate(x*(B*x**2+A)*(b*x**2+a)**(1/2),x)","\begin{cases} \frac{A a \sqrt{a + b x^{2}}}{3 b} + \frac{A x^{2} \sqrt{a + b x^{2}}}{3} - \frac{2 B a^{2} \sqrt{a + b x^{2}}}{15 b^{2}} + \frac{B a x^{2} \sqrt{a + b x^{2}}}{15 b} + \frac{B x^{4} \sqrt{a + b x^{2}}}{5} & \text{for}\: b \neq 0 \\\sqrt{a} \left(\frac{A x^{2}}{2} + \frac{B x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*sqrt(a + b*x**2)/(3*b) + A*x**2*sqrt(a + b*x**2)/3 - 2*B*a**2*sqrt(a + b*x**2)/(15*b**2) + B*a*x**2*sqrt(a + b*x**2)/(15*b) + B*x**4*sqrt(a + b*x**2)/5, Ne(b, 0)), (sqrt(a)*(A*x**2/2 + B*x**4/4), True))","A",0
509,1,144,0,6.303736," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2),x)","\frac{A \sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{A a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{B a^{\frac{3}{2}} x}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B \sqrt{a} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{B b x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*sqrt(a)*x*sqrt(1 + b*x**2/a)/2 + A*a*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b)) + B*a**(3/2)*x/(8*b*sqrt(1 + b*x**2/a)) + 3*B*sqrt(a)*x**3/(8*sqrt(1 + b*x**2/a)) - B*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(3/2)) + B*b*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
510,1,76,0,25.641235," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x,x)","- \frac{A \left(- \frac{2 a \operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} - 2 \sqrt{a + b x^{2}}\right)}{2} - \frac{B \left(\begin{cases} - \sqrt{a} x^{2} & \text{for}\: b = 0 \\- \frac{2 \left(a + b x^{2}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)}{2}"," ",0,"-A*(-2*a*atan(sqrt(a + b*x**2)/sqrt(-a))/sqrt(-a) - 2*sqrt(a + b*x**2))/2 - B*Piecewise((-sqrt(a)*x**2, Eq(b, 0)), (-2*(a + b*x**2)**(3/2)/(3*b), True))/2","A",0
511,1,107,0,4.414958," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**2,x)","- \frac{A \sqrt{a}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + A \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)} - \frac{A b x}{\sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{B \sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{B a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 \sqrt{b}}"," ",0,"-A*sqrt(a)/(x*sqrt(1 + b*x**2/a)) + A*sqrt(b)*asinh(sqrt(b)*x/sqrt(a)) - A*b*x/(sqrt(a)*sqrt(1 + b*x**2/a)) + B*sqrt(a)*x*sqrt(1 + b*x**2/a)/2 + B*a*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b))","A",0
512,1,107,0,43.703200," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**3,x)","- \frac{A \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} - \frac{A b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 \sqrt{a}} - B \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)} + \frac{B a}{\sqrt{b} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{B \sqrt{b} x}{\sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-A*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*x) - A*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*sqrt(a)) - B*sqrt(a)*asinh(sqrt(a)/(sqrt(b)*x)) + B*a/(sqrt(b)*x*sqrt(a/(b*x**2) + 1)) + B*sqrt(b)*x/sqrt(a/(b*x**2) + 1)","A",0
513,1,107,0,3.354484," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**4,x)","- \frac{A \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{A b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a} - \frac{B \sqrt{a}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + B \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)} - \frac{B b x}{\sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-A*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - A*b**(3/2)*sqrt(a/(b*x**2) + 1)/(3*a) - B*sqrt(a)/(x*sqrt(1 + b*x**2/a)) + B*sqrt(b)*asinh(sqrt(b)*x/sqrt(a)) - B*b*x/(sqrt(a)*sqrt(1 + b*x**2/a))","A",0
514,1,144,0,143.854645," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**5,x)","- \frac{A a}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 A \sqrt{b}}{8 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{A b^{\frac{3}{2}}}{8 a x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{3}{2}}} - \frac{B \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} - \frac{B b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 \sqrt{a}}"," ",0,"-A*a/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) - 3*A*sqrt(b)/(8*x**3*sqrt(a/(b*x**2) + 1)) - A*b**(3/2)/(8*a*x*sqrt(a/(b*x**2) + 1)) + A*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(3/2)) - B*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*x) - B*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*sqrt(a))","A",0
515,1,119,0,3.225889," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**6,x)","- \frac{A \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{A b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a x^{2}} + \frac{2 A b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{2}} - \frac{B \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{B b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a}"," ",0,"-A*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - A*b**(3/2)*sqrt(a/(b*x**2) + 1)/(15*a*x**2) + 2*A*b**(5/2)*sqrt(a/(b*x**2) + 1)/(15*a**2) - B*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - B*b**(3/2)*sqrt(a/(b*x**2) + 1)/(3*a)","B",0
516,1,226,0,144.349124," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**7,x)","- \frac{A a}{6 \sqrt{b} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5 A \sqrt{b}}{24 x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A b^{\frac{3}{2}}}{48 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A b^{\frac{5}{2}}}{16 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{A b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{16 a^{\frac{5}{2}}} - \frac{B a}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 B \sqrt{b}}{8 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{B b^{\frac{3}{2}}}{8 a x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{B b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{3}{2}}}"," ",0,"-A*a/(6*sqrt(b)*x**7*sqrt(a/(b*x**2) + 1)) - 5*A*sqrt(b)/(24*x**5*sqrt(a/(b*x**2) + 1)) + A*b**(3/2)/(48*a*x**3*sqrt(a/(b*x**2) + 1)) + A*b**(5/2)/(16*a**2*x*sqrt(a/(b*x**2) + 1)) - A*b**3*asinh(sqrt(a)/(sqrt(b)*x))/(16*a**(5/2)) - B*a/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) - 3*B*sqrt(b)/(8*x**3*sqrt(a/(b*x**2) + 1)) - B*b**(3/2)/(8*a*x*sqrt(a/(b*x**2) + 1)) + B*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(3/2))","B",0
517,1,442,0,3.888029," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**8,x)","- \frac{15 A a^{5} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{33 A a^{4} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{17 A a^{3} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{3 A a^{2} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{12 A a b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 A b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{B \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{B b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a x^{2}} + \frac{2 B b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{2}}"," ",0,"-15*A*a**5*b**(9/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 33*A*a**4*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 17*A*a**3*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 3*A*a**2*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 12*A*a*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*A*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - B*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - B*b**(3/2)*sqrt(a/(b*x**2) + 1)/(15*a*x**2) + 2*B*b**(5/2)*sqrt(a/(b*x**2) + 1)/(15*a**2)","B",0
518,-1,0,0,0.000000," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,1,957,0,5.239530," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**10,x)","- \frac{35 A a^{7} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{110 A a^{6} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{114 A a^{5} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{40 A a^{4} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{5 A a^{3} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{30 A a^{2} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{40 A a b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} + \frac{16 A b^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{15 B a^{5} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{33 B a^{4} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{17 B a^{3} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{3 B a^{2} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{12 B a b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 B b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}}"," ",0,"-35*A*a**7*b**(19/2)*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 110*A*a**6*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 114*A*a**5*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 40*A*a**4*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 5*A*a**3*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 30*A*a**2*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 40*A*a*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) + 16*A*b**(33/2)*x**14*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 15*B*a**5*b**(9/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 33*B*a**4*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 17*B*a**3*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 3*B*a**2*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 12*B*a*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*B*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10)","B",0
520,-1,0,0,0.000000," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,1,260,0,8.362219," ","integrate(x**5*(b*x**2+a)**(3/2)*(B*x**2+A),x)","\begin{cases} \frac{8 A a^{4} \sqrt{a + b x^{2}}}{315 b^{3}} - \frac{4 A a^{3} x^{2} \sqrt{a + b x^{2}}}{315 b^{2}} + \frac{A a^{2} x^{4} \sqrt{a + b x^{2}}}{105 b} + \frac{10 A a x^{6} \sqrt{a + b x^{2}}}{63} + \frac{A b x^{8} \sqrt{a + b x^{2}}}{9} - \frac{16 B a^{5} \sqrt{a + b x^{2}}}{1155 b^{4}} + \frac{8 B a^{4} x^{2} \sqrt{a + b x^{2}}}{1155 b^{3}} - \frac{2 B a^{3} x^{4} \sqrt{a + b x^{2}}}{385 b^{2}} + \frac{B a^{2} x^{6} \sqrt{a + b x^{2}}}{231 b} + \frac{4 B a x^{8} \sqrt{a + b x^{2}}}{33} + \frac{B b x^{10} \sqrt{a + b x^{2}}}{11} & \text{for}\: b \neq 0 \\a^{\frac{3}{2}} \left(\frac{A x^{6}}{6} + \frac{B x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a**4*sqrt(a + b*x**2)/(315*b**3) - 4*A*a**3*x**2*sqrt(a + b*x**2)/(315*b**2) + A*a**2*x**4*sqrt(a + b*x**2)/(105*b) + 10*A*a*x**6*sqrt(a + b*x**2)/63 + A*b*x**8*sqrt(a + b*x**2)/9 - 16*B*a**5*sqrt(a + b*x**2)/(1155*b**4) + 8*B*a**4*x**2*sqrt(a + b*x**2)/(1155*b**3) - 2*B*a**3*x**4*sqrt(a + b*x**2)/(385*b**2) + B*a**2*x**6*sqrt(a + b*x**2)/(231*b) + 4*B*a*x**8*sqrt(a + b*x**2)/33 + B*b*x**10*sqrt(a + b*x**2)/11, Ne(b, 0)), (a**(3/2)*(A*x**6/6 + B*x**8/8), True))","A",0
522,1,345,0,51.181241," ","integrate(x**4*(b*x**2+a)**(3/2)*(B*x**2+A),x)","- \frac{3 A a^{\frac{7}{2}} x}{128 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a^{\frac{5}{2}} x^{3}}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{13 A a^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 A \sqrt{a} b x^{7}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} + \frac{A b^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B a^{\frac{9}{2}} x}{256 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{B a^{\frac{7}{2}} x^{3}}{256 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{5}{2}} x^{5}}{640 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 B a^{\frac{3}{2}} x^{7}}{160 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{19 B \sqrt{a} b x^{9}}{80 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 B a^{5} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{7}{2}}} + \frac{B b^{2} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*A*a**(7/2)*x/(128*b**2*sqrt(1 + b*x**2/a)) - A*a**(5/2)*x**3/(128*b*sqrt(1 + b*x**2/a)) + 13*A*a**(3/2)*x**5/(64*sqrt(1 + b*x**2/a)) + 5*A*sqrt(a)*b*x**7/(16*sqrt(1 + b*x**2/a)) + 3*A*a**4*asinh(sqrt(b)*x/sqrt(a))/(128*b**(5/2)) + A*b**2*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a)) + 3*B*a**(9/2)*x/(256*b**3*sqrt(1 + b*x**2/a)) + B*a**(7/2)*x**3/(256*b**2*sqrt(1 + b*x**2/a)) - B*a**(5/2)*x**5/(640*b*sqrt(1 + b*x**2/a)) + 23*B*a**(3/2)*x**7/(160*sqrt(1 + b*x**2/a)) + 19*B*sqrt(a)*b*x**9/(80*sqrt(1 + b*x**2/a)) - 3*B*a**5*asinh(sqrt(b)*x/sqrt(a))/(256*b**(7/2)) + B*b**2*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
523,1,209,0,2.723604," ","integrate(x**3*(b*x**2+a)**(3/2)*(B*x**2+A),x)","\begin{cases} - \frac{2 A a^{3} \sqrt{a + b x^{2}}}{35 b^{2}} + \frac{A a^{2} x^{2} \sqrt{a + b x^{2}}}{35 b} + \frac{8 A a x^{4} \sqrt{a + b x^{2}}}{35} + \frac{A b x^{6} \sqrt{a + b x^{2}}}{7} + \frac{8 B a^{4} \sqrt{a + b x^{2}}}{315 b^{3}} - \frac{4 B a^{3} x^{2} \sqrt{a + b x^{2}}}{315 b^{2}} + \frac{B a^{2} x^{4} \sqrt{a + b x^{2}}}{105 b} + \frac{10 B a x^{6} \sqrt{a + b x^{2}}}{63} + \frac{B b x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\a^{\frac{3}{2}} \left(\frac{A x^{4}}{4} + \frac{B x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a**3*sqrt(a + b*x**2)/(35*b**2) + A*a**2*x**2*sqrt(a + b*x**2)/(35*b) + 8*A*a*x**4*sqrt(a + b*x**2)/35 + A*b*x**6*sqrt(a + b*x**2)/7 + 8*B*a**4*sqrt(a + b*x**2)/(315*b**3) - 4*B*a**3*x**2*sqrt(a + b*x**2)/(315*b**2) + B*a**2*x**4*sqrt(a + b*x**2)/(105*b) + 10*B*a*x**6*sqrt(a + b*x**2)/63 + B*b*x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (a**(3/2)*(A*x**4/4 + B*x**6/6), True))","A",0
524,1,287,0,26.192077," ","integrate(x**2*(b*x**2+a)**(3/2)*(B*x**2+A),x)","\frac{A a^{\frac{5}{2}} x}{16 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 A a^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{11 A \sqrt{a} b x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + \frac{A b^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 B a^{\frac{7}{2}} x}{128 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{5}{2}} x^{3}}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{13 B a^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B \sqrt{a} b x^{7}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} + \frac{B b^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*a**(5/2)*x/(16*b*sqrt(1 + b*x**2/a)) + 17*A*a**(3/2)*x**3/(48*sqrt(1 + b*x**2/a)) + 11*A*sqrt(a)*b*x**5/(24*sqrt(1 + b*x**2/a)) - A*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(3/2)) + A*b**2*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) - 3*B*a**(7/2)*x/(128*b**2*sqrt(1 + b*x**2/a)) - B*a**(5/2)*x**3/(128*b*sqrt(1 + b*x**2/a)) + 13*B*a**(3/2)*x**5/(64*sqrt(1 + b*x**2/a)) + 5*B*sqrt(a)*b*x**7/(16*sqrt(1 + b*x**2/a)) + 3*B*a**4*asinh(sqrt(b)*x/sqrt(a))/(128*b**(5/2)) + B*b**2*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
525,1,158,0,1.537433," ","integrate(x*(b*x**2+a)**(3/2)*(B*x**2+A),x)","\begin{cases} \frac{A a^{2} \sqrt{a + b x^{2}}}{5 b} + \frac{2 A a x^{2} \sqrt{a + b x^{2}}}{5} + \frac{A b x^{4} \sqrt{a + b x^{2}}}{5} - \frac{2 B a^{3} \sqrt{a + b x^{2}}}{35 b^{2}} + \frac{B a^{2} x^{2} \sqrt{a + b x^{2}}}{35 b} + \frac{8 B a x^{4} \sqrt{a + b x^{2}}}{35} + \frac{B b x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\a^{\frac{3}{2}} \left(\frac{A x^{2}}{2} + \frac{B x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*sqrt(a + b*x**2)/(5*b) + 2*A*a*x**2*sqrt(a + b*x**2)/5 + A*b*x**4*sqrt(a + b*x**2)/5 - 2*B*a**3*sqrt(a + b*x**2)/(35*b**2) + B*a**2*x**2*sqrt(a + b*x**2)/(35*b) + 8*B*a*x**4*sqrt(a + b*x**2)/35 + B*b*x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (a**(3/2)*(A*x**2/2 + B*x**4/4), True))","A",0
526,1,253,0,16.544757," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A),x)","\frac{A a^{\frac{3}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{A a^{\frac{3}{2}} x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A \sqrt{a} b x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 \sqrt{b}} + \frac{A b^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{B a^{\frac{5}{2}} x}{16 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 B a^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{11 B \sqrt{a} b x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + \frac{B b^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*a**(3/2)*x*sqrt(1 + b*x**2/a)/2 + A*a**(3/2)*x/(8*sqrt(1 + b*x**2/a)) + 3*A*sqrt(a)*b*x**3/(8*sqrt(1 + b*x**2/a)) + 3*A*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*sqrt(b)) + A*b**2*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + B*a**(5/2)*x/(16*b*sqrt(1 + b*x**2/a)) + 17*B*a**(3/2)*x**3/(48*sqrt(1 + b*x**2/a)) + 11*B*sqrt(a)*b*x**5/(24*sqrt(1 + b*x**2/a)) - B*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(3/2)) + B*b**2*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
527,1,71,0,61.943363," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x,x)","\frac{A a^{2} \operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + A a \sqrt{a + b x^{2}} + \frac{A \left(a + b x^{2}\right)^{\frac{3}{2}}}{3} + \frac{B \left(a + b x^{2}\right)^{\frac{5}{2}}}{5 b}"," ",0,"A*a**2*atan(sqrt(a + b*x**2)/sqrt(-a))/sqrt(-a) + A*a*sqrt(a + b*x**2) + A*(a + b*x**2)**(3/2)/3 + B*(a + b*x**2)**(5/2)/(5*b)","A",0
528,1,216,0,12.197334," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**2,x)","- \frac{A a^{\frac{3}{2}}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{A \sqrt{a} b x \sqrt{1 + \frac{b x^{2}}{a}}}{2} - \frac{A \sqrt{a} b x}{\sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A a \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2} + \frac{B a^{\frac{3}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{B a^{\frac{3}{2}} x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B \sqrt{a} b x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 \sqrt{b}} + \frac{B b^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-A*a**(3/2)/(x*sqrt(1 + b*x**2/a)) + A*sqrt(a)*b*x*sqrt(1 + b*x**2/a)/2 - A*sqrt(a)*b*x/sqrt(1 + b*x**2/a) + 3*A*a*sqrt(b)*asinh(sqrt(b)*x/sqrt(a))/2 + B*a**(3/2)*x*sqrt(1 + b*x**2/a)/2 + B*a**(3/2)*x/(8*sqrt(1 + b*x**2/a)) + 3*B*sqrt(a)*b*x**3/(8*sqrt(1 + b*x**2/a)) + 3*B*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*sqrt(b)) + B*b**2*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
529,1,184,0,71.664735," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**3,x)","- \frac{3 A \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2} - \frac{A a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} + \frac{A a \sqrt{b}}{x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A b^{\frac{3}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}} - B a^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)} + \frac{B a^{2}}{\sqrt{b} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{B a \sqrt{b} x}{\sqrt{\frac{a}{b x^{2}} + 1}} + B b \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"-3*A*sqrt(a)*b*asinh(sqrt(a)/(sqrt(b)*x))/2 - A*a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*x) + A*a*sqrt(b)/(x*sqrt(a/(b*x**2) + 1)) + A*b**(3/2)*x/sqrt(a/(b*x**2) + 1) - B*a**(3/2)*asinh(sqrt(a)/(sqrt(b)*x)) + B*a**2/(sqrt(b)*x*sqrt(a/(b*x**2) + 1)) + B*a*sqrt(b)*x/sqrt(a/(b*x**2) + 1) + B*b*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True))","A",0
530,1,202,0,7.754376," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**4,x)","- \frac{A \sqrt{a} b}{x \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{A b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3} + A b^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)} - \frac{A b^{2} x}{\sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{3}{2}}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{B \sqrt{a} b x \sqrt{1 + \frac{b x^{2}}{a}}}{2} - \frac{B \sqrt{a} b x}{\sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B a \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2}"," ",0,"-A*sqrt(a)*b/(x*sqrt(1 + b*x**2/a)) - A*a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - A*b**(3/2)*sqrt(a/(b*x**2) + 1)/3 + A*b**(3/2)*asinh(sqrt(b)*x/sqrt(a)) - A*b**2*x/(sqrt(a)*sqrt(1 + b*x**2/a)) - B*a**(3/2)/(x*sqrt(1 + b*x**2/a)) + B*sqrt(a)*b*x*sqrt(1 + b*x**2/a)/2 - B*sqrt(a)*b*x/sqrt(1 + b*x**2/a) + 3*B*a*sqrt(b)*asinh(sqrt(b)*x/sqrt(a))/2","A",0
531,1,216,0,154.890569," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**5,x)","- \frac{A a^{2}}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 A a \sqrt{b}}{8 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{A b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} - \frac{A b^{\frac{3}{2}}}{8 x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 A b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 \sqrt{a}} - \frac{3 B \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2} - \frac{B a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} + \frac{B a \sqrt{b}}{x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{B b^{\frac{3}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}}"," ",0,"-A*a**2/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) - 3*A*a*sqrt(b)/(8*x**3*sqrt(a/(b*x**2) + 1)) - A*b**(3/2)*sqrt(a/(b*x**2) + 1)/(2*x) - A*b**(3/2)/(8*x*sqrt(a/(b*x**2) + 1)) - 3*A*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*sqrt(a)) - 3*B*sqrt(a)*b*asinh(sqrt(a)/(sqrt(b)*x))/2 - B*a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*x) + B*a*sqrt(b)/(x*sqrt(a/(b*x**2) + 1)) + B*b**(3/2)*x/sqrt(a/(b*x**2) + 1)","B",0
532,1,184,0,6.740772," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**6,x)","- \frac{A a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{2 A b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{2}} - \frac{A b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a} - \frac{B \sqrt{a} b}{x \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{B b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3} + B b^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)} - \frac{B b^{2} x}{\sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-A*a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 2*A*b**(3/2)*sqrt(a/(b*x**2) + 1)/(5*x**2) - A*b**(5/2)*sqrt(a/(b*x**2) + 1)/(5*a) - B*sqrt(a)*b/(x*sqrt(1 + b*x**2/a)) - B*a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - B*b**(3/2)*sqrt(a/(b*x**2) + 1)/3 + B*b**(3/2)*asinh(sqrt(b)*x/sqrt(a)) - B*b**2*x/(sqrt(a)*sqrt(1 + b*x**2/a))","B",0
533,-1,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,1,518,0,6.485864," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**8,x)","- \frac{15 A a^{6} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{33 A a^{5} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{17 A a^{4} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{3 A a^{3} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{12 A a^{2} b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 A a b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{A b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{A b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a x^{2}} + \frac{2 A b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{2}} - \frac{B a \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{2 B b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{2}} - \frac{B b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a}"," ",0,"-15*A*a**6*b**(9/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 33*A*a**5*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 17*A*a**4*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 3*A*a**3*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 12*A*a**2*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*A*a*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - A*b**(3/2)*sqrt(a/(b*x**2) + 1)/(5*x**4) - A*b**(5/2)*sqrt(a/(b*x**2) + 1)/(15*a*x**2) + 2*A*b**(7/2)*sqrt(a/(b*x**2) + 1)/(15*a**2) - B*a*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 2*B*b**(3/2)*sqrt(a/(b*x**2) + 1)/(5*x**2) - B*b**(5/2)*sqrt(a/(b*x**2) + 1)/(5*a)","B",0
535,-1,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,1,1408,0,7.148828," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**10,x)","- \frac{35 A a^{8} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{110 A a^{7} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{114 A a^{6} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{40 A a^{5} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{15 A a^{5} b^{\frac{11}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{5 A a^{4} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{33 A a^{4} b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{30 A a^{3} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{17 A a^{3} b^{\frac{15}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{40 A a^{2} b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{3 A a^{2} b^{\frac{17}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{16 A a b^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{12 A a b^{\frac{19}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 A b^{\frac{21}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{15 B a^{6} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{33 B a^{5} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{17 B a^{4} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{3 B a^{3} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{12 B a^{2} b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 B a b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{B b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{B b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a x^{2}} + \frac{2 B b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{2}}"," ",0,"-35*A*a**8*b**(19/2)*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 110*A*a**7*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 114*A*a**6*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 40*A*a**5*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 15*A*a**5*b**(11/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 5*A*a**4*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 33*A*a**4*b**(13/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 30*A*a**3*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 17*A*a**3*b**(15/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 40*A*a**2*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 3*A*a**2*b**(17/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 16*A*a*b**(33/2)*x**14*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 12*A*a*b**(19/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*A*b**(21/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 15*B*a**6*b**(9/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 33*B*a**5*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 17*B*a**4*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 3*B*a**3*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 12*B*a**2*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*B*a*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - B*b**(3/2)*sqrt(a/(b*x**2) + 1)/(5*x**4) - B*b**(5/2)*sqrt(a/(b*x**2) + 1)/(15*a*x**2) + 2*B*b**(7/2)*sqrt(a/(b*x**2) + 1)/(15*a**2)","B",0
537,-1,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/x**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,1,313,0,10.416844," ","integrate(x**5*(b*x**2+a)**(5/2)*(B*x**2+A),x)","\begin{cases} \frac{8 A a^{5} \sqrt{a + b x^{2}}}{693 b^{3}} - \frac{4 A a^{4} x^{2} \sqrt{a + b x^{2}}}{693 b^{2}} + \frac{A a^{3} x^{4} \sqrt{a + b x^{2}}}{231 b} + \frac{113 A a^{2} x^{6} \sqrt{a + b x^{2}}}{693} + \frac{23 A a b x^{8} \sqrt{a + b x^{2}}}{99} + \frac{A b^{2} x^{10} \sqrt{a + b x^{2}}}{11} - \frac{16 B a^{6} \sqrt{a + b x^{2}}}{3003 b^{4}} + \frac{8 B a^{5} x^{2} \sqrt{a + b x^{2}}}{3003 b^{3}} - \frac{2 B a^{4} x^{4} \sqrt{a + b x^{2}}}{1001 b^{2}} + \frac{5 B a^{3} x^{6} \sqrt{a + b x^{2}}}{3003 b} + \frac{53 B a^{2} x^{8} \sqrt{a + b x^{2}}}{429} + \frac{27 B a b x^{10} \sqrt{a + b x^{2}}}{143} + \frac{B b^{2} x^{12} \sqrt{a + b x^{2}}}{13} & \text{for}\: b \neq 0 \\a^{\frac{5}{2}} \left(\frac{A x^{6}}{6} + \frac{B x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a**5*sqrt(a + b*x**2)/(693*b**3) - 4*A*a**4*x**2*sqrt(a + b*x**2)/(693*b**2) + A*a**3*x**4*sqrt(a + b*x**2)/(231*b) + 113*A*a**2*x**6*sqrt(a + b*x**2)/693 + 23*A*a*b*x**8*sqrt(a + b*x**2)/99 + A*b**2*x**10*sqrt(a + b*x**2)/11 - 16*B*a**6*sqrt(a + b*x**2)/(3003*b**4) + 8*B*a**5*x**2*sqrt(a + b*x**2)/(3003*b**3) - 2*B*a**4*x**4*sqrt(a + b*x**2)/(1001*b**2) + 5*B*a**3*x**6*sqrt(a + b*x**2)/(3003*b) + 53*B*a**2*x**8*sqrt(a + b*x**2)/429 + 27*B*a*b*x**10*sqrt(a + b*x**2)/143 + B*b**2*x**12*sqrt(a + b*x**2)/13, Ne(b, 0)), (a**(5/2)*(A*x**6/6 + B*x**8/8), True))","A",0
539,1,405,0,83.277612," ","integrate(x**4*(b*x**2+a)**(5/2)*(B*x**2+A),x)","- \frac{3 A a^{\frac{9}{2}} x}{256 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a^{\frac{7}{2}} x^{3}}{256 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{129 A a^{\frac{5}{2}} x^{5}}{640 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{73 A a^{\frac{3}{2}} b x^{7}}{160 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{29 A \sqrt{a} b^{2} x^{9}}{80 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A a^{5} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{5}{2}}} + \frac{A b^{3} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{\frac{11}{2}} x}{1024 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{\frac{9}{2}} x^{3}}{3072 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{7}{2}} x^{5}}{1536 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{55 B a^{\frac{5}{2}} x^{7}}{384 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{67 B a^{\frac{3}{2}} b x^{9}}{192 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{7 B \sqrt{a} b^{2} x^{11}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 B a^{6} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{1024 b^{\frac{7}{2}}} + \frac{B b^{3} x^{13}}{12 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*A*a**(9/2)*x/(256*b**2*sqrt(1 + b*x**2/a)) - A*a**(7/2)*x**3/(256*b*sqrt(1 + b*x**2/a)) + 129*A*a**(5/2)*x**5/(640*sqrt(1 + b*x**2/a)) + 73*A*a**(3/2)*b*x**7/(160*sqrt(1 + b*x**2/a)) + 29*A*sqrt(a)*b**2*x**9/(80*sqrt(1 + b*x**2/a)) + 3*A*a**5*asinh(sqrt(b)*x/sqrt(a))/(256*b**(5/2)) + A*b**3*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a)) + 5*B*a**(11/2)*x/(1024*b**3*sqrt(1 + b*x**2/a)) + 5*B*a**(9/2)*x**3/(3072*b**2*sqrt(1 + b*x**2/a)) - B*a**(7/2)*x**5/(1536*b*sqrt(1 + b*x**2/a)) + 55*B*a**(5/2)*x**7/(384*sqrt(1 + b*x**2/a)) + 67*B*a**(3/2)*b*x**9/(192*sqrt(1 + b*x**2/a)) + 7*B*sqrt(a)*b**2*x**11/(24*sqrt(1 + b*x**2/a)) - 5*B*a**6*asinh(sqrt(b)*x/sqrt(a))/(1024*b**(7/2)) + B*b**3*x**13/(12*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
540,1,260,0,8.851688," ","integrate(x**3*(b*x**2+a)**(5/2)*(B*x**2+A),x)","\begin{cases} - \frac{2 A a^{4} \sqrt{a + b x^{2}}}{63 b^{2}} + \frac{A a^{3} x^{2} \sqrt{a + b x^{2}}}{63 b} + \frac{5 A a^{2} x^{4} \sqrt{a + b x^{2}}}{21} + \frac{19 A a b x^{6} \sqrt{a + b x^{2}}}{63} + \frac{A b^{2} x^{8} \sqrt{a + b x^{2}}}{9} + \frac{8 B a^{5} \sqrt{a + b x^{2}}}{693 b^{3}} - \frac{4 B a^{4} x^{2} \sqrt{a + b x^{2}}}{693 b^{2}} + \frac{B a^{3} x^{4} \sqrt{a + b x^{2}}}{231 b} + \frac{113 B a^{2} x^{6} \sqrt{a + b x^{2}}}{693} + \frac{23 B a b x^{8} \sqrt{a + b x^{2}}}{99} + \frac{B b^{2} x^{10} \sqrt{a + b x^{2}}}{11} & \text{for}\: b \neq 0 \\a^{\frac{5}{2}} \left(\frac{A x^{4}}{4} + \frac{B x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a**4*sqrt(a + b*x**2)/(63*b**2) + A*a**3*x**2*sqrt(a + b*x**2)/(63*b) + 5*A*a**2*x**4*sqrt(a + b*x**2)/21 + 19*A*a*b*x**6*sqrt(a + b*x**2)/63 + A*b**2*x**8*sqrt(a + b*x**2)/9 + 8*B*a**5*sqrt(a + b*x**2)/(693*b**3) - 4*B*a**4*x**2*sqrt(a + b*x**2)/(693*b**2) + B*a**3*x**4*sqrt(a + b*x**2)/(231*b) + 113*B*a**2*x**6*sqrt(a + b*x**2)/693 + 23*B*a*b*x**8*sqrt(a + b*x**2)/99 + B*b**2*x**10*sqrt(a + b*x**2)/11, Ne(b, 0)), (a**(5/2)*(A*x**4/4 + B*x**6/6), True))","A",0
541,1,348,0,59.840660," ","integrate(x**2*(b*x**2+a)**(5/2)*(B*x**2+A),x)","\frac{5 A a^{\frac{7}{2}} x}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{133 A a^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{127 A a^{\frac{3}{2}} b x^{5}}{192 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 A \sqrt{a} b^{2} x^{7}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 A a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{3}{2}}} + \frac{A b^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 B a^{\frac{9}{2}} x}{256 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{\frac{7}{2}} x^{3}}{256 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{129 B a^{\frac{5}{2}} x^{5}}{640 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{73 B a^{\frac{3}{2}} b x^{7}}{160 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{29 B \sqrt{a} b^{2} x^{9}}{80 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B a^{5} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{5}{2}}} + \frac{B b^{3} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"5*A*a**(7/2)*x/(128*b*sqrt(1 + b*x**2/a)) + 133*A*a**(5/2)*x**3/(384*sqrt(1 + b*x**2/a)) + 127*A*a**(3/2)*b*x**5/(192*sqrt(1 + b*x**2/a)) + 23*A*sqrt(a)*b**2*x**7/(48*sqrt(1 + b*x**2/a)) - 5*A*a**4*asinh(sqrt(b)*x/sqrt(a))/(128*b**(3/2)) + A*b**3*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a)) - 3*B*a**(9/2)*x/(256*b**2*sqrt(1 + b*x**2/a)) - B*a**(7/2)*x**3/(256*b*sqrt(1 + b*x**2/a)) + 129*B*a**(5/2)*x**5/(640*sqrt(1 + b*x**2/a)) + 73*B*a**(3/2)*b*x**7/(160*sqrt(1 + b*x**2/a)) + 29*B*sqrt(a)*b**2*x**9/(80*sqrt(1 + b*x**2/a)) + 3*B*a**5*asinh(sqrt(b)*x/sqrt(a))/(256*b**(5/2)) + B*b**3*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
542,1,209,0,5.657923," ","integrate(x*(b*x**2+a)**(5/2)*(B*x**2+A),x)","\begin{cases} \frac{A a^{3} \sqrt{a + b x^{2}}}{7 b} + \frac{3 A a^{2} x^{2} \sqrt{a + b x^{2}}}{7} + \frac{3 A a b x^{4} \sqrt{a + b x^{2}}}{7} + \frac{A b^{2} x^{6} \sqrt{a + b x^{2}}}{7} - \frac{2 B a^{4} \sqrt{a + b x^{2}}}{63 b^{2}} + \frac{B a^{3} x^{2} \sqrt{a + b x^{2}}}{63 b} + \frac{5 B a^{2} x^{4} \sqrt{a + b x^{2}}}{21} + \frac{19 B a b x^{6} \sqrt{a + b x^{2}}}{63} + \frac{B b^{2} x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\a^{\frac{5}{2}} \left(\frac{A x^{2}}{2} + \frac{B x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*sqrt(a + b*x**2)/(7*b) + 3*A*a**2*x**2*sqrt(a + b*x**2)/7 + 3*A*a*b*x**4*sqrt(a + b*x**2)/7 + A*b**2*x**6*sqrt(a + b*x**2)/7 - 2*B*a**4*sqrt(a + b*x**2)/(63*b**2) + B*a**3*x**2*sqrt(a + b*x**2)/(63*b) + 5*B*a**2*x**4*sqrt(a + b*x**2)/21 + 19*B*a*b*x**6*sqrt(a + b*x**2)/63 + B*b**2*x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (a**(5/2)*(A*x**2/2 + B*x**4/4), True))","A",0
543,1,316,0,32.841850," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A),x)","\frac{A a^{\frac{5}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{3 A a^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 A a^{\frac{3}{2}} b x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 A \sqrt{a} b^{2} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 A a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 \sqrt{b}} + \frac{A b^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{\frac{7}{2}} x}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{133 B a^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{127 B a^{\frac{3}{2}} b x^{5}}{192 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 B \sqrt{a} b^{2} x^{7}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 B a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{3}{2}}} + \frac{B b^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*a**(5/2)*x*sqrt(1 + b*x**2/a)/2 + 3*A*a**(5/2)*x/(16*sqrt(1 + b*x**2/a)) + 35*A*a**(3/2)*b*x**3/(48*sqrt(1 + b*x**2/a)) + 17*A*sqrt(a)*b**2*x**5/(24*sqrt(1 + b*x**2/a)) + 5*A*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*sqrt(b)) + A*b**3*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) + 5*B*a**(7/2)*x/(128*b*sqrt(1 + b*x**2/a)) + 133*B*a**(5/2)*x**3/(384*sqrt(1 + b*x**2/a)) + 127*B*a**(3/2)*b*x**5/(192*sqrt(1 + b*x**2/a)) + 23*B*sqrt(a)*b**2*x**7/(48*sqrt(1 + b*x**2/a)) - 5*B*a**4*asinh(sqrt(b)*x/sqrt(a))/(128*b**(3/2)) + B*b**3*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
544,1,88,0,82.467761," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x,x)","\frac{A a^{3} \operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a}} \right)}}{\sqrt{- a}} + A a^{2} \sqrt{a + b x^{2}} + \frac{A a \left(a + b x^{2}\right)^{\frac{3}{2}}}{3} + \frac{A \left(a + b x^{2}\right)^{\frac{5}{2}}}{5} + \frac{B \left(a + b x^{2}\right)^{\frac{7}{2}}}{7 b}"," ",0,"A*a**3*atan(sqrt(a + b*x**2)/sqrt(-a))/sqrt(-a) + A*a**2*sqrt(a + b*x**2) + A*a*(a + b*x**2)**(3/2)/3 + A*(a + b*x**2)**(5/2)/5 + B*(a + b*x**2)**(7/2)/(7*b)","A",0
545,1,306,0,24.287880," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**2,x)","- \frac{A a^{\frac{5}{2}}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + A a^{\frac{3}{2}} b x \sqrt{1 + \frac{b x^{2}}{a}} - \frac{7 A a^{\frac{3}{2}} b x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A \sqrt{a} b^{2} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 A a^{2} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8} + \frac{A b^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{B a^{\frac{5}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{3 B a^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 B a^{\frac{3}{2}} b x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 B \sqrt{a} b^{2} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 \sqrt{b}} + \frac{B b^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-A*a**(5/2)/(x*sqrt(1 + b*x**2/a)) + A*a**(3/2)*b*x*sqrt(1 + b*x**2/a) - 7*A*a**(3/2)*b*x/(8*sqrt(1 + b*x**2/a)) + 3*A*sqrt(a)*b**2*x**3/(8*sqrt(1 + b*x**2/a)) + 15*A*a**2*sqrt(b)*asinh(sqrt(b)*x/sqrt(a))/8 + A*b**3*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + B*a**(5/2)*x*sqrt(1 + b*x**2/a)/2 + 3*B*a**(5/2)*x/(16*sqrt(1 + b*x**2/a)) + 35*B*a**(3/2)*b*x**3/(48*sqrt(1 + b*x**2/a)) + 17*B*sqrt(a)*b**2*x**5/(24*sqrt(1 + b*x**2/a)) + 5*B*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*sqrt(b)) + B*b**3*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
546,1,296,0,68.238016," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**3,x)","- \frac{5 A a^{\frac{3}{2}} b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2} - \frac{A a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} + \frac{2 A a^{2} \sqrt{b}}{x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{2 A a b^{\frac{3}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}} + A b^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) - B a^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)} + \frac{B a^{3}}{\sqrt{b} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{B a^{2} \sqrt{b} x}{\sqrt{\frac{a}{b x^{2}} + 1}} + 2 B a b \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right) + B b^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + b x^{2}}}{15 b^{2}} + \frac{a x^{2} \sqrt{a + b x^{2}}}{15 b} + \frac{x^{4} \sqrt{a + b x^{2}}}{5} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"-5*A*a**(3/2)*b*asinh(sqrt(a)/(sqrt(b)*x))/2 - A*a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*x) + 2*A*a**2*sqrt(b)/(x*sqrt(a/(b*x**2) + 1)) + 2*A*a*b**(3/2)*x/sqrt(a/(b*x**2) + 1) + A*b**2*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) - B*a**(5/2)*asinh(sqrt(a)/(sqrt(b)*x)) + B*a**3/(sqrt(b)*x*sqrt(a/(b*x**2) + 1)) + B*a**2*sqrt(b)*x/sqrt(a/(b*x**2) + 1) + 2*B*a*b*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + B*b**2*Piecewise((-2*a**2*sqrt(a + b*x**2)/(15*b**2) + a*x**2*sqrt(a + b*x**2)/(15*b) + x**4*sqrt(a + b*x**2)/5, Ne(b, 0)), (sqrt(a)*x**4/4, True))","A",0
547,1,299,0,15.708254," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**4,x)","- \frac{2 A a^{\frac{3}{2}} b}{x \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{A \sqrt{a} b^{2} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} - \frac{2 A \sqrt{a} b^{2} x}{\sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{A a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3} + \frac{5 A a b^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2} - \frac{B a^{\frac{5}{2}}}{x \sqrt{1 + \frac{b x^{2}}{a}}} + B a^{\frac{3}{2}} b x \sqrt{1 + \frac{b x^{2}}{a}} - \frac{7 B a^{\frac{3}{2}} b x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B \sqrt{a} b^{2} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 B a^{2} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8} + \frac{B b^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-2*A*a**(3/2)*b/(x*sqrt(1 + b*x**2/a)) + A*sqrt(a)*b**2*x*sqrt(1 + b*x**2/a)/2 - 2*A*sqrt(a)*b**2*x/sqrt(1 + b*x**2/a) - A*a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - A*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/3 + 5*A*a*b**(3/2)*asinh(sqrt(b)*x/sqrt(a))/2 - B*a**(5/2)/(x*sqrt(1 + b*x**2/a)) + B*a**(3/2)*b*x*sqrt(1 + b*x**2/a) - 7*B*a**(3/2)*b*x/(8*sqrt(1 + b*x**2/a)) + 3*B*sqrt(a)*b**2*x**3/(8*sqrt(1 + b*x**2/a)) + 15*B*a**2*sqrt(b)*asinh(sqrt(b)*x/sqrt(a))/8 + B*b**3*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
548,1,279,0,165.194290," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**5,x)","- \frac{15 A \sqrt{a} b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8} - \frac{A a^{3}}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 A a^{2} \sqrt{b}}{8 x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{A a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{x} + \frac{7 A a b^{\frac{3}{2}}}{8 x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A b^{\frac{5}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5 B a^{\frac{3}{2}} b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2} - \frac{B a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 x} + \frac{2 B a^{2} \sqrt{b}}{x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{2 B a b^{\frac{3}{2}} x}{\sqrt{\frac{a}{b x^{2}} + 1}} + B b^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{3 b} & \text{otherwise} \end{cases}\right)"," ",0,"-15*A*sqrt(a)*b**2*asinh(sqrt(a)/(sqrt(b)*x))/8 - A*a**3/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) - 3*A*a**2*sqrt(b)/(8*x**3*sqrt(a/(b*x**2) + 1)) - A*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/x + 7*A*a*b**(3/2)/(8*x*sqrt(a/(b*x**2) + 1)) + A*b**(5/2)*x/sqrt(a/(b*x**2) + 1) - 5*B*a**(3/2)*b*asinh(sqrt(a)/(sqrt(b)*x))/2 - B*a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*x) + 2*B*a**2*sqrt(b)/(x*sqrt(a/(b*x**2) + 1)) + 2*B*a*b**(3/2)*x/sqrt(a/(b*x**2) + 1) + B*b**2*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True))","A",0
549,1,292,0,11.538789," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**6,x)","- \frac{A \sqrt{a} b^{2}}{x \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{11 A a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 x^{2}} - \frac{8 A b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15} + A b^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)} - \frac{A b^{3} x}{\sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{2 B a^{\frac{3}{2}} b}{x \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{B \sqrt{a} b^{2} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} - \frac{2 B \sqrt{a} b^{2} x}{\sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 x^{2}} - \frac{B a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3} + \frac{5 B a b^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2}"," ",0,"-A*sqrt(a)*b**2/(x*sqrt(1 + b*x**2/a)) - A*a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 11*A*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(15*x**2) - 8*A*b**(5/2)*sqrt(a/(b*x**2) + 1)/15 + A*b**(5/2)*asinh(sqrt(b)*x/sqrt(a)) - A*b**3*x/(sqrt(a)*sqrt(1 + b*x**2/a)) - 2*B*a**(3/2)*b/(x*sqrt(1 + b*x**2/a)) + B*sqrt(a)*b**2*x*sqrt(1 + b*x**2/a)/2 - 2*B*sqrt(a)*b**2*x/sqrt(1 + b*x**2/a) - B*a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*x**2) - B*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/3 + 5*B*a*b**(3/2)*asinh(sqrt(b)*x/sqrt(a))/2","B",0
550,-1,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,1,592,0,14.265420," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**8,x)","- \frac{15 A a^{7} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{33 A a^{6} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{17 A a^{5} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{3 A a^{4} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{12 A a^{3} b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 A a^{2} b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{2 A a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{7 A b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 x^{2}} - \frac{A b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a} - \frac{B \sqrt{a} b^{2}}{x \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B a^{2} \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{11 B a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 x^{2}} - \frac{8 B b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15} + B b^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)} - \frac{B b^{3} x}{\sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-15*A*a**7*b**(9/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 33*A*a**6*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 17*A*a**5*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 3*A*a**4*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 12*A*a**3*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*A*a**2*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 2*A*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 7*A*b**(5/2)*sqrt(a/(b*x**2) + 1)/(15*x**2) - A*b**(7/2)*sqrt(a/(b*x**2) + 1)/(15*a) - B*sqrt(a)*b**2/(x*sqrt(1 + b*x**2/a)) - B*a**2*sqrt(b)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 11*B*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(15*x**2) - 8*B*b**(5/2)*sqrt(a/(b*x**2) + 1)/15 + B*b**(5/2)*asinh(sqrt(b)*x/sqrt(a)) - B*b**3*x/(sqrt(a)*sqrt(1 + b*x**2/a))","B",0
552,-1,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,1,1489,0,13.950455," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**10,x)","- \frac{35 A a^{9} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{110 A a^{8} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{114 A a^{7} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{40 A a^{6} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{30 A a^{6} b^{\frac{11}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{5 A a^{5} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{66 A a^{5} b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{30 A a^{4} b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{34 A a^{4} b^{\frac{15}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{40 A a^{3} b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{6 A a^{3} b^{\frac{17}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} + \frac{16 A a^{2} b^{\frac{33}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{7} b^{9} x^{8} + 945 a^{6} b^{10} x^{10} + 945 a^{5} b^{11} x^{12} + 315 a^{4} b^{12} x^{14}} - \frac{24 A a^{2} b^{\frac{19}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{16 A a b^{\frac{21}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{A b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{A b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a x^{2}} + \frac{2 A b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{2}} - \frac{15 B a^{7} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{33 B a^{6} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{17 B a^{5} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{3 B a^{4} b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{12 B a^{3} b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{8 B a^{2} b^{\frac{19}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{105 a^{5} b^{4} x^{6} + 210 a^{4} b^{5} x^{8} + 105 a^{3} b^{6} x^{10}} - \frac{2 B a b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 x^{4}} - \frac{7 B b^{\frac{5}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 x^{2}} - \frac{B b^{\frac{7}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a}"," ",0,"-35*A*a**9*b**(19/2)*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 110*A*a**8*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 114*A*a**7*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 40*A*a**6*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 30*A*a**6*b**(11/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 5*A*a**5*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 66*A*a**5*b**(13/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 30*A*a**4*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 34*A*a**4*b**(15/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 40*A*a**3*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 6*A*a**3*b**(17/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) + 16*A*a**2*b**(33/2)*x**14*sqrt(a/(b*x**2) + 1)/(315*a**7*b**9*x**8 + 945*a**6*b**10*x**10 + 945*a**5*b**11*x**12 + 315*a**4*b**12*x**14) - 24*A*a**2*b**(19/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 16*A*a*b**(21/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - A*b**(5/2)*sqrt(a/(b*x**2) + 1)/(5*x**4) - A*b**(7/2)*sqrt(a/(b*x**2) + 1)/(15*a*x**2) + 2*A*b**(9/2)*sqrt(a/(b*x**2) + 1)/(15*a**2) - 15*B*a**7*b**(9/2)*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 33*B*a**6*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 17*B*a**5*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 3*B*a**4*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 12*B*a**3*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 8*B*a**2*b**(19/2)*x**10*sqrt(a/(b*x**2) + 1)/(105*a**5*b**4*x**6 + 210*a**4*b**5*x**8 + 105*a**3*b**6*x**10) - 2*B*a*b**(3/2)*sqrt(a/(b*x**2) + 1)/(5*x**4) - 7*B*b**(5/2)*sqrt(a/(b*x**2) + 1)/(15*x**2) - B*b**(7/2)*sqrt(a/(b*x**2) + 1)/(15*a)","B",0
554,-1,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,1,172,0,2.502089," ","integrate(x**5*(B*x**2+A)/(b*x**2+a)**(1/2),x)","\begin{cases} \frac{8 A a^{2} \sqrt{a + b x^{2}}}{15 b^{3}} - \frac{4 A a x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} + \frac{A x^{4} \sqrt{a + b x^{2}}}{5 b} - \frac{16 B a^{3} \sqrt{a + b x^{2}}}{35 b^{4}} + \frac{8 B a^{2} x^{2} \sqrt{a + b x^{2}}}{35 b^{3}} - \frac{6 B a x^{4} \sqrt{a + b x^{2}}}{35 b^{2}} + \frac{B x^{6} \sqrt{a + b x^{2}}}{7 b} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{6}}{6} + \frac{B x^{8}}{8}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a**2*sqrt(a + b*x**2)/(15*b**3) - 4*A*a*x**2*sqrt(a + b*x**2)/(15*b**2) + A*x**4*sqrt(a + b*x**2)/(5*b) - 16*B*a**3*sqrt(a + b*x**2)/(35*b**4) + 8*B*a**2*x**2*sqrt(a + b*x**2)/(35*b**3) - 6*B*a*x**4*sqrt(a + b*x**2)/(35*b**2) + B*x**6*sqrt(a + b*x**2)/(7*b), Ne(b, 0)), ((A*x**6/6 + B*x**8/8)/sqrt(a), True))","A",0
556,1,235,0,12.430141," ","integrate(x**4*(B*x**2+A)/(b*x**2+a)**(1/2),x)","- \frac{3 A a^{\frac{3}{2}} x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{A \sqrt{a} x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 A a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} + \frac{A x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{\frac{5}{2}} x}{16 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 B a^{\frac{3}{2}} x^{3}}{48 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B \sqrt{a} x^{5}}{24 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 B a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{7}{2}}} + \frac{B x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*A*a**(3/2)*x/(8*b**2*sqrt(1 + b*x**2/a)) - A*sqrt(a)*x**3/(8*b*sqrt(1 + b*x**2/a)) + 3*A*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) + A*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + 5*B*a**(5/2)*x/(16*b**3*sqrt(1 + b*x**2/a)) + 5*B*a**(3/2)*x**3/(48*b**2*sqrt(1 + b*x**2/a)) - B*sqrt(a)*x**5/(24*b*sqrt(1 + b*x**2/a)) - 5*B*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(7/2)) + B*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
557,1,121,0,1.216951," ","integrate(x**3*(B*x**2+A)/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{2 A a \sqrt{a + b x^{2}}}{3 b^{2}} + \frac{A x^{2} \sqrt{a + b x^{2}}}{3 b} + \frac{8 B a^{2} \sqrt{a + b x^{2}}}{15 b^{3}} - \frac{4 B a x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} + \frac{B x^{4} \sqrt{a + b x^{2}}}{5 b} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{4}}{4} + \frac{B x^{6}}{6}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a*sqrt(a + b*x**2)/(3*b**2) + A*x**2*sqrt(a + b*x**2)/(3*b) + 8*B*a**2*sqrt(a + b*x**2)/(15*b**3) - 4*B*a*x**2*sqrt(a + b*x**2)/(15*b**2) + B*x**4*sqrt(a + b*x**2)/(5*b), Ne(b, 0)), ((A*x**4/4 + B*x**6/6)/sqrt(a), True))","A",0
558,1,150,0,7.778883," ","integrate(x**2*(B*x**2+A)/(b*x**2+a)**(1/2),x)","\frac{A \sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{A a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} - \frac{3 B a^{\frac{3}{2}} x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{B \sqrt{a} x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 B a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} + \frac{B x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*sqrt(a)*x*sqrt(1 + b*x**2/a)/(2*b) - A*a*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2)) - 3*B*a**(3/2)*x/(8*b**2*sqrt(1 + b*x**2/a)) - B*sqrt(a)*x**3/(8*b*sqrt(1 + b*x**2/a)) + 3*B*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) + B*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
559,1,70,0,0.647101," ","integrate(x*(B*x**2+A)/(b*x**2+a)**(1/2),x)","\begin{cases} \frac{A \sqrt{a + b x^{2}}}{b} - \frac{2 B a \sqrt{a + b x^{2}}}{3 b^{2}} + \frac{B x^{2} \sqrt{a + b x^{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{2}}{2} + \frac{B x^{4}}{4}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*sqrt(a + b*x**2)/b - 2*B*a*sqrt(a + b*x**2)/(3*b**2) + B*x**2*sqrt(a + b*x**2)/(3*b), Ne(b, 0)), ((A*x**2/2 + B*x**4/4)/sqrt(a), True))","A",0
560,1,126,0,3.306094," ","integrate((B*x**2+A)/(b*x**2+a)**(1/2),x)","A \left(\begin{cases} \frac{\sqrt{- \frac{a}{b}} \operatorname{asin}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b < 0 \\\frac{\sqrt{\frac{a}{b}} \operatorname{asinh}{\left(x \sqrt{\frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b > 0 \\\frac{\sqrt{- \frac{a}{b}} \operatorname{acosh}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{- a}} & \text{for}\: b > 0 \wedge a < 0 \end{cases}\right) + \frac{B \sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{B a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}}"," ",0,"A*Piecewise((sqrt(-a/b)*asin(x*sqrt(-b/a))/sqrt(a), (a > 0) & (b < 0)), (sqrt(a/b)*asinh(x*sqrt(b/a))/sqrt(a), (a > 0) & (b > 0)), (sqrt(-a/b)*acosh(x*sqrt(-b/a))/sqrt(-a), (b > 0) & (a < 0))) + B*sqrt(a)*x*sqrt(1 + b*x**2/a)/(2*b) - B*a*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2))","A",0
561,1,61,0,13.199832," ","integrate((B*x**2+A)/x/(b*x**2+a)**(1/2),x)","\frac{A \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{a}} \sqrt{a + b x^{2}}} \right)}}{a \sqrt{- \frac{1}{a}}} - \frac{B \left(\begin{cases} - \frac{x^{2}}{\sqrt{a}} & \text{for}\: b = 0 \\- \frac{2 \sqrt{a + b x^{2}}}{b} & \text{otherwise} \end{cases}\right)}{2}"," ",0,"A*atan(1/(sqrt(-1/a)*sqrt(a + b*x**2)))/(a*sqrt(-1/a)) - B*Piecewise((-x**2/sqrt(a), Eq(b, 0)), (-2*sqrt(a + b*x**2)/b, True))/2","A",0
562,1,99,0,2.644599," ","integrate((B*x**2+A)/x**2/(b*x**2+a)**(1/2),x)","- \frac{A \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{a} + B \left(\begin{cases} \frac{\sqrt{- \frac{a}{b}} \operatorname{asin}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b < 0 \\\frac{\sqrt{\frac{a}{b}} \operatorname{asinh}{\left(x \sqrt{\frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b > 0 \\\frac{\sqrt{- \frac{a}{b}} \operatorname{acosh}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{- a}} & \text{for}\: b > 0 \wedge a < 0 \end{cases}\right)"," ",0,"-A*sqrt(b)*sqrt(a/(b*x**2) + 1)/a + B*Piecewise((sqrt(-a/b)*asin(x*sqrt(-b/a))/sqrt(a), (a > 0) & (b < 0)), (sqrt(a/b)*asinh(x*sqrt(b/a))/sqrt(a), (a > 0) & (b > 0)), (sqrt(-a/b)*acosh(x*sqrt(-b/a))/sqrt(-a), (b > 0) & (a < 0)))","A",0
563,1,66,0,39.416442," ","integrate((B*x**2+A)/x**3/(b*x**2+a)**(1/2),x)","- \frac{A \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 a x} + \frac{A b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{3}{2}}} - \frac{B \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{\sqrt{a}}"," ",0,"-A*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*a*x) + A*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(3/2)) - B*asinh(sqrt(a)/(sqrt(b)*x))/sqrt(a)","A",0
564,1,70,0,3.869299," ","integrate((B*x**2+A)/x**4/(b*x**2+a)**(1/2),x)","- \frac{A \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} + \frac{2 A b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}} - \frac{B \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{a}"," ",0,"-A*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*a*x**2) + 2*A*b**(3/2)*sqrt(a/(b*x**2) + 1)/(3*a**2) - B*sqrt(b)*sqrt(a/(b*x**2) + 1)/a","A",0
565,1,150,0,88.379838," ","integrate((B*x**2+A)/x**5/(b*x**2+a)**(1/2),x)","- \frac{A}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A \sqrt{b}}{8 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 A b^{\frac{3}{2}}}{8 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 A b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{5}{2}}} - \frac{B \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{2 a x} + \frac{B b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{3}{2}}}"," ",0,"-A/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) + A*sqrt(b)/(8*a*x**3*sqrt(a/(b*x**2) + 1)) + 3*A*b**(3/2)/(8*a**2*x*sqrt(a/(b*x**2) + 1)) - 3*A*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(5/2)) - B*sqrt(b)*sqrt(a/(b*x**2) + 1)/(2*a*x) + B*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(3/2))","A",0
566,1,355,0,3.174340," ","integrate((B*x**2+A)/x**6/(b*x**2+a)**(1/2),x)","- \frac{3 A a^{4} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{2 A a^{3} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{3 A a^{2} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{12 A a b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{8 A b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{B \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} + \frac{2 B b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}}"," ",0,"-3*A*a**4*b**(9/2)*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 2*A*a**3*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 3*A*a**2*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 12*A*a*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 8*A*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - B*sqrt(b)*sqrt(a/(b*x**2) + 1)/(3*a*x**2) + 2*B*b**(3/2)*sqrt(a/(b*x**2) + 1)/(3*a**2)","B",0
567,1,235,0,133.683066," ","integrate((B*x**2+A)/x**7/(b*x**2+a)**(1/2),x)","- \frac{A}{6 \sqrt{b} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A \sqrt{b}}{24 a x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5 A b^{\frac{3}{2}}}{48 a^{2} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{5 A b^{\frac{5}{2}}}{16 a^{3} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{5 A b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{16 a^{\frac{7}{2}}} - \frac{B}{4 \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{B \sqrt{b}}{8 a x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 B b^{\frac{3}{2}}}{8 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 B b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{5}{2}}}"," ",0,"-A/(6*sqrt(b)*x**7*sqrt(a/(b*x**2) + 1)) + A*sqrt(b)/(24*a*x**5*sqrt(a/(b*x**2) + 1)) - 5*A*b**(3/2)/(48*a**2*x**3*sqrt(a/(b*x**2) + 1)) - 5*A*b**(5/2)/(16*a**3*x*sqrt(a/(b*x**2) + 1)) + 5*A*b**3*asinh(sqrt(a)/(sqrt(b)*x))/(16*a**(7/2)) - B/(4*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) + B*sqrt(b)/(8*a*x**3*sqrt(a/(b*x**2) + 1)) + 3*B*b**(3/2)/(8*a**2*x*sqrt(a/(b*x**2) + 1)) - 3*B*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(5/2))","B",0
568,1,819,0,3.679207," ","integrate((B*x**2+A)/x**8/(b*x**2+a)**(1/2),x)","- \frac{5 A a^{6} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{7} b^{9} x^{6} + 105 a^{6} b^{10} x^{8} + 105 a^{5} b^{11} x^{10} + 35 a^{4} b^{12} x^{12}} - \frac{9 A a^{5} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{7} b^{9} x^{6} + 105 a^{6} b^{10} x^{8} + 105 a^{5} b^{11} x^{10} + 35 a^{4} b^{12} x^{12}} - \frac{5 A a^{4} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{7} b^{9} x^{6} + 105 a^{6} b^{10} x^{8} + 105 a^{5} b^{11} x^{10} + 35 a^{4} b^{12} x^{12}} + \frac{5 A a^{3} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{7} b^{9} x^{6} + 105 a^{6} b^{10} x^{8} + 105 a^{5} b^{11} x^{10} + 35 a^{4} b^{12} x^{12}} + \frac{30 A a^{2} b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{7} b^{9} x^{6} + 105 a^{6} b^{10} x^{8} + 105 a^{5} b^{11} x^{10} + 35 a^{4} b^{12} x^{12}} + \frac{40 A a b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{7} b^{9} x^{6} + 105 a^{6} b^{10} x^{8} + 105 a^{5} b^{11} x^{10} + 35 a^{4} b^{12} x^{12}} + \frac{16 A b^{\frac{31}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{7} b^{9} x^{6} + 105 a^{6} b^{10} x^{8} + 105 a^{5} b^{11} x^{10} + 35 a^{4} b^{12} x^{12}} - \frac{3 B a^{4} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{2 B a^{3} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{3 B a^{2} b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{12 B a b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}} - \frac{8 B b^{\frac{17}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{5} b^{4} x^{4} + 30 a^{4} b^{5} x^{6} + 15 a^{3} b^{6} x^{8}}"," ",0,"-5*A*a**6*b**(19/2)*sqrt(a/(b*x**2) + 1)/(35*a**7*b**9*x**6 + 105*a**6*b**10*x**8 + 105*a**5*b**11*x**10 + 35*a**4*b**12*x**12) - 9*A*a**5*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(35*a**7*b**9*x**6 + 105*a**6*b**10*x**8 + 105*a**5*b**11*x**10 + 35*a**4*b**12*x**12) - 5*A*a**4*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(35*a**7*b**9*x**6 + 105*a**6*b**10*x**8 + 105*a**5*b**11*x**10 + 35*a**4*b**12*x**12) + 5*A*a**3*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(35*a**7*b**9*x**6 + 105*a**6*b**10*x**8 + 105*a**5*b**11*x**10 + 35*a**4*b**12*x**12) + 30*A*a**2*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(35*a**7*b**9*x**6 + 105*a**6*b**10*x**8 + 105*a**5*b**11*x**10 + 35*a**4*b**12*x**12) + 40*A*a*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(35*a**7*b**9*x**6 + 105*a**6*b**10*x**8 + 105*a**5*b**11*x**10 + 35*a**4*b**12*x**12) + 16*A*b**(31/2)*x**12*sqrt(a/(b*x**2) + 1)/(35*a**7*b**9*x**6 + 105*a**6*b**10*x**8 + 105*a**5*b**11*x**10 + 35*a**4*b**12*x**12) - 3*B*a**4*b**(9/2)*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 2*B*a**3*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 3*B*a**2*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 12*B*a*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8) - 8*B*b**(17/2)*x**8*sqrt(a/(b*x**2) + 1)/(15*a**5*b**4*x**4 + 30*a**4*b**5*x**6 + 15*a**3*b**6*x**8)","B",0
569,1,233,0,35.608153," ","integrate(x**6*(B*x**2+A)/(b*x**2+a)**(3/2),x)","A \left(- \frac{15 a^{\frac{3}{2}} x}{8 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 \sqrt{a} x^{3}}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{7}{2}}} + \frac{x^{5}}{4 \sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right) + B \left(\frac{35 a^{\frac{5}{2}} x}{16 b^{4} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} x^{3}}{48 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{7 \sqrt{a} x^{5}}{24 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{35 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{9}{2}}} + \frac{x^{7}}{6 \sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(-15*a**(3/2)*x/(8*b**3*sqrt(1 + b*x**2/a)) - 5*sqrt(a)*x**3/(8*b**2*sqrt(1 + b*x**2/a)) + 15*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(7/2)) + x**5/(4*sqrt(a)*b*sqrt(1 + b*x**2/a))) + B*(35*a**(5/2)*x/(16*b**4*sqrt(1 + b*x**2/a)) + 35*a**(3/2)*x**3/(48*b**3*sqrt(1 + b*x**2/a)) - 7*sqrt(a)*x**5/(24*b**2*sqrt(1 + b*x**2/a)) - 35*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(9/2)) + x**7/(6*sqrt(a)*b*sqrt(1 + b*x**2/a)))","A",0
570,1,172,0,3.637974," ","integrate(x**5*(B*x**2+A)/(b*x**2+a)**(3/2),x)","\begin{cases} - \frac{8 A a^{2}}{3 b^{3} \sqrt{a + b x^{2}}} - \frac{4 A a x^{2}}{3 b^{2} \sqrt{a + b x^{2}}} + \frac{A x^{4}}{3 b \sqrt{a + b x^{2}}} + \frac{16 B a^{3}}{5 b^{4} \sqrt{a + b x^{2}}} + \frac{8 B a^{2} x^{2}}{5 b^{3} \sqrt{a + b x^{2}}} - \frac{2 B a x^{4}}{5 b^{2} \sqrt{a + b x^{2}}} + \frac{B x^{6}}{5 b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{6}}{6} + \frac{B x^{8}}{8}}{a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*A*a**2/(3*b**3*sqrt(a + b*x**2)) - 4*A*a*x**2/(3*b**2*sqrt(a + b*x**2)) + A*x**4/(3*b*sqrt(a + b*x**2)) + 16*B*a**3/(5*b**4*sqrt(a + b*x**2)) + 8*B*a**2*x**2/(5*b**3*sqrt(a + b*x**2)) - 2*B*a*x**4/(5*b**2*sqrt(a + b*x**2)) + B*x**6/(5*b*sqrt(a + b*x**2)), Ne(b, 0)), ((A*x**6/6 + B*x**8/8)/a**(3/2), True))","A",0
571,1,177,0,16.630909," ","integrate(x**4*(B*x**2+A)/(b*x**2+a)**(3/2),x)","A \left(\frac{3 \sqrt{a} x}{2 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{5}{2}}} + \frac{x^{3}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right) + B \left(- \frac{15 a^{\frac{3}{2}} x}{8 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 \sqrt{a} x^{3}}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{7}{2}}} + \frac{x^{5}}{4 \sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(3*sqrt(a)*x/(2*b**2*sqrt(1 + b*x**2/a)) - 3*a*asinh(sqrt(b)*x/sqrt(a))/(2*b**(5/2)) + x**3/(2*sqrt(a)*b*sqrt(1 + b*x**2/a))) + B*(-15*a**(3/2)*x/(8*b**3*sqrt(1 + b*x**2/a)) - 5*sqrt(a)*x**3/(8*b**2*sqrt(1 + b*x**2/a)) + 15*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(7/2)) + x**5/(4*sqrt(a)*b*sqrt(1 + b*x**2/a)))","A",0
572,1,117,0,2.022304," ","integrate(x**3*(B*x**2+A)/(b*x**2+a)**(3/2),x)","\begin{cases} \frac{2 A a}{b^{2} \sqrt{a + b x^{2}}} + \frac{A x^{2}}{b \sqrt{a + b x^{2}}} - \frac{8 B a^{2}}{3 b^{3} \sqrt{a + b x^{2}}} - \frac{4 B a x^{2}}{3 b^{2} \sqrt{a + b x^{2}}} + \frac{B x^{4}}{3 b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{4}}{4} + \frac{B x^{6}}{6}}{a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a/(b**2*sqrt(a + b*x**2)) + A*x**2/(b*sqrt(a + b*x**2)) - 8*B*a**2/(3*b**3*sqrt(a + b*x**2)) - 4*B*a*x**2/(3*b**2*sqrt(a + b*x**2)) + B*x**4/(3*b*sqrt(a + b*x**2)), Ne(b, 0)), ((A*x**4/4 + B*x**6/6)/a**(3/2), True))","A",0
573,1,114,0,14.257987," ","integrate(x**2*(B*x**2+A)/(b*x**2+a)**(3/2),x)","A \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} - \frac{x}{\sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right) + B \left(\frac{3 \sqrt{a} x}{2 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{5}{2}}} + \frac{x^{3}}{2 \sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(asinh(sqrt(b)*x/sqrt(a))/b**(3/2) - x/(sqrt(a)*b*sqrt(1 + b*x**2/a))) + B*(3*sqrt(a)*x/(2*b**2*sqrt(1 + b*x**2/a)) - 3*a*asinh(sqrt(b)*x/sqrt(a))/(2*b**(5/2)) + x**3/(2*sqrt(a)*b*sqrt(1 + b*x**2/a)))","A",0
574,1,66,0,0.677269," ","integrate(x*(B*x**2+A)/(b*x**2+a)**(3/2),x)","\begin{cases} - \frac{A}{b \sqrt{a + b x^{2}}} + \frac{2 B a}{b^{2} \sqrt{a + b x^{2}}} + \frac{B x^{2}}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{2}}{2} + \frac{B x^{4}}{4}}{a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A/(b*sqrt(a + b*x**2)) + 2*B*a/(b**2*sqrt(a + b*x**2)) + B*x**2/(b*sqrt(a + b*x**2)), Ne(b, 0)), ((A*x**2/2 + B*x**4/4)/a**(3/2), True))","A",0
575,1,60,0,10.195802," ","integrate((B*x**2+A)/(b*x**2+a)**(3/2),x)","\frac{A x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}} + B \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} - \frac{x}{\sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*x/(a**(3/2)*sqrt(1 + b*x**2/a)) + B*(asinh(sqrt(b)*x/sqrt(a))/b**(3/2) - x/(sqrt(a)*b*sqrt(1 + b*x**2/a)))","A",0
576,1,48,0,23.904763," ","integrate((B*x**2+A)/x/(b*x**2+a)**(3/2),x)","\frac{A \operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a}} \right)}}{a \sqrt{- a}} - \frac{- A b + B a}{a b \sqrt{a + b x^{2}}}"," ",0,"A*atan(sqrt(a + b*x**2)/sqrt(-a))/(a*sqrt(-a)) - (-A*b + B*a)/(a*b*sqrt(a + b*x**2))","A",0
577,1,68,0,13.665607," ","integrate((B*x**2+A)/x**2/(b*x**2+a)**(3/2),x)","A \left(- \frac{1}{a \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{2 \sqrt{b}}{a^{2} \sqrt{\frac{a}{b x^{2}} + 1}}\right) + \frac{B x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*(-1/(a*sqrt(b)*x**2*sqrt(a/(b*x**2) + 1)) - 2*sqrt(b)/(a**2*sqrt(a/(b*x**2) + 1))) + B*x/(a**(3/2)*sqrt(1 + b*x**2/a))","A",0
578,1,262,0,41.260417," ","integrate((B*x**2+A)/x**3/(b*x**2+a)**(3/2),x)","A \left(- \frac{1}{2 a \sqrt{b} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 \sqrt{b}}{2 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{5}{2}}}\right) + B \left(\frac{2 a^{3} \sqrt{1 + \frac{b x^{2}}{a}}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} + \frac{a^{3} \log{\left(\frac{b x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} + \frac{a^{2} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}} - \frac{2 a^{2} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{2 a^{\frac{9}{2}} + 2 a^{\frac{7}{2}} b x^{2}}\right)"," ",0,"A*(-1/(2*a*sqrt(b)*x**3*sqrt(a/(b*x**2) + 1)) - 3*sqrt(b)/(2*a**2*x*sqrt(a/(b*x**2) + 1)) + 3*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(5/2))) + B*(2*a**3*sqrt(1 + b*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) + a**3*log(b*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) - 2*a**3*log(sqrt(1 + b*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) + a**2*b*x**2*log(b*x**2/a)/(2*a**(9/2) + 2*a**(7/2)*b*x**2) - 2*a**2*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(2*a**(9/2) + 2*a**(7/2)*b*x**2))","B",0
579,1,284,0,9.986878," ","integrate((B*x**2+A)/x**4/(b*x**2+a)**(3/2),x)","A \left(- \frac{a^{3} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{3 a^{2} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{12 a b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{8 b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}}\right) + B \left(- \frac{1}{a \sqrt{b} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{2 \sqrt{b}}{a^{2} \sqrt{\frac{a}{b x^{2}} + 1}}\right)"," ",0,"A*(-a**3*b**(9/2)*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 3*a**2*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 12*a*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 8*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6)) + B*(-1/(a*sqrt(b)*x**2*sqrt(a/(b*x**2) + 1)) - 2*sqrt(b)/(a**2*sqrt(a/(b*x**2) + 1)))","B",0
580,1,180,0,84.399434," ","integrate((B*x**2+A)/x**5/(b*x**2+a)**(3/2),x)","A \left(- \frac{1}{4 a \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{5 \sqrt{b}}{8 a^{2} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{15 b^{\frac{3}{2}}}{8 a^{3} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{15 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{7}{2}}}\right) + B \left(- \frac{1}{2 a \sqrt{b} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{3 \sqrt{b}}{2 a^{2} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{5}{2}}}\right)"," ",0,"A*(-1/(4*a*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) + 5*sqrt(b)/(8*a**2*x**3*sqrt(a/(b*x**2) + 1)) + 15*b**(3/2)/(8*a**3*x*sqrt(a/(b*x**2) + 1)) - 15*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(7/2))) + B*(-1/(2*a*sqrt(b)*x**3*sqrt(a/(b*x**2) + 1)) - 3*sqrt(b)/(2*a**2*x*sqrt(a/(b*x**2) + 1)) + 3*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(5/2)))","A",0
581,1,593,0,17.524910," ","integrate((B*x**2+A)/x**6/(b*x**2+a)**(3/2),x)","A \left(- \frac{a^{5} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{5 a^{3} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{30 a^{2} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{40 a b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{16 b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}}\right) + B \left(- \frac{a^{3} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{3 a^{2} b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{12 a b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}} + \frac{8 b^{\frac{15}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} x^{2} + 6 a^{4} b^{5} x^{4} + 3 a^{3} b^{6} x^{6}}\right)"," ",0,"A*(-a**5*b**(19/2)*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 5*a**3*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 30*a**2*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 40*a*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 16*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10)) + B*(-a**3*b**(9/2)*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 3*a**2*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 12*a*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6) + 8*b**(15/2)*x**6*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4*x**2 + 6*a**4*b**5*x**4 + 3*a**3*b**6*x**6))","B",0
582,1,236,0,141.329818," ","integrate((B*x**2+A)/x**7/(b*x**2+a)**(3/2),x)","A \left(- \frac{1}{6 a \sqrt{b} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{7 \sqrt{b}}{24 a^{2} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{35 b^{\frac{3}{2}}}{48 a^{3} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{35 b^{\frac{5}{2}}}{16 a^{4} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{35 b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{16 a^{\frac{9}{2}}}\right) + B \left(- \frac{1}{4 a \sqrt{b} x^{5} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{5 \sqrt{b}}{8 a^{2} x^{3} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{15 b^{\frac{3}{2}}}{8 a^{3} x \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{15 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{8 a^{\frac{7}{2}}}\right)"," ",0,"A*(-1/(6*a*sqrt(b)*x**7*sqrt(a/(b*x**2) + 1)) + 7*sqrt(b)/(24*a**2*x**5*sqrt(a/(b*x**2) + 1)) - 35*b**(3/2)/(48*a**3*x**3*sqrt(a/(b*x**2) + 1)) - 35*b**(5/2)/(16*a**4*x*sqrt(a/(b*x**2) + 1)) + 35*b**3*asinh(sqrt(a)/(sqrt(b)*x))/(16*a**(9/2))) + B*(-1/(4*a*sqrt(b)*x**5*sqrt(a/(b*x**2) + 1)) + 5*sqrt(b)/(8*a**2*x**3*sqrt(a/(b*x**2) + 1)) + 15*b**(3/2)/(8*a**3*x*sqrt(a/(b*x**2) + 1)) - 15*b**2*asinh(sqrt(a)/(sqrt(b)*x))/(8*a**(7/2)))","A",0
583,1,1030,0,19.080047," ","integrate((B*x**2+A)/x**8/(b*x**2+a)**(3/2),x)","A \left(- \frac{5 a^{7} b^{\frac{33}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}} - \frac{7 a^{6} b^{\frac{35}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}} - \frac{7 a^{5} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}} + \frac{35 a^{4} b^{\frac{39}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}} + \frac{280 a^{3} b^{\frac{41}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}} + \frac{560 a^{2} b^{\frac{43}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}} + \frac{448 a b^{\frac{45}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}} + \frac{128 b^{\frac{47}{2}} x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} x^{6} + 140 a^{8} b^{17} x^{8} + 210 a^{7} b^{18} x^{10} + 140 a^{6} b^{19} x^{12} + 35 a^{5} b^{20} x^{14}}\right) + B \left(- \frac{a^{5} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{5 a^{3} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{30 a^{2} b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{40 a b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}} - \frac{16 b^{\frac{29}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{5 a^{7} b^{9} x^{4} + 15 a^{6} b^{10} x^{6} + 15 a^{5} b^{11} x^{8} + 5 a^{4} b^{12} x^{10}}\right)"," ",0,"A*(-5*a**7*b**(33/2)*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14) - 7*a**6*b**(35/2)*x**2*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14) - 7*a**5*b**(37/2)*x**4*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14) + 35*a**4*b**(39/2)*x**6*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14) + 280*a**3*b**(41/2)*x**8*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14) + 560*a**2*b**(43/2)*x**10*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14) + 448*a*b**(45/2)*x**12*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14) + 128*b**(47/2)*x**14*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16*x**6 + 140*a**8*b**17*x**8 + 210*a**7*b**18*x**10 + 140*a**6*b**19*x**12 + 35*a**5*b**20*x**14)) + B*(-a**5*b**(19/2)*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 5*a**3*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 30*a**2*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 40*a*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10) - 16*b**(29/2)*x**10*sqrt(a/(b*x**2) + 1)/(5*a**7*b**9*x**4 + 15*a**6*b**10*x**6 + 15*a**5*b**11*x**8 + 5*a**4*b**12*x**10))","B",0
584,1,437,0,4.207140," ","integrate(x**7*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\begin{cases} - \frac{80 A a^{3} b}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} - \frac{120 A a^{2} b^{2} x^{2}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} - \frac{30 A a b^{3} x^{4}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} + \frac{5 A b^{4} x^{6}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} + \frac{128 B a^{4}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} + \frac{192 B a^{3} b x^{2}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} + \frac{48 B a^{2} b^{2} x^{4}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} - \frac{8 B a b^{3} x^{6}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} + \frac{3 B b^{4} x^{8}}{15 a b^{5} \sqrt{a + b x^{2}} + 15 b^{6} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{8}}{8} + \frac{B x^{10}}{10}}{a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-80*A*a**3*b/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) - 120*A*a**2*b**2*x**2/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) - 30*A*a*b**3*x**4/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) + 5*A*b**4*x**6/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) + 128*B*a**4/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) + 192*B*a**3*b*x**2/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) + 48*B*a**2*b**2*x**4/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) - 8*B*a*b**3*x**6/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)) + 3*B*b**4*x**8/(15*a*b**5*sqrt(a + b*x**2) + 15*b**6*x**2*sqrt(a + b*x**2)), Ne(b, 0)), ((A*x**8/8 + B*x**10/10)/a**(5/2), True))","A",0
585,1,804,0,38.816330," ","integrate(x**6*(B*x**2+A)/(b*x**2+a)**(5/2),x)","A \left(- \frac{15 a^{\frac{81}{2}} b^{22} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{15 a^{\frac{79}{2}} b^{23} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{40} b^{\frac{45}{2}} x}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{20 a^{39} b^{\frac{47}{2}} x^{3}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{38} b^{\frac{49}{2}} x^{5}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + B \left(\frac{105 a^{\frac{157}{2}} b^{41} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{24 a^{\frac{153}{2}} b^{\frac{91}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 24 a^{\frac{151}{2}} b^{\frac{93}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{105 a^{\frac{155}{2}} b^{42} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{24 a^{\frac{153}{2}} b^{\frac{91}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 24 a^{\frac{151}{2}} b^{\frac{93}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{105 a^{78} b^{\frac{83}{2}} x}{24 a^{\frac{153}{2}} b^{\frac{91}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 24 a^{\frac{151}{2}} b^{\frac{93}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{140 a^{77} b^{\frac{85}{2}} x^{3}}{24 a^{\frac{153}{2}} b^{\frac{91}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 24 a^{\frac{151}{2}} b^{\frac{93}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{21 a^{76} b^{\frac{87}{2}} x^{5}}{24 a^{\frac{153}{2}} b^{\frac{91}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 24 a^{\frac{151}{2}} b^{\frac{93}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{6 a^{75} b^{\frac{89}{2}} x^{7}}{24 a^{\frac{153}{2}} b^{\frac{91}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 24 a^{\frac{151}{2}} b^{\frac{93}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(-15*a**(81/2)*b**22*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) - 15*a**(79/2)*b**23*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 15*a**40*b**(45/2)*x/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 20*a**39*b**(47/2)*x**3/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 3*a**38*b**(49/2)*x**5/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a))) + B*(105*a**(157/2)*b**41*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(24*a**(153/2)*b**(91/2)*sqrt(1 + b*x**2/a) + 24*a**(151/2)*b**(93/2)*x**2*sqrt(1 + b*x**2/a)) + 105*a**(155/2)*b**42*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(24*a**(153/2)*b**(91/2)*sqrt(1 + b*x**2/a) + 24*a**(151/2)*b**(93/2)*x**2*sqrt(1 + b*x**2/a)) - 105*a**78*b**(83/2)*x/(24*a**(153/2)*b**(91/2)*sqrt(1 + b*x**2/a) + 24*a**(151/2)*b**(93/2)*x**2*sqrt(1 + b*x**2/a)) - 140*a**77*b**(85/2)*x**3/(24*a**(153/2)*b**(91/2)*sqrt(1 + b*x**2/a) + 24*a**(151/2)*b**(93/2)*x**2*sqrt(1 + b*x**2/a)) - 21*a**76*b**(87/2)*x**5/(24*a**(153/2)*b**(91/2)*sqrt(1 + b*x**2/a) + 24*a**(151/2)*b**(93/2)*x**2*sqrt(1 + b*x**2/a)) + 6*a**75*b**(89/2)*x**7/(24*a**(153/2)*b**(91/2)*sqrt(1 + b*x**2/a) + 24*a**(151/2)*b**(93/2)*x**2*sqrt(1 + b*x**2/a)))","B",0
586,1,337,0,1.987260," ","integrate(x**5*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\begin{cases} \frac{8 A a^{2} b}{3 a b^{4} \sqrt{a + b x^{2}} + 3 b^{5} x^{2} \sqrt{a + b x^{2}}} + \frac{12 A a b^{2} x^{2}}{3 a b^{4} \sqrt{a + b x^{2}} + 3 b^{5} x^{2} \sqrt{a + b x^{2}}} + \frac{3 A b^{3} x^{4}}{3 a b^{4} \sqrt{a + b x^{2}} + 3 b^{5} x^{2} \sqrt{a + b x^{2}}} - \frac{16 B a^{3}}{3 a b^{4} \sqrt{a + b x^{2}} + 3 b^{5} x^{2} \sqrt{a + b x^{2}}} - \frac{24 B a^{2} b x^{2}}{3 a b^{4} \sqrt{a + b x^{2}} + 3 b^{5} x^{2} \sqrt{a + b x^{2}}} - \frac{6 B a b^{2} x^{4}}{3 a b^{4} \sqrt{a + b x^{2}} + 3 b^{5} x^{2} \sqrt{a + b x^{2}}} + \frac{B b^{3} x^{6}}{3 a b^{4} \sqrt{a + b x^{2}} + 3 b^{5} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{6}}{6} + \frac{B x^{8}}{8}}{a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a**2*b/(3*a*b**4*sqrt(a + b*x**2) + 3*b**5*x**2*sqrt(a + b*x**2)) + 12*A*a*b**2*x**2/(3*a*b**4*sqrt(a + b*x**2) + 3*b**5*x**2*sqrt(a + b*x**2)) + 3*A*b**3*x**4/(3*a*b**4*sqrt(a + b*x**2) + 3*b**5*x**2*sqrt(a + b*x**2)) - 16*B*a**3/(3*a*b**4*sqrt(a + b*x**2) + 3*b**5*x**2*sqrt(a + b*x**2)) - 24*B*a**2*b*x**2/(3*a*b**4*sqrt(a + b*x**2) + 3*b**5*x**2*sqrt(a + b*x**2)) - 6*B*a*b**2*x**4/(3*a*b**4*sqrt(a + b*x**2) + 3*b**5*x**2*sqrt(a + b*x**2)) + B*b**3*x**6/(3*a*b**4*sqrt(a + b*x**2) + 3*b**5*x**2*sqrt(a + b*x**2)), Ne(b, 0)), ((A*x**6/6 + B*x**8/8)/a**(5/2), True))","A",0
587,1,675,0,20.567262," ","integrate(x**4*(B*x**2+A)/(b*x**2+a)**(5/2),x)","A \left(\frac{3 a^{\frac{39}{2}} b^{11} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{\frac{37}{2}} b^{12} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{19} b^{\frac{23}{2}} x}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{4 a^{18} b^{\frac{25}{2}} x^{3}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + B \left(- \frac{15 a^{\frac{81}{2}} b^{22} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{15 a^{\frac{79}{2}} b^{23} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{40} b^{\frac{45}{2}} x}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{20 a^{39} b^{\frac{47}{2}} x^{3}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{38} b^{\frac{49}{2}} x^{5}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(3*a**(39/2)*b**11*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) + 3*a**(37/2)*b**12*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) - 3*a**19*b**(23/2)*x/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) - 4*a**18*b**(25/2)*x**3/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a))) + B*(-15*a**(81/2)*b**22*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) - 15*a**(79/2)*b**23*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 15*a**40*b**(45/2)*x/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 20*a**39*b**(47/2)*x**3/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)) + 3*a**38*b**(49/2)*x**5/(6*a**(79/2)*b**(51/2)*sqrt(1 + b*x**2/a) + 6*a**(77/2)*b**(53/2)*x**2*sqrt(1 + b*x**2/a)))","B",0
588,1,240,0,1.972084," ","integrate(x**3*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\begin{cases} - \frac{2 A a b}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} - \frac{3 A b^{2} x^{2}}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} + \frac{8 B a^{2}}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} + \frac{12 B a b x^{2}}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} + \frac{3 B b^{2} x^{4}}{3 a b^{3} \sqrt{a + b x^{2}} + 3 b^{4} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{4}}{4} + \frac{B x^{6}}{6}}{a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a*b/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)) - 3*A*b**2*x**2/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)) + 8*B*a**2/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)) + 12*B*a*b*x**2/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)) + 3*B*b**2*x**4/(3*a*b**3*sqrt(a + b*x**2) + 3*b**4*x**2*sqrt(a + b*x**2)), Ne(b, 0)), ((A*x**4/4 + B*x**6/6)/a**(5/2), True))","A",0
589,1,352,0,14.516531," ","integrate(x**2*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\frac{A x^{3}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{3}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + B \left(\frac{3 a^{\frac{39}{2}} b^{11} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{\frac{37}{2}} b^{12} x^{2} \sqrt{1 + \frac{b x^{2}}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{19} b^{\frac{23}{2}} x}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{4 a^{18} b^{\frac{25}{2}} x^{3}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*x**3/(3*a**(5/2)*sqrt(1 + b*x**2/a) + 3*a**(3/2)*b*x**2*sqrt(1 + b*x**2/a)) + B*(3*a**(39/2)*b**11*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) + 3*a**(37/2)*b**12*x**2*sqrt(1 + b*x**2/a)*asinh(sqrt(b)*x/sqrt(a))/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) - 3*a**19*b**(23/2)*x/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)) - 4*a**18*b**(25/2)*x**3/(3*a**(39/2)*b**(27/2)*sqrt(1 + b*x**2/a) + 3*a**(37/2)*b**(29/2)*x**2*sqrt(1 + b*x**2/a)))","B",0
590,1,143,0,1.475135," ","integrate(x*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\begin{cases} - \frac{A b}{3 a b^{2} \sqrt{a + b x^{2}} + 3 b^{3} x^{2} \sqrt{a + b x^{2}}} - \frac{2 B a}{3 a b^{2} \sqrt{a + b x^{2}} + 3 b^{3} x^{2} \sqrt{a + b x^{2}}} - \frac{3 B b x^{2}}{3 a b^{2} \sqrt{a + b x^{2}} + 3 b^{3} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{\frac{A x^{2}}{2} + \frac{B x^{4}}{4}}{a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*b/(3*a*b**2*sqrt(a + b*x**2) + 3*b**3*x**2*sqrt(a + b*x**2)) - 2*B*a/(3*a*b**2*sqrt(a + b*x**2) + 3*b**3*x**2*sqrt(a + b*x**2)) - 3*B*b*x**2/(3*a*b**2*sqrt(a + b*x**2) + 3*b**3*x**2*sqrt(a + b*x**2)), Ne(b, 0)), ((A*x**2/2 + B*x**4/4)/a**(5/2), True))","A",0
591,1,144,0,11.432616," ","integrate((B*x**2+A)/(b*x**2+a)**(5/2),x)","A \left(\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + \frac{B x^{3}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{3}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*(3*a*x/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a)) + 2*b*x**3/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a))) + B*x**3/(3*a**(5/2)*sqrt(1 + b*x**2/a) + 3*a**(3/2)*b*x**2*sqrt(1 + b*x**2/a))","B",0
592,1,66,0,42.167688," ","integrate((B*x**2+A)/x/(b*x**2+a)**(5/2),x)","\frac{A}{a^{2} \sqrt{a + b x^{2}}} + \frac{A \operatorname{atan}{\left(\frac{\sqrt{a + b x^{2}}}{\sqrt{- a}} \right)}}{a^{2} \sqrt{- a}} - \frac{- A b + B a}{3 a b \left(a + b x^{2}\right)^{\frac{3}{2}}}"," ",0,"A/(a**2*sqrt(a + b*x**2)) + A*atan(sqrt(a + b*x**2)/sqrt(-a))/(a**2*sqrt(-a)) - (-A*b + B*a)/(3*a*b*(a + b*x**2)**(3/2))","A",0
593,1,265,0,21.735947," ","integrate((B*x**2+A)/x**2/(b*x**2+a)**(5/2),x)","A \left(- \frac{3 a^{2} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}} - \frac{12 a b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}} - \frac{8 b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}}\right) + B \left(\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(-3*a**2*b**(9/2)*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4) - 12*a*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4) - 8*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4)) + B*(3*a*x/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a)) + 2*b*x**3/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a)))","B",0
594,1,1608,0,68.639241," ","integrate((B*x**2+A)/x**3/(b*x**2+a)**(5/2),x)","A \left(- \frac{6 a^{17} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{46 a^{16} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{15 a^{16} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{30 a^{16} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{70 a^{15} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{45 a^{15} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{90 a^{15} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{30 a^{14} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{45 a^{14} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{90 a^{14} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{15 a^{13} b^{4} x^{8} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{30 a^{13} b^{4} x^{8} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}}\right) + B \left(\frac{8 a^{7} \sqrt{1 + \frac{b x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{3 a^{7} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{6 a^{7} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{14 a^{6} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{9 a^{6} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{18 a^{6} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{6 a^{5} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{9 a^{5} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{18 a^{5} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} + \frac{3 a^{4} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}} - \frac{6 a^{4} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{6 a^{\frac{19}{2}} + 18 a^{\frac{17}{2}} b x^{2} + 18 a^{\frac{15}{2}} b^{2} x^{4} + 6 a^{\frac{13}{2}} b^{3} x^{6}}\right)"," ",0,"A*(-6*a**17*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 46*a**16*b*x**2*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 15*a**16*b*x**2*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 30*a**16*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 70*a**15*b**2*x**4*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 45*a**15*b**2*x**4*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 90*a**15*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 30*a**14*b**3*x**6*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 45*a**14*b**3*x**6*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 90*a**14*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 15*a**13*b**4*x**8*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 30*a**13*b**4*x**8*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8)) + B*(8*a**7*sqrt(1 + b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 3*a**7*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 6*a**7*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 14*a**6*b*x**2*sqrt(1 + b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 9*a**6*b*x**2*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 18*a**6*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 6*a**5*b**2*x**4*sqrt(1 + b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 9*a**5*b**2*x**4*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 18*a**5*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) + 3*a**4*b**3*x**6*log(b*x**2/a)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6) - 6*a**4*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(6*a**(19/2) + 18*a**(17/2)*b*x**2 + 18*a**(15/2)*b**2*x**4 + 6*a**(13/2)*b**3*x**6))","B",0
595,1,524,0,30.024722," ","integrate((B*x**2+A)/x**4/(b*x**2+a)**(5/2),x)","A \left(- \frac{a^{4} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{5 a^{3} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{30 a^{2} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{40 a b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{16 b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}}\right) + B \left(- \frac{3 a^{2} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}} - \frac{12 a b^{\frac{11}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}} - \frac{8 b^{\frac{13}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{4}}\right)"," ",0,"A*(-a**4*b**(19/2)*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 5*a**3*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 30*a**2*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 40*a*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 16*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8)) + B*(-3*a**2*b**(9/2)*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4) - 12*a*b**(11/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4) - 8*b**(13/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**4))","B",0
596,1,1323,0,139.238799," ","integrate((B*x**2+A)/x**5/(b*x**2+a)**(5/2),x)","A \left(- \frac{6 a^{\frac{89}{2}} b^{75}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{5} \sqrt{\frac{a}{b x^{2}} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{21 a^{\frac{87}{2}} b^{76} x^{2}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{5} \sqrt{\frac{a}{b x^{2}} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{140 a^{\frac{85}{2}} b^{77} x^{4}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{5} \sqrt{\frac{a}{b x^{2}} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{105 a^{\frac{83}{2}} b^{78} x^{6}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{5} \sqrt{\frac{a}{b x^{2}} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{105 a^{42} b^{\frac{155}{2}} x^{5} \sqrt{\frac{a}{b x^{2}} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{5} \sqrt{\frac{a}{b x^{2}} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}} - \frac{105 a^{41} b^{\frac{157}{2}} x^{7} \sqrt{\frac{a}{b x^{2}} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{5} \sqrt{\frac{a}{b x^{2}} + 1} + 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{7} \sqrt{\frac{a}{b x^{2}} + 1}}\right) + B \left(- \frac{6 a^{17} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{46 a^{16} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{15 a^{16} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{30 a^{16} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{70 a^{15} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{45 a^{15} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{90 a^{15} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{30 a^{14} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{45 a^{14} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{90 a^{14} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} - \frac{15 a^{13} b^{4} x^{8} \log{\left(\frac{b x^{2}}{a} \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}} + \frac{30 a^{13} b^{4} x^{8} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{12 a^{\frac{39}{2}} x^{2} + 36 a^{\frac{37}{2}} b x^{4} + 36 a^{\frac{35}{2}} b^{2} x^{6} + 12 a^{\frac{33}{2}} b^{3} x^{8}}\right)"," ",0,"A*(-6*a**(89/2)*b**75/(24*a**(93/2)*b**(151/2)*x**5*sqrt(a/(b*x**2) + 1) + 24*a**(91/2)*b**(153/2)*x**7*sqrt(a/(b*x**2) + 1)) + 21*a**(87/2)*b**76*x**2/(24*a**(93/2)*b**(151/2)*x**5*sqrt(a/(b*x**2) + 1) + 24*a**(91/2)*b**(153/2)*x**7*sqrt(a/(b*x**2) + 1)) + 140*a**(85/2)*b**77*x**4/(24*a**(93/2)*b**(151/2)*x**5*sqrt(a/(b*x**2) + 1) + 24*a**(91/2)*b**(153/2)*x**7*sqrt(a/(b*x**2) + 1)) + 105*a**(83/2)*b**78*x**6/(24*a**(93/2)*b**(151/2)*x**5*sqrt(a/(b*x**2) + 1) + 24*a**(91/2)*b**(153/2)*x**7*sqrt(a/(b*x**2) + 1)) - 105*a**42*b**(155/2)*x**5*sqrt(a/(b*x**2) + 1)*asinh(sqrt(a)/(sqrt(b)*x))/(24*a**(93/2)*b**(151/2)*x**5*sqrt(a/(b*x**2) + 1) + 24*a**(91/2)*b**(153/2)*x**7*sqrt(a/(b*x**2) + 1)) - 105*a**41*b**(157/2)*x**7*sqrt(a/(b*x**2) + 1)*asinh(sqrt(a)/(sqrt(b)*x))/(24*a**(93/2)*b**(151/2)*x**5*sqrt(a/(b*x**2) + 1) + 24*a**(91/2)*b**(153/2)*x**7*sqrt(a/(b*x**2) + 1))) + B*(-6*a**17*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 46*a**16*b*x**2*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 15*a**16*b*x**2*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 30*a**16*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 70*a**15*b**2*x**4*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 45*a**15*b**2*x**4*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 90*a**15*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 30*a**14*b**3*x**6*sqrt(1 + b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 45*a**14*b**3*x**6*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 90*a**14*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) - 15*a**13*b**4*x**8*log(b*x**2/a)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8) + 30*a**13*b**4*x**8*log(sqrt(1 + b*x**2/a) + 1)/(12*a**(39/2)*x**2 + 36*a**(37/2)*b*x**4 + 36*a**(35/2)*b**2*x**6 + 12*a**(33/2)*b**3*x**8))","B",0
597,1,944,0,60.742413," ","integrate((B*x**2+A)/x**6/(b*x**2+a)**(5/2),x)","A \left(- \frac{3 a^{6} b^{\frac{33}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{6} + 90 a^{7} b^{18} x^{8} + 60 a^{6} b^{19} x^{10} + 15 a^{5} b^{20} x^{12}} + \frac{2 a^{5} b^{\frac{35}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{6} + 90 a^{7} b^{18} x^{8} + 60 a^{6} b^{19} x^{10} + 15 a^{5} b^{20} x^{12}} - \frac{35 a^{4} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{6} + 90 a^{7} b^{18} x^{8} + 60 a^{6} b^{19} x^{10} + 15 a^{5} b^{20} x^{12}} - \frac{280 a^{3} b^{\frac{39}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{6} + 90 a^{7} b^{18} x^{8} + 60 a^{6} b^{19} x^{10} + 15 a^{5} b^{20} x^{12}} - \frac{560 a^{2} b^{\frac{41}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{6} + 90 a^{7} b^{18} x^{8} + 60 a^{6} b^{19} x^{10} + 15 a^{5} b^{20} x^{12}} - \frac{448 a b^{\frac{43}{2}} x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{6} + 90 a^{7} b^{18} x^{8} + 60 a^{6} b^{19} x^{10} + 15 a^{5} b^{20} x^{12}} - \frac{128 b^{\frac{45}{2}} x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{15 a^{9} b^{16} x^{4} + 60 a^{8} b^{17} x^{6} + 90 a^{7} b^{18} x^{8} + 60 a^{6} b^{19} x^{10} + 15 a^{5} b^{20} x^{12}}\right) + B \left(- \frac{a^{4} b^{\frac{19}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{5 a^{3} b^{\frac{21}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{30 a^{2} b^{\frac{23}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{40 a b^{\frac{25}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}} + \frac{16 b^{\frac{27}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{7} b^{9} x^{2} + 9 a^{6} b^{10} x^{4} + 9 a^{5} b^{11} x^{6} + 3 a^{4} b^{12} x^{8}}\right)"," ",0,"A*(-3*a**6*b**(33/2)*sqrt(a/(b*x**2) + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**6 + 90*a**7*b**18*x**8 + 60*a**6*b**19*x**10 + 15*a**5*b**20*x**12) + 2*a**5*b**(35/2)*x**2*sqrt(a/(b*x**2) + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**6 + 90*a**7*b**18*x**8 + 60*a**6*b**19*x**10 + 15*a**5*b**20*x**12) - 35*a**4*b**(37/2)*x**4*sqrt(a/(b*x**2) + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**6 + 90*a**7*b**18*x**8 + 60*a**6*b**19*x**10 + 15*a**5*b**20*x**12) - 280*a**3*b**(39/2)*x**6*sqrt(a/(b*x**2) + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**6 + 90*a**7*b**18*x**8 + 60*a**6*b**19*x**10 + 15*a**5*b**20*x**12) - 560*a**2*b**(41/2)*x**8*sqrt(a/(b*x**2) + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**6 + 90*a**7*b**18*x**8 + 60*a**6*b**19*x**10 + 15*a**5*b**20*x**12) - 448*a*b**(43/2)*x**10*sqrt(a/(b*x**2) + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**6 + 90*a**7*b**18*x**8 + 60*a**6*b**19*x**10 + 15*a**5*b**20*x**12) - 128*b**(45/2)*x**12*sqrt(a/(b*x**2) + 1)/(15*a**9*b**16*x**4 + 60*a**8*b**17*x**6 + 90*a**7*b**18*x**8 + 60*a**6*b**19*x**10 + 15*a**5*b**20*x**12)) + B*(-a**4*b**(19/2)*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 5*a**3*b**(21/2)*x**2*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 30*a**2*b**(23/2)*x**4*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 40*a*b**(25/2)*x**6*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8) + 16*b**(27/2)*x**8*sqrt(a/(b*x**2) + 1)/(3*a**7*b**9*x**2 + 9*a**6*b**10*x**4 + 9*a**5*b**11*x**6 + 3*a**4*b**12*x**8))","B",0
598,1,389,0,5.957665," ","integrate(x**5*(b*x**2+a)**2*(d*x**2+c)**(1/2),x)","\begin{cases} \frac{8 a^{2} c^{3} \sqrt{c + d x^{2}}}{105 d^{3}} - \frac{4 a^{2} c^{2} x^{2} \sqrt{c + d x^{2}}}{105 d^{2}} + \frac{a^{2} c x^{4} \sqrt{c + d x^{2}}}{35 d} + \frac{a^{2} x^{6} \sqrt{c + d x^{2}}}{7} - \frac{32 a b c^{4} \sqrt{c + d x^{2}}}{315 d^{4}} + \frac{16 a b c^{3} x^{2} \sqrt{c + d x^{2}}}{315 d^{3}} - \frac{4 a b c^{2} x^{4} \sqrt{c + d x^{2}}}{105 d^{2}} + \frac{2 a b c x^{6} \sqrt{c + d x^{2}}}{63 d} + \frac{2 a b x^{8} \sqrt{c + d x^{2}}}{9} + \frac{128 b^{2} c^{5} \sqrt{c + d x^{2}}}{3465 d^{5}} - \frac{64 b^{2} c^{4} x^{2} \sqrt{c + d x^{2}}}{3465 d^{4}} + \frac{16 b^{2} c^{3} x^{4} \sqrt{c + d x^{2}}}{1155 d^{3}} - \frac{8 b^{2} c^{2} x^{6} \sqrt{c + d x^{2}}}{693 d^{2}} + \frac{b^{2} c x^{8} \sqrt{c + d x^{2}}}{99 d} + \frac{b^{2} x^{10} \sqrt{c + d x^{2}}}{11} & \text{for}\: d \neq 0 \\\sqrt{c} \left(\frac{a^{2} x^{6}}{6} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{10}}{10}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2*c**3*sqrt(c + d*x**2)/(105*d**3) - 4*a**2*c**2*x**2*sqrt(c + d*x**2)/(105*d**2) + a**2*c*x**4*sqrt(c + d*x**2)/(35*d) + a**2*x**6*sqrt(c + d*x**2)/7 - 32*a*b*c**4*sqrt(c + d*x**2)/(315*d**4) + 16*a*b*c**3*x**2*sqrt(c + d*x**2)/(315*d**3) - 4*a*b*c**2*x**4*sqrt(c + d*x**2)/(105*d**2) + 2*a*b*c*x**6*sqrt(c + d*x**2)/(63*d) + 2*a*b*x**8*sqrt(c + d*x**2)/9 + 128*b**2*c**5*sqrt(c + d*x**2)/(3465*d**5) - 64*b**2*c**4*x**2*sqrt(c + d*x**2)/(3465*d**4) + 16*b**2*c**3*x**4*sqrt(c + d*x**2)/(1155*d**3) - 8*b**2*c**2*x**6*sqrt(c + d*x**2)/(693*d**2) + b**2*c*x**8*sqrt(c + d*x**2)/(99*d) + b**2*x**10*sqrt(c + d*x**2)/11, Ne(d, 0)), (sqrt(c)*(a**2*x**6/6 + a*b*x**8/4 + b**2*x**10/10), True))","A",0
599,1,308,0,3.240814," ","integrate(x**3*(b*x**2+a)**2*(d*x**2+c)**(1/2),x)","\begin{cases} - \frac{2 a^{2} c^{2} \sqrt{c + d x^{2}}}{15 d^{2}} + \frac{a^{2} c x^{2} \sqrt{c + d x^{2}}}{15 d} + \frac{a^{2} x^{4} \sqrt{c + d x^{2}}}{5} + \frac{16 a b c^{3} \sqrt{c + d x^{2}}}{105 d^{3}} - \frac{8 a b c^{2} x^{2} \sqrt{c + d x^{2}}}{105 d^{2}} + \frac{2 a b c x^{4} \sqrt{c + d x^{2}}}{35 d} + \frac{2 a b x^{6} \sqrt{c + d x^{2}}}{7} - \frac{16 b^{2} c^{4} \sqrt{c + d x^{2}}}{315 d^{4}} + \frac{8 b^{2} c^{3} x^{2} \sqrt{c + d x^{2}}}{315 d^{3}} - \frac{2 b^{2} c^{2} x^{4} \sqrt{c + d x^{2}}}{105 d^{2}} + \frac{b^{2} c x^{6} \sqrt{c + d x^{2}}}{63 d} + \frac{b^{2} x^{8} \sqrt{c + d x^{2}}}{9} & \text{for}\: d \neq 0 \\\sqrt{c} \left(\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*c**2*sqrt(c + d*x**2)/(15*d**2) + a**2*c*x**2*sqrt(c + d*x**2)/(15*d) + a**2*x**4*sqrt(c + d*x**2)/5 + 16*a*b*c**3*sqrt(c + d*x**2)/(105*d**3) - 8*a*b*c**2*x**2*sqrt(c + d*x**2)/(105*d**2) + 2*a*b*c*x**4*sqrt(c + d*x**2)/(35*d) + 2*a*b*x**6*sqrt(c + d*x**2)/7 - 16*b**2*c**4*sqrt(c + d*x**2)/(315*d**4) + 8*b**2*c**3*x**2*sqrt(c + d*x**2)/(315*d**3) - 2*b**2*c**2*x**4*sqrt(c + d*x**2)/(105*d**2) + b**2*c*x**6*sqrt(c + d*x**2)/(63*d) + b**2*x**8*sqrt(c + d*x**2)/9, Ne(d, 0)), (sqrt(c)*(a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8), True))","A",0
600,1,226,0,1.602574," ","integrate(x*(b*x**2+a)**2*(d*x**2+c)**(1/2),x)","\begin{cases} \frac{a^{2} c \sqrt{c + d x^{2}}}{3 d} + \frac{a^{2} x^{2} \sqrt{c + d x^{2}}}{3} - \frac{4 a b c^{2} \sqrt{c + d x^{2}}}{15 d^{2}} + \frac{2 a b c x^{2} \sqrt{c + d x^{2}}}{15 d} + \frac{2 a b x^{4} \sqrt{c + d x^{2}}}{5} + \frac{8 b^{2} c^{3} \sqrt{c + d x^{2}}}{105 d^{3}} - \frac{4 b^{2} c^{2} x^{2} \sqrt{c + d x^{2}}}{105 d^{2}} + \frac{b^{2} c x^{4} \sqrt{c + d x^{2}}}{35 d} + \frac{b^{2} x^{6} \sqrt{c + d x^{2}}}{7} & \text{for}\: d \neq 0 \\\sqrt{c} \left(\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*sqrt(c + d*x**2)/(3*d) + a**2*x**2*sqrt(c + d*x**2)/3 - 4*a*b*c**2*sqrt(c + d*x**2)/(15*d**2) + 2*a*b*c*x**2*sqrt(c + d*x**2)/(15*d) + 2*a*b*x**4*sqrt(c + d*x**2)/5 + 8*b**2*c**3*sqrt(c + d*x**2)/(105*d**3) - 4*b**2*c**2*x**2*sqrt(c + d*x**2)/(105*d**2) + b**2*c*x**4*sqrt(c + d*x**2)/(35*d) + b**2*x**6*sqrt(c + d*x**2)/7, Ne(d, 0)), (sqrt(c)*(a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6), True))","A",0
601,1,90,0,72.464699," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x,x)","\frac{a^{2} c \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + a^{2} \sqrt{c + d x^{2}} + \frac{b^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}{5 d^{2}} + \frac{\left(c + d x^{2}\right)^{\frac{3}{2}} \left(4 a b d - 2 b^{2} c\right)}{6 d^{2}}"," ",0,"a**2*c*atan(sqrt(c + d*x**2)/sqrt(-c))/sqrt(-c) + a**2*sqrt(c + d*x**2) + b**2*(c + d*x**2)**(5/2)/(5*d**2) + (c + d*x**2)**(3/2)*(4*a*b*d - 2*b**2*c)/(6*d**2)","A",0
602,1,148,0,73.978577," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**3,x)","- \frac{a^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{2 x} - \frac{a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)}}{2 \sqrt{c}} - 2 a b \sqrt{c} \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)} + \frac{2 a b c}{\sqrt{d} x \sqrt{\frac{c}{d x^{2}} + 1}} + \frac{2 a b \sqrt{d} x}{\sqrt{\frac{c}{d x^{2}} + 1}} + b^{2} \left(\begin{cases} \frac{\sqrt{c} x^{2}}{2} & \text{for}\: d = 0 \\\frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right)"," ",0,"-a**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(2*x) - a**2*d*asinh(sqrt(c)/(sqrt(d)*x))/(2*sqrt(c)) - 2*a*b*sqrt(c)*asinh(sqrt(c)/(sqrt(d)*x)) + 2*a*b*c/(sqrt(d)*x*sqrt(c/(d*x**2) + 1)) + 2*a*b*sqrt(d)*x/sqrt(c/(d*x**2) + 1) + b**2*Piecewise((sqrt(c)*x**2/2, Eq(d, 0)), ((c + d*x**2)**(3/2)/(3*d), True))","A",0
603,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,1,411,0,21.912173," ","integrate(x**2*(b*x**2+a)**2*(d*x**2+c)**(1/2),x)","\frac{a^{2} c^{\frac{3}{2}} x}{8 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a^{2} \sqrt{c} x^{3}}{8 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a^{2} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 d^{\frac{3}{2}}} + \frac{a^{2} d x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b c^{\frac{5}{2}} x}{8 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b c^{\frac{3}{2}} x^{3}}{24 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a b \sqrt{c} x^{5}}{12 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{a b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 d^{\frac{5}{2}}} + \frac{a b d x^{7}}{3 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{\frac{7}{2}} x}{128 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{\frac{5}{2}} x^{3}}{384 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{3}{2}} x^{5}}{192 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{7 b^{2} \sqrt{c} x^{7}}{48 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{5 b^{2} c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{7}{2}}} + \frac{b^{2} d x^{9}}{8 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"a**2*c**(3/2)*x/(8*d*sqrt(1 + d*x**2/c)) + 3*a**2*sqrt(c)*x**3/(8*sqrt(1 + d*x**2/c)) - a**2*c**2*asinh(sqrt(d)*x/sqrt(c))/(8*d**(3/2)) + a**2*d*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c)) - a*b*c**(5/2)*x/(8*d**2*sqrt(1 + d*x**2/c)) - a*b*c**(3/2)*x**3/(24*d*sqrt(1 + d*x**2/c)) + 5*a*b*sqrt(c)*x**5/(12*sqrt(1 + d*x**2/c)) + a*b*c**3*asinh(sqrt(d)*x/sqrt(c))/(8*d**(5/2)) + a*b*d*x**7/(3*sqrt(c)*sqrt(1 + d*x**2/c)) + 5*b**2*c**(7/2)*x/(128*d**3*sqrt(1 + d*x**2/c)) + 5*b**2*c**(5/2)*x**3/(384*d**2*sqrt(1 + d*x**2/c)) - b**2*c**(3/2)*x**5/(192*d*sqrt(1 + d*x**2/c)) + 7*b**2*sqrt(c)*x**7/(48*sqrt(1 + d*x**2/c)) - 5*b**2*c**4*asinh(sqrt(d)*x/sqrt(c))/(128*d**(7/2)) + b**2*d*x**9/(8*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
606,1,291,0,13.722477," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2),x)","\frac{a^{2} \sqrt{c} x \sqrt{1 + \frac{d x^{2}}{c}}}{2} + \frac{a^{2} c \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{2 \sqrt{d}} + \frac{a b c^{\frac{3}{2}} x}{4 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b \sqrt{c} x^{3}}{4 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{4 d^{\frac{3}{2}}} + \frac{a b d x^{5}}{2 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{5}{2}} x}{16 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{3}{2}} x^{3}}{48 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} \sqrt{c} x^{5}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{b^{2} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{16 d^{\frac{5}{2}}} + \frac{b^{2} d x^{7}}{6 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"a**2*sqrt(c)*x*sqrt(1 + d*x**2/c)/2 + a**2*c*asinh(sqrt(d)*x/sqrt(c))/(2*sqrt(d)) + a*b*c**(3/2)*x/(4*d*sqrt(1 + d*x**2/c)) + 3*a*b*sqrt(c)*x**3/(4*sqrt(1 + d*x**2/c)) - a*b*c**2*asinh(sqrt(d)*x/sqrt(c))/(4*d**(3/2)) + a*b*d*x**5/(2*sqrt(c)*sqrt(1 + d*x**2/c)) - b**2*c**(5/2)*x/(16*d**2*sqrt(1 + d*x**2/c)) - b**2*c**(3/2)*x**3/(48*d*sqrt(1 + d*x**2/c)) + 5*b**2*sqrt(c)*x**5/(24*sqrt(1 + d*x**2/c)) + b**2*c**3*asinh(sqrt(d)*x/sqrt(c))/(16*d**(5/2)) + b**2*d*x**7/(6*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
607,1,219,0,9.048685," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**2,x)","- \frac{a^{2} \sqrt{c}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + a^{2} \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} - \frac{a^{2} d x}{\sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + a b \sqrt{c} x \sqrt{1 + \frac{d x^{2}}{c}} + \frac{a b c \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{\sqrt{d}} + \frac{b^{2} c^{\frac{3}{2}} x}{8 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} \sqrt{c} x^{3}}{8 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 d^{\frac{3}{2}}} + \frac{b^{2} d x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-a**2*sqrt(c)/(x*sqrt(1 + d*x**2/c)) + a**2*sqrt(d)*asinh(sqrt(d)*x/sqrt(c)) - a**2*d*x/(sqrt(c)*sqrt(1 + d*x**2/c)) + a*b*sqrt(c)*x*sqrt(1 + d*x**2/c) + a*b*c*asinh(sqrt(d)*x/sqrt(c))/sqrt(d) + b**2*c**(3/2)*x/(8*d*sqrt(1 + d*x**2/c)) + 3*b**2*sqrt(c)*x**3/(8*sqrt(1 + d*x**2/c)) - b**2*c**2*asinh(sqrt(d)*x/sqrt(c))/(8*d**(3/2)) + b**2*d*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c))","A",0
608,1,170,0,5.464563," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**4,x)","- \frac{a^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 x^{2}} - \frac{a^{2} d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3 c} - \frac{2 a b \sqrt{c}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + 2 a b \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} - \frac{2 a b d x}{\sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{b^{2} \sqrt{c} x \sqrt{1 + \frac{d x^{2}}{c}}}{2} + \frac{b^{2} c \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{2 \sqrt{d}}"," ",0,"-a**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*x**2) - a**2*d**(3/2)*sqrt(c/(d*x**2) + 1)/(3*c) - 2*a*b*sqrt(c)/(x*sqrt(1 + d*x**2/c)) + 2*a*b*sqrt(d)*asinh(sqrt(d)*x/sqrt(c)) - 2*a*b*d*x/(sqrt(c)*sqrt(1 + d*x**2/c)) + b**2*sqrt(c)*x*sqrt(1 + d*x**2/c)/2 + b**2*c*asinh(sqrt(d)*x/sqrt(c))/(2*sqrt(d))","A",0
609,1,199,0,5.499803," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**6,x)","- \frac{a^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{5 x^{4}} - \frac{a^{2} d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c x^{2}} + \frac{2 a^{2} d^{\frac{5}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{2}} - \frac{2 a b \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 x^{2}} - \frac{2 a b d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3 c} - \frac{b^{2} \sqrt{c}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + b^{2} \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} - \frac{b^{2} d x}{\sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-a**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(5*x**4) - a**2*d**(3/2)*sqrt(c/(d*x**2) + 1)/(15*c*x**2) + 2*a**2*d**(5/2)*sqrt(c/(d*x**2) + 1)/(15*c**2) - 2*a*b*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*x**2) - 2*a*b*d**(3/2)*sqrt(c/(d*x**2) + 1)/(3*c) - b**2*sqrt(c)/(x*sqrt(1 + d*x**2/c)) + b**2*sqrt(d)*asinh(sqrt(d)*x/sqrt(c)) - b**2*d*x/(sqrt(c)*sqrt(1 + d*x**2/c))","B",0
610,1,510,0,4.513848," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**8,x)","- \frac{15 a^{2} c^{5} d^{\frac{9}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{33 a^{2} c^{4} d^{\frac{11}{2}} x^{2} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{17 a^{2} c^{3} d^{\frac{13}{2}} x^{4} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{3 a^{2} c^{2} d^{\frac{15}{2}} x^{6} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{12 a^{2} c d^{\frac{17}{2}} x^{8} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{8 a^{2} d^{\frac{19}{2}} x^{10} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{2 a b \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{5 x^{4}} - \frac{2 a b d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c x^{2}} + \frac{4 a b d^{\frac{5}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{2}} - \frac{b^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 x^{2}} - \frac{b^{2} d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3 c}"," ",0,"-15*a**2*c**5*d**(9/2)*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 33*a**2*c**4*d**(11/2)*x**2*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 17*a**2*c**3*d**(13/2)*x**4*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 3*a**2*c**2*d**(15/2)*x**6*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 12*a**2*c*d**(17/2)*x**8*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 8*a**2*d**(19/2)*x**10*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 2*a*b*sqrt(d)*sqrt(c/(d*x**2) + 1)/(5*x**4) - 2*a*b*d**(3/2)*sqrt(c/(d*x**2) + 1)/(15*c*x**2) + 4*a*b*d**(5/2)*sqrt(c/(d*x**2) + 1)/(15*c**2) - b**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*x**2) - b**2*d**(3/2)*sqrt(c/(d*x**2) + 1)/(3*c)","B",0
611,1,1061,0,5.358623," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**10,x)","- \frac{35 a^{2} c^{7} d^{\frac{19}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{110 a^{2} c^{6} d^{\frac{21}{2}} x^{2} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{114 a^{2} c^{5} d^{\frac{23}{2}} x^{4} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{40 a^{2} c^{4} d^{\frac{25}{2}} x^{6} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{5 a^{2} c^{3} d^{\frac{27}{2}} x^{8} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{30 a^{2} c^{2} d^{\frac{29}{2}} x^{10} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{40 a^{2} c d^{\frac{31}{2}} x^{12} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{16 a^{2} d^{\frac{33}{2}} x^{14} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{30 a b c^{5} d^{\frac{9}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{66 a b c^{4} d^{\frac{11}{2}} x^{2} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{34 a b c^{3} d^{\frac{13}{2}} x^{4} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{6 a b c^{2} d^{\frac{15}{2}} x^{6} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{24 a b c d^{\frac{17}{2}} x^{8} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{16 a b d^{\frac{19}{2}} x^{10} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{b^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{5 x^{4}} - \frac{b^{2} d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c x^{2}} + \frac{2 b^{2} d^{\frac{5}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{2}}"," ",0,"-35*a**2*c**7*d**(19/2)*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 110*a**2*c**6*d**(21/2)*x**2*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 114*a**2*c**5*d**(23/2)*x**4*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 40*a**2*c**4*d**(25/2)*x**6*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 5*a**2*c**3*d**(27/2)*x**8*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 30*a**2*c**2*d**(29/2)*x**10*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 40*a**2*c*d**(31/2)*x**12*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 16*a**2*d**(33/2)*x**14*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 30*a*b*c**5*d**(9/2)*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 66*a*b*c**4*d**(11/2)*x**2*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 34*a*b*c**3*d**(13/2)*x**4*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 6*a*b*c**2*d**(15/2)*x**6*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 24*a*b*c*d**(17/2)*x**8*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 16*a*b*d**(19/2)*x**10*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - b**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(5*x**4) - b**2*d**(3/2)*sqrt(c/(d*x**2) + 1)/(15*c*x**2) + 2*b**2*d**(5/2)*sqrt(c/(d*x**2) + 1)/(15*c**2)","B",0
612,1,1856,0,8.284372," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**12,x)","- \frac{315 a^{2} c^{9} d^{\frac{33}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{1295 a^{2} c^{8} d^{\frac{35}{2}} x^{2} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{1990 a^{2} c^{7} d^{\frac{37}{2}} x^{4} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{1358 a^{2} c^{6} d^{\frac{39}{2}} x^{6} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{343 a^{2} c^{5} d^{\frac{41}{2}} x^{8} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{35 a^{2} c^{4} d^{\frac{43}{2}} x^{10} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{280 a^{2} c^{3} d^{\frac{45}{2}} x^{12} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{560 a^{2} c^{2} d^{\frac{47}{2}} x^{14} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{448 a^{2} c d^{\frac{49}{2}} x^{16} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{128 a^{2} d^{\frac{51}{2}} x^{18} \sqrt{\frac{c}{d x^{2}} + 1}}{3465 c^{9} d^{16} x^{10} + 13860 c^{8} d^{17} x^{12} + 20790 c^{7} d^{18} x^{14} + 13860 c^{6} d^{19} x^{16} + 3465 c^{5} d^{20} x^{18}} - \frac{70 a b c^{7} d^{\frac{19}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{220 a b c^{6} d^{\frac{21}{2}} x^{2} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{228 a b c^{5} d^{\frac{23}{2}} x^{4} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{80 a b c^{4} d^{\frac{25}{2}} x^{6} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{10 a b c^{3} d^{\frac{27}{2}} x^{8} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{60 a b c^{2} d^{\frac{29}{2}} x^{10} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{80 a b c d^{\frac{31}{2}} x^{12} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} + \frac{32 a b d^{\frac{33}{2}} x^{14} \sqrt{\frac{c}{d x^{2}} + 1}}{315 c^{7} d^{9} x^{8} + 945 c^{6} d^{10} x^{10} + 945 c^{5} d^{11} x^{12} + 315 c^{4} d^{12} x^{14}} - \frac{15 b^{2} c^{5} d^{\frac{9}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{33 b^{2} c^{4} d^{\frac{11}{2}} x^{2} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{17 b^{2} c^{3} d^{\frac{13}{2}} x^{4} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{3 b^{2} c^{2} d^{\frac{15}{2}} x^{6} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{12 b^{2} c d^{\frac{17}{2}} x^{8} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}} - \frac{8 b^{2} d^{\frac{19}{2}} x^{10} \sqrt{\frac{c}{d x^{2}} + 1}}{105 c^{5} d^{4} x^{6} + 210 c^{4} d^{5} x^{8} + 105 c^{3} d^{6} x^{10}}"," ",0,"-315*a**2*c**9*d**(33/2)*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 1295*a**2*c**8*d**(35/2)*x**2*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 1990*a**2*c**7*d**(37/2)*x**4*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 1358*a**2*c**6*d**(39/2)*x**6*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 343*a**2*c**5*d**(41/2)*x**8*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 35*a**2*c**4*d**(43/2)*x**10*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 280*a**2*c**3*d**(45/2)*x**12*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 560*a**2*c**2*d**(47/2)*x**14*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 448*a**2*c*d**(49/2)*x**16*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 128*a**2*d**(51/2)*x**18*sqrt(c/(d*x**2) + 1)/(3465*c**9*d**16*x**10 + 13860*c**8*d**17*x**12 + 20790*c**7*d**18*x**14 + 13860*c**6*d**19*x**16 + 3465*c**5*d**20*x**18) - 70*a*b*c**7*d**(19/2)*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 220*a*b*c**6*d**(21/2)*x**2*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 228*a*b*c**5*d**(23/2)*x**4*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 80*a*b*c**4*d**(25/2)*x**6*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 10*a*b*c**3*d**(27/2)*x**8*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 60*a*b*c**2*d**(29/2)*x**10*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 80*a*b*c*d**(31/2)*x**12*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) + 32*a*b*d**(33/2)*x**14*sqrt(c/(d*x**2) + 1)/(315*c**7*d**9*x**8 + 945*c**6*d**10*x**10 + 945*c**5*d**11*x**12 + 315*c**4*d**12*x**14) - 15*b**2*c**5*d**(9/2)*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 33*b**2*c**4*d**(11/2)*x**2*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 17*b**2*c**3*d**(13/2)*x**4*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 3*b**2*c**2*d**(15/2)*x**6*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 12*b**2*c*d**(17/2)*x**8*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10) - 8*b**2*d**(19/2)*x**10*sqrt(c/(d*x**2) + 1)/(105*c**5*d**4*x**6 + 210*c**4*d**5*x**8 + 105*c**3*d**6*x**10)","B",0
613,1,598,0,83.439147," ","integrate(x**4*(b*x**2+a)**2*(d*x**2+c)**(3/2),x)","- \frac{3 a^{2} c^{\frac{7}{2}} x}{128 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a^{2} c^{\frac{5}{2}} x^{3}}{128 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{13 a^{2} c^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a^{2} \sqrt{c} d x^{7}}{16 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a^{2} c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{5}{2}}} + \frac{a^{2} d^{2} x^{9}}{8 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b c^{\frac{9}{2}} x}{128 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{a b c^{\frac{7}{2}} x^{3}}{128 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b c^{\frac{5}{2}} x^{5}}{320 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{23 a b c^{\frac{3}{2}} x^{7}}{80 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{19 a b \sqrt{c} d x^{9}}{40 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{3 a b c^{5} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{7}{2}}} + \frac{a b d^{2} x^{11}}{5 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{7 b^{2} c^{\frac{11}{2}} x}{1024 d^{4} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{7 b^{2} c^{\frac{9}{2}} x^{3}}{3072 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{7 b^{2} c^{\frac{7}{2}} x^{5}}{7680 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{5}{2}} x^{7}}{1920 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{107 b^{2} c^{\frac{3}{2}} x^{9}}{960 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{23 b^{2} \sqrt{c} d x^{11}}{120 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{7 b^{2} c^{6} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{1024 d^{\frac{9}{2}}} + \frac{b^{2} d^{2} x^{13}}{12 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-3*a**2*c**(7/2)*x/(128*d**2*sqrt(1 + d*x**2/c)) - a**2*c**(5/2)*x**3/(128*d*sqrt(1 + d*x**2/c)) + 13*a**2*c**(3/2)*x**5/(64*sqrt(1 + d*x**2/c)) + 5*a**2*sqrt(c)*d*x**7/(16*sqrt(1 + d*x**2/c)) + 3*a**2*c**4*asinh(sqrt(d)*x/sqrt(c))/(128*d**(5/2)) + a**2*d**2*x**9/(8*sqrt(c)*sqrt(1 + d*x**2/c)) + 3*a*b*c**(9/2)*x/(128*d**3*sqrt(1 + d*x**2/c)) + a*b*c**(7/2)*x**3/(128*d**2*sqrt(1 + d*x**2/c)) - a*b*c**(5/2)*x**5/(320*d*sqrt(1 + d*x**2/c)) + 23*a*b*c**(3/2)*x**7/(80*sqrt(1 + d*x**2/c)) + 19*a*b*sqrt(c)*d*x**9/(40*sqrt(1 + d*x**2/c)) - 3*a*b*c**5*asinh(sqrt(d)*x/sqrt(c))/(128*d**(7/2)) + a*b*d**2*x**11/(5*sqrt(c)*sqrt(1 + d*x**2/c)) - 7*b**2*c**(11/2)*x/(1024*d**4*sqrt(1 + d*x**2/c)) - 7*b**2*c**(9/2)*x**3/(3072*d**3*sqrt(1 + d*x**2/c)) + 7*b**2*c**(7/2)*x**5/(7680*d**2*sqrt(1 + d*x**2/c)) - b**2*c**(5/2)*x**7/(1920*d*sqrt(1 + d*x**2/c)) + 107*b**2*c**(3/2)*x**9/(960*sqrt(1 + d*x**2/c)) + 23*b**2*sqrt(c)*d*x**11/(120*sqrt(1 + d*x**2/c)) + 7*b**2*c**6*asinh(sqrt(d)*x/sqrt(c))/(1024*d**(9/2)) + b**2*d**2*x**13/(12*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
614,1,384,0,8.399191," ","integrate(x**3*(b*x**2+a)**2*(d*x**2+c)**(3/2),x)","\begin{cases} - \frac{2 a^{2} c^{3} \sqrt{c + d x^{2}}}{35 d^{2}} + \frac{a^{2} c^{2} x^{2} \sqrt{c + d x^{2}}}{35 d} + \frac{8 a^{2} c x^{4} \sqrt{c + d x^{2}}}{35} + \frac{a^{2} d x^{6} \sqrt{c + d x^{2}}}{7} + \frac{16 a b c^{4} \sqrt{c + d x^{2}}}{315 d^{3}} - \frac{8 a b c^{3} x^{2} \sqrt{c + d x^{2}}}{315 d^{2}} + \frac{2 a b c^{2} x^{4} \sqrt{c + d x^{2}}}{105 d} + \frac{20 a b c x^{6} \sqrt{c + d x^{2}}}{63} + \frac{2 a b d x^{8} \sqrt{c + d x^{2}}}{9} - \frac{16 b^{2} c^{5} \sqrt{c + d x^{2}}}{1155 d^{4}} + \frac{8 b^{2} c^{4} x^{2} \sqrt{c + d x^{2}}}{1155 d^{3}} - \frac{2 b^{2} c^{3} x^{4} \sqrt{c + d x^{2}}}{385 d^{2}} + \frac{b^{2} c^{2} x^{6} \sqrt{c + d x^{2}}}{231 d} + \frac{4 b^{2} c x^{8} \sqrt{c + d x^{2}}}{33} + \frac{b^{2} d x^{10} \sqrt{c + d x^{2}}}{11} & \text{for}\: d \neq 0 \\c^{\frac{3}{2}} \left(\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*c**3*sqrt(c + d*x**2)/(35*d**2) + a**2*c**2*x**2*sqrt(c + d*x**2)/(35*d) + 8*a**2*c*x**4*sqrt(c + d*x**2)/35 + a**2*d*x**6*sqrt(c + d*x**2)/7 + 16*a*b*c**4*sqrt(c + d*x**2)/(315*d**3) - 8*a*b*c**3*x**2*sqrt(c + d*x**2)/(315*d**2) + 2*a*b*c**2*x**4*sqrt(c + d*x**2)/(105*d) + 20*a*b*c*x**6*sqrt(c + d*x**2)/63 + 2*a*b*d*x**8*sqrt(c + d*x**2)/9 - 16*b**2*c**5*sqrt(c + d*x**2)/(1155*d**4) + 8*b**2*c**4*x**2*sqrt(c + d*x**2)/(1155*d**3) - 2*b**2*c**3*x**4*sqrt(c + d*x**2)/(385*d**2) + b**2*c**2*x**6*sqrt(c + d*x**2)/(231*d) + 4*b**2*c*x**8*sqrt(c + d*x**2)/33 + b**2*d*x**10*sqrt(c + d*x**2)/11, Ne(d, 0)), (c**(3/2)*(a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8), True))","A",0
615,1,505,0,53.693828," ","integrate(x**2*(b*x**2+a)**2*(d*x**2+c)**(3/2),x)","\frac{a^{2} c^{\frac{5}{2}} x}{16 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{17 a^{2} c^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{11 a^{2} \sqrt{c} d x^{5}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a^{2} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{16 d^{\frac{3}{2}}} + \frac{a^{2} d^{2} x^{7}}{6 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{3 a b c^{\frac{7}{2}} x}{64 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b c^{\frac{5}{2}} x^{3}}{64 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{13 a b c^{\frac{3}{2}} x^{5}}{32 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a b \sqrt{c} d x^{7}}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{64 d^{\frac{5}{2}}} + \frac{a b d^{2} x^{9}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} c^{\frac{9}{2}} x}{256 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{b^{2} c^{\frac{7}{2}} x^{3}}{256 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{5}{2}} x^{5}}{640 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{23 b^{2} c^{\frac{3}{2}} x^{7}}{160 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{19 b^{2} \sqrt{c} d x^{9}}{80 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{3 b^{2} c^{5} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{256 d^{\frac{7}{2}}} + \frac{b^{2} d^{2} x^{11}}{10 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"a**2*c**(5/2)*x/(16*d*sqrt(1 + d*x**2/c)) + 17*a**2*c**(3/2)*x**3/(48*sqrt(1 + d*x**2/c)) + 11*a**2*sqrt(c)*d*x**5/(24*sqrt(1 + d*x**2/c)) - a**2*c**3*asinh(sqrt(d)*x/sqrt(c))/(16*d**(3/2)) + a**2*d**2*x**7/(6*sqrt(c)*sqrt(1 + d*x**2/c)) - 3*a*b*c**(7/2)*x/(64*d**2*sqrt(1 + d*x**2/c)) - a*b*c**(5/2)*x**3/(64*d*sqrt(1 + d*x**2/c)) + 13*a*b*c**(3/2)*x**5/(32*sqrt(1 + d*x**2/c)) + 5*a*b*sqrt(c)*d*x**7/(8*sqrt(1 + d*x**2/c)) + 3*a*b*c**4*asinh(sqrt(d)*x/sqrt(c))/(64*d**(5/2)) + a*b*d**2*x**9/(4*sqrt(c)*sqrt(1 + d*x**2/c)) + 3*b**2*c**(9/2)*x/(256*d**3*sqrt(1 + d*x**2/c)) + b**2*c**(7/2)*x**3/(256*d**2*sqrt(1 + d*x**2/c)) - b**2*c**(5/2)*x**5/(640*d*sqrt(1 + d*x**2/c)) + 23*b**2*c**(3/2)*x**7/(160*sqrt(1 + d*x**2/c)) + 19*b**2*sqrt(c)*d*x**9/(80*sqrt(1 + d*x**2/c)) - 3*b**2*c**5*asinh(sqrt(d)*x/sqrt(c))/(256*d**(7/2)) + b**2*d**2*x**11/(10*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
616,1,303,0,3.678226," ","integrate(x*(b*x**2+a)**2*(d*x**2+c)**(3/2),x)","\begin{cases} \frac{a^{2} c^{2} \sqrt{c + d x^{2}}}{5 d} + \frac{2 a^{2} c x^{2} \sqrt{c + d x^{2}}}{5} + \frac{a^{2} d x^{4} \sqrt{c + d x^{2}}}{5} - \frac{4 a b c^{3} \sqrt{c + d x^{2}}}{35 d^{2}} + \frac{2 a b c^{2} x^{2} \sqrt{c + d x^{2}}}{35 d} + \frac{16 a b c x^{4} \sqrt{c + d x^{2}}}{35} + \frac{2 a b d x^{6} \sqrt{c + d x^{2}}}{7} + \frac{8 b^{2} c^{4} \sqrt{c + d x^{2}}}{315 d^{3}} - \frac{4 b^{2} c^{3} x^{2} \sqrt{c + d x^{2}}}{315 d^{2}} + \frac{b^{2} c^{2} x^{4} \sqrt{c + d x^{2}}}{105 d} + \frac{10 b^{2} c x^{6} \sqrt{c + d x^{2}}}{63} + \frac{b^{2} d x^{8} \sqrt{c + d x^{2}}}{9} & \text{for}\: d \neq 0 \\c^{\frac{3}{2}} \left(\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*sqrt(c + d*x**2)/(5*d) + 2*a**2*c*x**2*sqrt(c + d*x**2)/5 + a**2*d*x**4*sqrt(c + d*x**2)/5 - 4*a*b*c**3*sqrt(c + d*x**2)/(35*d**2) + 2*a*b*c**2*x**2*sqrt(c + d*x**2)/(35*d) + 16*a*b*c*x**4*sqrt(c + d*x**2)/35 + 2*a*b*d*x**6*sqrt(c + d*x**2)/7 + 8*b**2*c**4*sqrt(c + d*x**2)/(315*d**3) - 4*b**2*c**3*x**2*sqrt(c + d*x**2)/(315*d**2) + b**2*c**2*x**4*sqrt(c + d*x**2)/(105*d) + 10*b**2*c*x**6*sqrt(c + d*x**2)/63 + b**2*d*x**8*sqrt(c + d*x**2)/9, Ne(d, 0)), (c**(3/2)*(a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6), True))","A",0
617,1,440,0,30.552387," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2),x)","\frac{a^{2} c^{\frac{3}{2}} x \sqrt{1 + \frac{d x^{2}}{c}}}{2} + \frac{a^{2} c^{\frac{3}{2}} x}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a^{2} \sqrt{c} d x^{3}}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a^{2} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 \sqrt{d}} + \frac{a^{2} d^{2} x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{a b c^{\frac{5}{2}} x}{8 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{17 a b c^{\frac{3}{2}} x^{3}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{11 a b \sqrt{c} d x^{5}}{12 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 d^{\frac{3}{2}}} + \frac{a b d^{2} x^{7}}{3 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{3 b^{2} c^{\frac{7}{2}} x}{128 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{5}{2}} x^{3}}{128 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{13 b^{2} c^{\frac{3}{2}} x^{5}}{64 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} \sqrt{c} d x^{7}}{16 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{5}{2}}} + \frac{b^{2} d^{2} x^{9}}{8 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"a**2*c**(3/2)*x*sqrt(1 + d*x**2/c)/2 + a**2*c**(3/2)*x/(8*sqrt(1 + d*x**2/c)) + 3*a**2*sqrt(c)*d*x**3/(8*sqrt(1 + d*x**2/c)) + 3*a**2*c**2*asinh(sqrt(d)*x/sqrt(c))/(8*sqrt(d)) + a**2*d**2*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c)) + a*b*c**(5/2)*x/(8*d*sqrt(1 + d*x**2/c)) + 17*a*b*c**(3/2)*x**3/(24*sqrt(1 + d*x**2/c)) + 11*a*b*sqrt(c)*d*x**5/(12*sqrt(1 + d*x**2/c)) - a*b*c**3*asinh(sqrt(d)*x/sqrt(c))/(8*d**(3/2)) + a*b*d**2*x**7/(3*sqrt(c)*sqrt(1 + d*x**2/c)) - 3*b**2*c**(7/2)*x/(128*d**2*sqrt(1 + d*x**2/c)) - b**2*c**(5/2)*x**3/(128*d*sqrt(1 + d*x**2/c)) + 13*b**2*c**(3/2)*x**5/(64*sqrt(1 + d*x**2/c)) + 5*b**2*sqrt(c)*d*x**7/(16*sqrt(1 + d*x**2/c)) + 3*b**2*c**4*asinh(sqrt(d)*x/sqrt(c))/(128*d**(5/2)) + b**2*d**2*x**9/(8*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
618,1,109,0,103.741062," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/x,x)","\frac{a^{2} c^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + a^{2} c \sqrt{c + d x^{2}} + \frac{a^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}{3} + \frac{b^{2} \left(c + d x^{2}\right)^{\frac{7}{2}}}{7 d^{2}} + \frac{\left(c + d x^{2}\right)^{\frac{5}{2}} \left(4 a b d - 2 b^{2} c\right)}{10 d^{2}}"," ",0,"a**2*c**2*atan(sqrt(c + d*x**2)/sqrt(-c))/sqrt(-c) + a**2*c*sqrt(c + d*x**2) + a**2*(c + d*x**2)**(3/2)/3 + b**2*(c + d*x**2)**(7/2)/(7*d**2) + (c + d*x**2)**(5/2)*(4*a*b*d - 2*b**2*c)/(10*d**2)","A",0
619,1,367,0,22.413358," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/x**2,x)","- \frac{a^{2} c^{\frac{3}{2}}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{a^{2} \sqrt{c} d x \sqrt{1 + \frac{d x^{2}}{c}}}{2} - \frac{a^{2} \sqrt{c} d x}{\sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a^{2} c \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{2} + a b c^{\frac{3}{2}} x \sqrt{1 + \frac{d x^{2}}{c}} + \frac{a b c^{\frac{3}{2}} x}{4 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b \sqrt{c} d x^{3}}{4 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{4 \sqrt{d}} + \frac{a b d^{2} x^{5}}{2 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{b^{2} c^{\frac{5}{2}} x}{16 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{17 b^{2} c^{\frac{3}{2}} x^{3}}{48 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{11 b^{2} \sqrt{c} d x^{5}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{16 d^{\frac{3}{2}}} + \frac{b^{2} d^{2} x^{7}}{6 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-a**2*c**(3/2)/(x*sqrt(1 + d*x**2/c)) + a**2*sqrt(c)*d*x*sqrt(1 + d*x**2/c)/2 - a**2*sqrt(c)*d*x/sqrt(1 + d*x**2/c) + 3*a**2*c*sqrt(d)*asinh(sqrt(d)*x/sqrt(c))/2 + a*b*c**(3/2)*x*sqrt(1 + d*x**2/c) + a*b*c**(3/2)*x/(4*sqrt(1 + d*x**2/c)) + 3*a*b*sqrt(c)*d*x**3/(4*sqrt(1 + d*x**2/c)) + 3*a*b*c**2*asinh(sqrt(d)*x/sqrt(c))/(4*sqrt(d)) + a*b*d**2*x**5/(2*sqrt(c)*sqrt(1 + d*x**2/c)) + b**2*c**(5/2)*x/(16*d*sqrt(1 + d*x**2/c)) + 17*b**2*c**(3/2)*x**3/(48*sqrt(1 + d*x**2/c)) + 11*b**2*sqrt(c)*d*x**5/(24*sqrt(1 + d*x**2/c)) - b**2*c**3*asinh(sqrt(d)*x/sqrt(c))/(16*d**(3/2)) + b**2*d**2*x**7/(6*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
620,1,303,0,88.856943," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/x**3,x)","- \frac{3 a^{2} \sqrt{c} d \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)}}{2} - \frac{a^{2} c \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{2 x} + \frac{a^{2} c \sqrt{d}}{x \sqrt{\frac{c}{d x^{2}} + 1}} + \frac{a^{2} d^{\frac{3}{2}} x}{\sqrt{\frac{c}{d x^{2}} + 1}} - 2 a b c^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)} + \frac{2 a b c^{2}}{\sqrt{d} x \sqrt{\frac{c}{d x^{2}} + 1}} + \frac{2 a b c \sqrt{d} x}{\sqrt{\frac{c}{d x^{2}} + 1}} + 2 a b d \left(\begin{cases} \frac{\sqrt{c} x^{2}}{2} & \text{for}\: d = 0 \\\frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + b^{2} c \left(\begin{cases} \frac{\sqrt{c} x^{2}}{2} & \text{for}\: d = 0 \\\frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + b^{2} d \left(\begin{cases} - \frac{2 c^{2} \sqrt{c + d x^{2}}}{15 d^{2}} + \frac{c x^{2} \sqrt{c + d x^{2}}}{15 d} + \frac{x^{4} \sqrt{c + d x^{2}}}{5} & \text{for}\: d \neq 0 \\\frac{\sqrt{c} x^{4}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"-3*a**2*sqrt(c)*d*asinh(sqrt(c)/(sqrt(d)*x))/2 - a**2*c*sqrt(d)*sqrt(c/(d*x**2) + 1)/(2*x) + a**2*c*sqrt(d)/(x*sqrt(c/(d*x**2) + 1)) + a**2*d**(3/2)*x/sqrt(c/(d*x**2) + 1) - 2*a*b*c**(3/2)*asinh(sqrt(c)/(sqrt(d)*x)) + 2*a*b*c**2/(sqrt(d)*x*sqrt(c/(d*x**2) + 1)) + 2*a*b*c*sqrt(d)*x/sqrt(c/(d*x**2) + 1) + 2*a*b*d*Piecewise((sqrt(c)*x**2/2, Eq(d, 0)), ((c + d*x**2)**(3/2)/(3*d), True)) + b**2*c*Piecewise((sqrt(c)*x**2/2, Eq(d, 0)), ((c + d*x**2)**(3/2)/(3*d), True)) + b**2*d*Piecewise((-2*c**2*sqrt(c + d*x**2)/(15*d**2) + c*x**2*sqrt(c + d*x**2)/(15*d) + x**4*sqrt(c + d*x**2)/5, Ne(d, 0)), (sqrt(c)*x**4/4, True))","A",0
621,1,352,0,14.126518," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/x**4,x)","- \frac{a^{2} \sqrt{c} d}{x \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a^{2} c \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 x^{2}} - \frac{a^{2} d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3} + a^{2} d^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} - \frac{a^{2} d^{2} x}{\sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{2 a b c^{\frac{3}{2}}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + a b \sqrt{c} d x \sqrt{1 + \frac{d x^{2}}{c}} - \frac{2 a b \sqrt{c} d x}{\sqrt{1 + \frac{d x^{2}}{c}}} + 3 a b c \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} + \frac{b^{2} c^{\frac{3}{2}} x \sqrt{1 + \frac{d x^{2}}{c}}}{2} + \frac{b^{2} c^{\frac{3}{2}} x}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} \sqrt{c} d x^{3}}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 \sqrt{d}} + \frac{b^{2} d^{2} x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-a**2*sqrt(c)*d/(x*sqrt(1 + d*x**2/c)) - a**2*c*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*x**2) - a**2*d**(3/2)*sqrt(c/(d*x**2) + 1)/3 + a**2*d**(3/2)*asinh(sqrt(d)*x/sqrt(c)) - a**2*d**2*x/(sqrt(c)*sqrt(1 + d*x**2/c)) - 2*a*b*c**(3/2)/(x*sqrt(1 + d*x**2/c)) + a*b*sqrt(c)*d*x*sqrt(1 + d*x**2/c) - 2*a*b*sqrt(c)*d*x/sqrt(1 + d*x**2/c) + 3*a*b*c*sqrt(d)*asinh(sqrt(d)*x/sqrt(c)) + b**2*c**(3/2)*x*sqrt(1 + d*x**2/c)/2 + b**2*c**(3/2)*x/(8*sqrt(1 + d*x**2/c)) + 3*b**2*sqrt(c)*d*x**3/(8*sqrt(1 + d*x**2/c)) + 3*b**2*c**2*asinh(sqrt(d)*x/sqrt(c))/(8*sqrt(d)) + b**2*d**2*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
622,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,1,304,0,8.786021," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/x**6,x)","- \frac{a^{2} c \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{5 x^{4}} - \frac{2 a^{2} d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{5 x^{2}} - \frac{a^{2} d^{\frac{5}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{5 c} - \frac{2 a b \sqrt{c} d}{x \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{2 a b c \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 x^{2}} - \frac{2 a b d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3} + 2 a b d^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} - \frac{2 a b d^{2} x}{\sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{3}{2}}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{b^{2} \sqrt{c} d x \sqrt{1 + \frac{d x^{2}}{c}}}{2} - \frac{b^{2} \sqrt{c} d x}{\sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} c \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{2}"," ",0,"-a**2*c*sqrt(d)*sqrt(c/(d*x**2) + 1)/(5*x**4) - 2*a**2*d**(3/2)*sqrt(c/(d*x**2) + 1)/(5*x**2) - a**2*d**(5/2)*sqrt(c/(d*x**2) + 1)/(5*c) - 2*a*b*sqrt(c)*d/(x*sqrt(1 + d*x**2/c)) - 2*a*b*c*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*x**2) - 2*a*b*d**(3/2)*sqrt(c/(d*x**2) + 1)/3 + 2*a*b*d**(3/2)*asinh(sqrt(d)*x/sqrt(c)) - 2*a*b*d**2*x/(sqrt(c)*sqrt(1 + d*x**2/c)) - b**2*c**(3/2)/(x*sqrt(1 + d*x**2/c)) + b**2*sqrt(c)*d*x*sqrt(1 + d*x**2/c)/2 - b**2*sqrt(c)*d*x/sqrt(1 + d*x**2/c) + 3*b**2*c*sqrt(d)*asinh(sqrt(d)*x/sqrt(c))/2","B",0
624,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,1,468,0,19.939945," ","integrate(x**3*(b*x**2+a)**2*(d*x**2+c)**(5/2),x)","\begin{cases} - \frac{2 a^{2} c^{4} \sqrt{c + d x^{2}}}{63 d^{2}} + \frac{a^{2} c^{3} x^{2} \sqrt{c + d x^{2}}}{63 d} + \frac{5 a^{2} c^{2} x^{4} \sqrt{c + d x^{2}}}{21} + \frac{19 a^{2} c d x^{6} \sqrt{c + d x^{2}}}{63} + \frac{a^{2} d^{2} x^{8} \sqrt{c + d x^{2}}}{9} + \frac{16 a b c^{5} \sqrt{c + d x^{2}}}{693 d^{3}} - \frac{8 a b c^{4} x^{2} \sqrt{c + d x^{2}}}{693 d^{2}} + \frac{2 a b c^{3} x^{4} \sqrt{c + d x^{2}}}{231 d} + \frac{226 a b c^{2} x^{6} \sqrt{c + d x^{2}}}{693} + \frac{46 a b c d x^{8} \sqrt{c + d x^{2}}}{99} + \frac{2 a b d^{2} x^{10} \sqrt{c + d x^{2}}}{11} - \frac{16 b^{2} c^{6} \sqrt{c + d x^{2}}}{3003 d^{4}} + \frac{8 b^{2} c^{5} x^{2} \sqrt{c + d x^{2}}}{3003 d^{3}} - \frac{2 b^{2} c^{4} x^{4} \sqrt{c + d x^{2}}}{1001 d^{2}} + \frac{5 b^{2} c^{3} x^{6} \sqrt{c + d x^{2}}}{3003 d} + \frac{53 b^{2} c^{2} x^{8} \sqrt{c + d x^{2}}}{429} + \frac{27 b^{2} c d x^{10} \sqrt{c + d x^{2}}}{143} + \frac{b^{2} d^{2} x^{12} \sqrt{c + d x^{2}}}{13} & \text{for}\: d \neq 0 \\c^{\frac{5}{2}} \left(\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*c**4*sqrt(c + d*x**2)/(63*d**2) + a**2*c**3*x**2*sqrt(c + d*x**2)/(63*d) + 5*a**2*c**2*x**4*sqrt(c + d*x**2)/21 + 19*a**2*c*d*x**6*sqrt(c + d*x**2)/63 + a**2*d**2*x**8*sqrt(c + d*x**2)/9 + 16*a*b*c**5*sqrt(c + d*x**2)/(693*d**3) - 8*a*b*c**4*x**2*sqrt(c + d*x**2)/(693*d**2) + 2*a*b*c**3*x**4*sqrt(c + d*x**2)/(231*d) + 226*a*b*c**2*x**6*sqrt(c + d*x**2)/693 + 46*a*b*c*d*x**8*sqrt(c + d*x**2)/99 + 2*a*b*d**2*x**10*sqrt(c + d*x**2)/11 - 16*b**2*c**6*sqrt(c + d*x**2)/(3003*d**4) + 8*b**2*c**5*x**2*sqrt(c + d*x**2)/(3003*d**3) - 2*b**2*c**4*x**4*sqrt(c + d*x**2)/(1001*d**2) + 5*b**2*c**3*x**6*sqrt(c + d*x**2)/(3003*d) + 53*b**2*c**2*x**8*sqrt(c + d*x**2)/429 + 27*b**2*c*d*x**10*sqrt(c + d*x**2)/143 + b**2*d**2*x**12*sqrt(c + d*x**2)/13, Ne(d, 0)), (c**(5/2)*(a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8), True))","A",0
626,1,602,0,96.020060," ","integrate(x**2*(b*x**2+a)**2*(d*x**2+c)**(5/2),x)","\frac{5 a^{2} c^{\frac{7}{2}} x}{128 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{133 a^{2} c^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{127 a^{2} c^{\frac{3}{2}} d x^{5}}{192 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{23 a^{2} \sqrt{c} d^{2} x^{7}}{48 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{5 a^{2} c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{3}{2}}} + \frac{a^{2} d^{3} x^{9}}{8 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{3 a b c^{\frac{9}{2}} x}{128 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b c^{\frac{7}{2}} x^{3}}{128 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{129 a b c^{\frac{5}{2}} x^{5}}{320 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{73 a b c^{\frac{3}{2}} d x^{7}}{80 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{29 a b \sqrt{c} d^{2} x^{9}}{40 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b c^{5} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{5}{2}}} + \frac{a b d^{3} x^{11}}{5 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{\frac{11}{2}} x}{1024 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{\frac{9}{2}} x^{3}}{3072 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{7}{2}} x^{5}}{1536 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{55 b^{2} c^{\frac{5}{2}} x^{7}}{384 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{67 b^{2} c^{\frac{3}{2}} d x^{9}}{192 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{7 b^{2} \sqrt{c} d^{2} x^{11}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{5 b^{2} c^{6} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{1024 d^{\frac{7}{2}}} + \frac{b^{2} d^{3} x^{13}}{12 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"5*a**2*c**(7/2)*x/(128*d*sqrt(1 + d*x**2/c)) + 133*a**2*c**(5/2)*x**3/(384*sqrt(1 + d*x**2/c)) + 127*a**2*c**(3/2)*d*x**5/(192*sqrt(1 + d*x**2/c)) + 23*a**2*sqrt(c)*d**2*x**7/(48*sqrt(1 + d*x**2/c)) - 5*a**2*c**4*asinh(sqrt(d)*x/sqrt(c))/(128*d**(3/2)) + a**2*d**3*x**9/(8*sqrt(c)*sqrt(1 + d*x**2/c)) - 3*a*b*c**(9/2)*x/(128*d**2*sqrt(1 + d*x**2/c)) - a*b*c**(7/2)*x**3/(128*d*sqrt(1 + d*x**2/c)) + 129*a*b*c**(5/2)*x**5/(320*sqrt(1 + d*x**2/c)) + 73*a*b*c**(3/2)*d*x**7/(80*sqrt(1 + d*x**2/c)) + 29*a*b*sqrt(c)*d**2*x**9/(40*sqrt(1 + d*x**2/c)) + 3*a*b*c**5*asinh(sqrt(d)*x/sqrt(c))/(128*d**(5/2)) + a*b*d**3*x**11/(5*sqrt(c)*sqrt(1 + d*x**2/c)) + 5*b**2*c**(11/2)*x/(1024*d**3*sqrt(1 + d*x**2/c)) + 5*b**2*c**(9/2)*x**3/(3072*d**2*sqrt(1 + d*x**2/c)) - b**2*c**(7/2)*x**5/(1536*d*sqrt(1 + d*x**2/c)) + 55*b**2*c**(5/2)*x**7/(384*sqrt(1 + d*x**2/c)) + 67*b**2*c**(3/2)*d*x**9/(192*sqrt(1 + d*x**2/c)) + 7*b**2*sqrt(c)*d**2*x**11/(24*sqrt(1 + d*x**2/c)) - 5*b**2*c**6*asinh(sqrt(d)*x/sqrt(c))/(1024*d**(7/2)) + b**2*d**3*x**13/(12*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
627,1,384,0,14.545347," ","integrate(x*(b*x**2+a)**2*(d*x**2+c)**(5/2),x)","\begin{cases} \frac{a^{2} c^{3} \sqrt{c + d x^{2}}}{7 d} + \frac{3 a^{2} c^{2} x^{2} \sqrt{c + d x^{2}}}{7} + \frac{3 a^{2} c d x^{4} \sqrt{c + d x^{2}}}{7} + \frac{a^{2} d^{2} x^{6} \sqrt{c + d x^{2}}}{7} - \frac{4 a b c^{4} \sqrt{c + d x^{2}}}{63 d^{2}} + \frac{2 a b c^{3} x^{2} \sqrt{c + d x^{2}}}{63 d} + \frac{10 a b c^{2} x^{4} \sqrt{c + d x^{2}}}{21} + \frac{38 a b c d x^{6} \sqrt{c + d x^{2}}}{63} + \frac{2 a b d^{2} x^{8} \sqrt{c + d x^{2}}}{9} + \frac{8 b^{2} c^{5} \sqrt{c + d x^{2}}}{693 d^{3}} - \frac{4 b^{2} c^{4} x^{2} \sqrt{c + d x^{2}}}{693 d^{2}} + \frac{b^{2} c^{3} x^{4} \sqrt{c + d x^{2}}}{231 d} + \frac{113 b^{2} c^{2} x^{6} \sqrt{c + d x^{2}}}{693} + \frac{23 b^{2} c d x^{8} \sqrt{c + d x^{2}}}{99} + \frac{b^{2} d^{2} x^{10} \sqrt{c + d x^{2}}}{11} & \text{for}\: d \neq 0 \\c^{\frac{5}{2}} \left(\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**3*sqrt(c + d*x**2)/(7*d) + 3*a**2*c**2*x**2*sqrt(c + d*x**2)/7 + 3*a**2*c*d*x**4*sqrt(c + d*x**2)/7 + a**2*d**2*x**6*sqrt(c + d*x**2)/7 - 4*a*b*c**4*sqrt(c + d*x**2)/(63*d**2) + 2*a*b*c**3*x**2*sqrt(c + d*x**2)/(63*d) + 10*a*b*c**2*x**4*sqrt(c + d*x**2)/21 + 38*a*b*c*d*x**6*sqrt(c + d*x**2)/63 + 2*a*b*d**2*x**8*sqrt(c + d*x**2)/9 + 8*b**2*c**5*sqrt(c + d*x**2)/(693*d**3) - 4*b**2*c**4*x**2*sqrt(c + d*x**2)/(693*d**2) + b**2*c**3*x**4*sqrt(c + d*x**2)/(231*d) + 113*b**2*c**2*x**6*sqrt(c + d*x**2)/693 + 23*b**2*c*d*x**8*sqrt(c + d*x**2)/99 + b**2*d**2*x**10*sqrt(c + d*x**2)/11, Ne(d, 0)), (c**(5/2)*(a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6), True))","A",0
628,1,537,0,96.678361," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2),x)","\frac{a^{2} c^{\frac{5}{2}} x \sqrt{1 + \frac{d x^{2}}{c}}}{2} + \frac{3 a^{2} c^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{35 a^{2} c^{\frac{3}{2}} d x^{3}}{48 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{17 a^{2} \sqrt{c} d^{2} x^{5}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a^{2} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{16 \sqrt{d}} + \frac{a^{2} d^{3} x^{7}}{6 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a b c^{\frac{7}{2}} x}{64 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{133 a b c^{\frac{5}{2}} x^{3}}{192 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{127 a b c^{\frac{3}{2}} d x^{5}}{96 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{23 a b \sqrt{c} d^{2} x^{7}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{5 a b c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{64 d^{\frac{3}{2}}} + \frac{a b d^{3} x^{9}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{3 b^{2} c^{\frac{9}{2}} x}{256 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} c^{\frac{7}{2}} x^{3}}{256 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{129 b^{2} c^{\frac{5}{2}} x^{5}}{640 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{73 b^{2} c^{\frac{3}{2}} d x^{7}}{160 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{29 b^{2} \sqrt{c} d^{2} x^{9}}{80 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} c^{5} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{256 d^{\frac{5}{2}}} + \frac{b^{2} d^{3} x^{11}}{10 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"a**2*c**(5/2)*x*sqrt(1 + d*x**2/c)/2 + 3*a**2*c**(5/2)*x/(16*sqrt(1 + d*x**2/c)) + 35*a**2*c**(3/2)*d*x**3/(48*sqrt(1 + d*x**2/c)) + 17*a**2*sqrt(c)*d**2*x**5/(24*sqrt(1 + d*x**2/c)) + 5*a**2*c**3*asinh(sqrt(d)*x/sqrt(c))/(16*sqrt(d)) + a**2*d**3*x**7/(6*sqrt(c)*sqrt(1 + d*x**2/c)) + 5*a*b*c**(7/2)*x/(64*d*sqrt(1 + d*x**2/c)) + 133*a*b*c**(5/2)*x**3/(192*sqrt(1 + d*x**2/c)) + 127*a*b*c**(3/2)*d*x**5/(96*sqrt(1 + d*x**2/c)) + 23*a*b*sqrt(c)*d**2*x**7/(24*sqrt(1 + d*x**2/c)) - 5*a*b*c**4*asinh(sqrt(d)*x/sqrt(c))/(64*d**(3/2)) + a*b*d**3*x**9/(4*sqrt(c)*sqrt(1 + d*x**2/c)) - 3*b**2*c**(9/2)*x/(256*d**2*sqrt(1 + d*x**2/c)) - b**2*c**(7/2)*x**3/(256*d*sqrt(1 + d*x**2/c)) + 129*b**2*c**(5/2)*x**5/(640*sqrt(1 + d*x**2/c)) + 73*b**2*c**(3/2)*d*x**7/(160*sqrt(1 + d*x**2/c)) + 29*b**2*sqrt(c)*d**2*x**9/(80*sqrt(1 + d*x**2/c)) + 3*b**2*c**5*asinh(sqrt(d)*x/sqrt(c))/(256*d**(5/2)) + b**2*d**3*x**11/(10*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
629,1,128,0,128.707430," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2)/x,x)","\frac{a^{2} c^{3} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{\sqrt{- c}} + a^{2} c^{2} \sqrt{c + d x^{2}} + \frac{a^{2} c \left(c + d x^{2}\right)^{\frac{3}{2}}}{3} + \frac{a^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}{5} + \frac{b^{2} \left(c + d x^{2}\right)^{\frac{9}{2}}}{9 d^{2}} + \frac{\left(c + d x^{2}\right)^{\frac{7}{2}} \left(4 a b d - 2 b^{2} c\right)}{14 d^{2}}"," ",0,"a**2*c**3*atan(sqrt(c + d*x**2)/sqrt(-c))/sqrt(-c) + a**2*c**2*sqrt(c + d*x**2) + a**2*c*(c + d*x**2)**(3/2)/3 + a**2*(c + d*x**2)**(5/2)/5 + b**2*(c + d*x**2)**(9/2)/(9*d**2) + (c + d*x**2)**(7/2)*(4*a*b*d - 2*b**2*c)/(14*d**2)","A",0
630,1,496,0,44.324202," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2)/x**2,x)","- \frac{a^{2} c^{\frac{5}{2}}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + a^{2} c^{\frac{3}{2}} d x \sqrt{1 + \frac{d x^{2}}{c}} - \frac{7 a^{2} c^{\frac{3}{2}} d x}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a^{2} \sqrt{c} d^{2} x^{3}}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{15 a^{2} c^{2} \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8} + \frac{a^{2} d^{3} x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + a b c^{\frac{5}{2}} x \sqrt{1 + \frac{d x^{2}}{c}} + \frac{3 a b c^{\frac{5}{2}} x}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{35 a b c^{\frac{3}{2}} d x^{3}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{17 a b \sqrt{c} d^{2} x^{5}}{12 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 \sqrt{d}} + \frac{a b d^{3} x^{7}}{3 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{\frac{7}{2}} x}{128 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{133 b^{2} c^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{127 b^{2} c^{\frac{3}{2}} d x^{5}}{192 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{23 b^{2} \sqrt{c} d^{2} x^{7}}{48 \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{5 b^{2} c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{3}{2}}} + \frac{b^{2} d^{3} x^{9}}{8 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-a**2*c**(5/2)/(x*sqrt(1 + d*x**2/c)) + a**2*c**(3/2)*d*x*sqrt(1 + d*x**2/c) - 7*a**2*c**(3/2)*d*x/(8*sqrt(1 + d*x**2/c)) + 3*a**2*sqrt(c)*d**2*x**3/(8*sqrt(1 + d*x**2/c)) + 15*a**2*c**2*sqrt(d)*asinh(sqrt(d)*x/sqrt(c))/8 + a**2*d**3*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c)) + a*b*c**(5/2)*x*sqrt(1 + d*x**2/c) + 3*a*b*c**(5/2)*x/(8*sqrt(1 + d*x**2/c)) + 35*a*b*c**(3/2)*d*x**3/(24*sqrt(1 + d*x**2/c)) + 17*a*b*sqrt(c)*d**2*x**5/(12*sqrt(1 + d*x**2/c)) + 5*a*b*c**3*asinh(sqrt(d)*x/sqrt(c))/(8*sqrt(d)) + a*b*d**3*x**7/(3*sqrt(c)*sqrt(1 + d*x**2/c)) + 5*b**2*c**(7/2)*x/(128*d*sqrt(1 + d*x**2/c)) + 133*b**2*c**(5/2)*x**3/(384*sqrt(1 + d*x**2/c)) + 127*b**2*c**(3/2)*d*x**5/(192*sqrt(1 + d*x**2/c)) + 23*b**2*sqrt(c)*d**2*x**7/(48*sqrt(1 + d*x**2/c)) - 5*b**2*c**4*asinh(sqrt(d)*x/sqrt(c))/(128*d**(3/2)) + b**2*d**3*x**9/(8*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
631,1,518,0,91.814894," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2)/x**3,x)","- \frac{5 a^{2} c^{\frac{3}{2}} d \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)}}{2} - \frac{a^{2} c^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{2 x} + \frac{2 a^{2} c^{2} \sqrt{d}}{x \sqrt{\frac{c}{d x^{2}} + 1}} + \frac{2 a^{2} c d^{\frac{3}{2}} x}{\sqrt{\frac{c}{d x^{2}} + 1}} + a^{2} d^{2} \left(\begin{cases} \frac{\sqrt{c} x^{2}}{2} & \text{for}\: d = 0 \\\frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) - 2 a b c^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)} + \frac{2 a b c^{3}}{\sqrt{d} x \sqrt{\frac{c}{d x^{2}} + 1}} + \frac{2 a b c^{2} \sqrt{d} x}{\sqrt{\frac{c}{d x^{2}} + 1}} + 4 a b c d \left(\begin{cases} \frac{\sqrt{c} x^{2}}{2} & \text{for}\: d = 0 \\\frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + 2 a b d^{2} \left(\begin{cases} - \frac{2 c^{2} \sqrt{c + d x^{2}}}{15 d^{2}} + \frac{c x^{2} \sqrt{c + d x^{2}}}{15 d} + \frac{x^{4} \sqrt{c + d x^{2}}}{5} & \text{for}\: d \neq 0 \\\frac{\sqrt{c} x^{4}}{4} & \text{otherwise} \end{cases}\right) + b^{2} c^{2} \left(\begin{cases} \frac{\sqrt{c} x^{2}}{2} & \text{for}\: d = 0 \\\frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + 2 b^{2} c d \left(\begin{cases} - \frac{2 c^{2} \sqrt{c + d x^{2}}}{15 d^{2}} + \frac{c x^{2} \sqrt{c + d x^{2}}}{15 d} + \frac{x^{4} \sqrt{c + d x^{2}}}{5} & \text{for}\: d \neq 0 \\\frac{\sqrt{c} x^{4}}{4} & \text{otherwise} \end{cases}\right) + b^{2} d^{2} \left(\begin{cases} \frac{8 c^{3} \sqrt{c + d x^{2}}}{105 d^{3}} - \frac{4 c^{2} x^{2} \sqrt{c + d x^{2}}}{105 d^{2}} + \frac{c x^{4} \sqrt{c + d x^{2}}}{35 d} + \frac{x^{6} \sqrt{c + d x^{2}}}{7} & \text{for}\: d \neq 0 \\\frac{\sqrt{c} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"-5*a**2*c**(3/2)*d*asinh(sqrt(c)/(sqrt(d)*x))/2 - a**2*c**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(2*x) + 2*a**2*c**2*sqrt(d)/(x*sqrt(c/(d*x**2) + 1)) + 2*a**2*c*d**(3/2)*x/sqrt(c/(d*x**2) + 1) + a**2*d**2*Piecewise((sqrt(c)*x**2/2, Eq(d, 0)), ((c + d*x**2)**(3/2)/(3*d), True)) - 2*a*b*c**(5/2)*asinh(sqrt(c)/(sqrt(d)*x)) + 2*a*b*c**3/(sqrt(d)*x*sqrt(c/(d*x**2) + 1)) + 2*a*b*c**2*sqrt(d)*x/sqrt(c/(d*x**2) + 1) + 4*a*b*c*d*Piecewise((sqrt(c)*x**2/2, Eq(d, 0)), ((c + d*x**2)**(3/2)/(3*d), True)) + 2*a*b*d**2*Piecewise((-2*c**2*sqrt(c + d*x**2)/(15*d**2) + c*x**2*sqrt(c + d*x**2)/(15*d) + x**4*sqrt(c + d*x**2)/5, Ne(d, 0)), (sqrt(c)*x**4/4, True)) + b**2*c**2*Piecewise((sqrt(c)*x**2/2, Eq(d, 0)), ((c + d*x**2)**(3/2)/(3*d), True)) + 2*b**2*c*d*Piecewise((-2*c**2*sqrt(c + d*x**2)/(15*d**2) + c*x**2*sqrt(c + d*x**2)/(15*d) + x**4*sqrt(c + d*x**2)/5, Ne(d, 0)), (sqrt(c)*x**4/4, True)) + b**2*d**2*Piecewise((8*c**3*sqrt(c + d*x**2)/(105*d**3) - 4*c**2*x**2*sqrt(c + d*x**2)/(105*d**2) + c*x**4*sqrt(c + d*x**2)/(35*d) + x**6*sqrt(c + d*x**2)/7, Ne(d, 0)), (sqrt(c)*x**6/6, True))","A",0
632,1,490,0,24.420352," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2)/x**4,x)","- \frac{2 a^{2} c^{\frac{3}{2}} d}{x \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{a^{2} \sqrt{c} d^{2} x \sqrt{1 + \frac{d x^{2}}{c}}}{2} - \frac{2 a^{2} \sqrt{c} d^{2} x}{\sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a^{2} c^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 x^{2}} - \frac{a^{2} c d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3} + \frac{5 a^{2} c d^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{2} - \frac{2 a b c^{\frac{5}{2}}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + 2 a b c^{\frac{3}{2}} d x \sqrt{1 + \frac{d x^{2}}{c}} - \frac{7 a b c^{\frac{3}{2}} d x}{4 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b \sqrt{c} d^{2} x^{3}}{4 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{15 a b c^{2} \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{4} + \frac{a b d^{3} x^{5}}{2 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{b^{2} c^{\frac{5}{2}} x \sqrt{1 + \frac{d x^{2}}{c}}}{2} + \frac{3 b^{2} c^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{35 b^{2} c^{\frac{3}{2}} d x^{3}}{48 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{17 b^{2} \sqrt{c} d^{2} x^{5}}{24 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{16 \sqrt{d}} + \frac{b^{2} d^{3} x^{7}}{6 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-2*a**2*c**(3/2)*d/(x*sqrt(1 + d*x**2/c)) + a**2*sqrt(c)*d**2*x*sqrt(1 + d*x**2/c)/2 - 2*a**2*sqrt(c)*d**2*x/sqrt(1 + d*x**2/c) - a**2*c**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*x**2) - a**2*c*d**(3/2)*sqrt(c/(d*x**2) + 1)/3 + 5*a**2*c*d**(3/2)*asinh(sqrt(d)*x/sqrt(c))/2 - 2*a*b*c**(5/2)/(x*sqrt(1 + d*x**2/c)) + 2*a*b*c**(3/2)*d*x*sqrt(1 + d*x**2/c) - 7*a*b*c**(3/2)*d*x/(4*sqrt(1 + d*x**2/c)) + 3*a*b*sqrt(c)*d**2*x**3/(4*sqrt(1 + d*x**2/c)) + 15*a*b*c**2*sqrt(d)*asinh(sqrt(d)*x/sqrt(c))/4 + a*b*d**3*x**5/(2*sqrt(c)*sqrt(1 + d*x**2/c)) + b**2*c**(5/2)*x*sqrt(1 + d*x**2/c)/2 + 3*b**2*c**(5/2)*x/(16*sqrt(1 + d*x**2/c)) + 35*b**2*c**(3/2)*d*x**3/(48*sqrt(1 + d*x**2/c)) + 17*b**2*sqrt(c)*d**2*x**5/(24*sqrt(1 + d*x**2/c)) + 5*b**2*c**3*asinh(sqrt(d)*x/sqrt(c))/(16*sqrt(d)) + b**2*d**3*x**7/(6*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
633,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2)/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,1,474,0,20.407740," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2)/x**6,x)","- \frac{a^{2} \sqrt{c} d^{2}}{x \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a^{2} c^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{5 x^{4}} - \frac{11 a^{2} c d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 x^{2}} - \frac{8 a^{2} d^{\frac{5}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15} + a^{2} d^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} - \frac{a^{2} d^{3} x}{\sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{4 a b c^{\frac{3}{2}} d}{x \sqrt{1 + \frac{d x^{2}}{c}}} + a b \sqrt{c} d^{2} x \sqrt{1 + \frac{d x^{2}}{c}} - \frac{4 a b \sqrt{c} d^{2} x}{\sqrt{1 + \frac{d x^{2}}{c}}} - \frac{2 a b c^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 x^{2}} - \frac{2 a b c d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3} + 5 a b c d^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)} - \frac{b^{2} c^{\frac{5}{2}}}{x \sqrt{1 + \frac{d x^{2}}{c}}} + b^{2} c^{\frac{3}{2}} d x \sqrt{1 + \frac{d x^{2}}{c}} - \frac{7 b^{2} c^{\frac{3}{2}} d x}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} \sqrt{c} d^{2} x^{3}}{8 \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{15 b^{2} c^{2} \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8} + \frac{b^{2} d^{3} x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-a**2*sqrt(c)*d**2/(x*sqrt(1 + d*x**2/c)) - a**2*c**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(5*x**4) - 11*a**2*c*d**(3/2)*sqrt(c/(d*x**2) + 1)/(15*x**2) - 8*a**2*d**(5/2)*sqrt(c/(d*x**2) + 1)/15 + a**2*d**(5/2)*asinh(sqrt(d)*x/sqrt(c)) - a**2*d**3*x/(sqrt(c)*sqrt(1 + d*x**2/c)) - 4*a*b*c**(3/2)*d/(x*sqrt(1 + d*x**2/c)) + a*b*sqrt(c)*d**2*x*sqrt(1 + d*x**2/c) - 4*a*b*sqrt(c)*d**2*x/sqrt(1 + d*x**2/c) - 2*a*b*c**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*x**2) - 2*a*b*c*d**(3/2)*sqrt(c/(d*x**2) + 1)/3 + 5*a*b*c*d**(3/2)*asinh(sqrt(d)*x/sqrt(c)) - b**2*c**(5/2)/(x*sqrt(1 + d*x**2/c)) + b**2*c**(3/2)*d*x*sqrt(1 + d*x**2/c) - 7*b**2*c**(3/2)*d*x/(8*sqrt(1 + d*x**2/c)) + 3*b**2*sqrt(c)*d**2*x**3/(8*sqrt(1 + d*x**2/c)) + 15*b**2*c**2*sqrt(d)*asinh(sqrt(d)*x/sqrt(c))/8 + b**2*d**3*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
635,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(d*x**2+c)**(5/2)/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,1,422,0,28.183028," ","integrate(x**4*(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","- \frac{3 a^{2} c^{\frac{3}{2}} x}{8 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a^{2} \sqrt{c} x^{3}}{8 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a^{2} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 d^{\frac{5}{2}}} + \frac{a^{2} x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a b c^{\frac{5}{2}} x}{8 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 a b c^{\frac{3}{2}} x^{3}}{24 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b \sqrt{c} x^{5}}{12 d \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{5 a b c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 d^{\frac{7}{2}}} + \frac{a b x^{7}}{3 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{35 b^{2} c^{\frac{7}{2}} x}{128 d^{4} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{35 b^{2} c^{\frac{5}{2}} x^{3}}{384 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{7 b^{2} c^{\frac{3}{2}} x^{5}}{192 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} \sqrt{c} x^{7}}{48 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{35 b^{2} c^{4} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{128 d^{\frac{9}{2}}} + \frac{b^{2} x^{9}}{8 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"-3*a**2*c**(3/2)*x/(8*d**2*sqrt(1 + d*x**2/c)) - a**2*sqrt(c)*x**3/(8*d*sqrt(1 + d*x**2/c)) + 3*a**2*c**2*asinh(sqrt(d)*x/sqrt(c))/(8*d**(5/2)) + a**2*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c)) + 5*a*b*c**(5/2)*x/(8*d**3*sqrt(1 + d*x**2/c)) + 5*a*b*c**(3/2)*x**3/(24*d**2*sqrt(1 + d*x**2/c)) - a*b*sqrt(c)*x**5/(12*d*sqrt(1 + d*x**2/c)) - 5*a*b*c**3*asinh(sqrt(d)*x/sqrt(c))/(8*d**(7/2)) + a*b*x**7/(3*sqrt(c)*sqrt(1 + d*x**2/c)) - 35*b**2*c**(7/2)*x/(128*d**4*sqrt(1 + d*x**2/c)) - 35*b**2*c**(5/2)*x**3/(384*d**3*sqrt(1 + d*x**2/c)) + 7*b**2*c**(3/2)*x**5/(192*d**2*sqrt(1 + d*x**2/c)) - b**2*sqrt(c)*x**7/(48*d*sqrt(1 + d*x**2/c)) + 35*b**2*c**4*asinh(sqrt(d)*x/sqrt(c))/(128*d**(9/2)) + b**2*x**9/(8*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
637,1,240,0,1.809932," ","integrate(x**3*(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\begin{cases} - \frac{2 a^{2} c \sqrt{c + d x^{2}}}{3 d^{2}} + \frac{a^{2} x^{2} \sqrt{c + d x^{2}}}{3 d} + \frac{16 a b c^{2} \sqrt{c + d x^{2}}}{15 d^{3}} - \frac{8 a b c x^{2} \sqrt{c + d x^{2}}}{15 d^{2}} + \frac{2 a b x^{4} \sqrt{c + d x^{2}}}{5 d} - \frac{16 b^{2} c^{3} \sqrt{c + d x^{2}}}{35 d^{4}} + \frac{8 b^{2} c^{2} x^{2} \sqrt{c + d x^{2}}}{35 d^{3}} - \frac{6 b^{2} c x^{4} \sqrt{c + d x^{2}}}{35 d^{2}} + \frac{b^{2} x^{6} \sqrt{c + d x^{2}}}{7 d} & \text{for}\: d \neq 0 \\\frac{\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*c*sqrt(c + d*x**2)/(3*d**2) + a**2*x**2*sqrt(c + d*x**2)/(3*d) + 16*a*b*c**2*sqrt(c + d*x**2)/(15*d**3) - 8*a*b*c*x**2*sqrt(c + d*x**2)/(15*d**2) + 2*a*b*x**4*sqrt(c + d*x**2)/(5*d) - 16*b**2*c**3*sqrt(c + d*x**2)/(35*d**4) + 8*b**2*c**2*x**2*sqrt(c + d*x**2)/(35*d**3) - 6*b**2*c*x**4*sqrt(c + d*x**2)/(35*d**2) + b**2*x**6*sqrt(c + d*x**2)/(7*d), Ne(d, 0)), ((a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8)/sqrt(c), True))","A",0
638,1,301,0,16.346203," ","integrate(x**2*(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\frac{a^{2} \sqrt{c} x \sqrt{1 + \frac{d x^{2}}{c}}}{2 d} - \frac{a^{2} c \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{2 d^{\frac{3}{2}}} - \frac{3 a b c^{\frac{3}{2}} x}{4 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{a b \sqrt{c} x^{3}}{4 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 a b c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{4 d^{\frac{5}{2}}} + \frac{a b x^{5}}{2 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{\frac{5}{2}} x}{16 d^{3} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{5 b^{2} c^{\frac{3}{2}} x^{3}}{48 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} \sqrt{c} x^{5}}{24 d \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{5 b^{2} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{16 d^{\frac{7}{2}}} + \frac{b^{2} x^{7}}{6 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"a**2*sqrt(c)*x*sqrt(1 + d*x**2/c)/(2*d) - a**2*c*asinh(sqrt(d)*x/sqrt(c))/(2*d**(3/2)) - 3*a*b*c**(3/2)*x/(4*d**2*sqrt(1 + d*x**2/c)) - a*b*sqrt(c)*x**3/(4*d*sqrt(1 + d*x**2/c)) + 3*a*b*c**2*asinh(sqrt(d)*x/sqrt(c))/(4*d**(5/2)) + a*b*x**5/(2*sqrt(c)*sqrt(1 + d*x**2/c)) + 5*b**2*c**(5/2)*x/(16*d**3*sqrt(1 + d*x**2/c)) + 5*b**2*c**(3/2)*x**3/(48*d**2*sqrt(1 + d*x**2/c)) - b**2*sqrt(c)*x**5/(24*d*sqrt(1 + d*x**2/c)) - 5*b**2*c**3*asinh(sqrt(d)*x/sqrt(c))/(16*d**(7/2)) + b**2*x**7/(6*sqrt(c)*sqrt(1 + d*x**2/c))","B",0
639,1,158,0,1.884901," ","integrate(x*(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\begin{cases} \frac{a^{2} \sqrt{c + d x^{2}}}{d} - \frac{4 a b c \sqrt{c + d x^{2}}}{3 d^{2}} + \frac{2 a b x^{2} \sqrt{c + d x^{2}}}{3 d} + \frac{8 b^{2} c^{2} \sqrt{c + d x^{2}}}{15 d^{3}} - \frac{4 b^{2} c x^{2} \sqrt{c + d x^{2}}}{15 d^{2}} + \frac{b^{2} x^{4} \sqrt{c + d x^{2}}}{5 d} & \text{for}\: d \neq 0 \\\frac{\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sqrt(c + d*x**2)/d - 4*a*b*c*sqrt(c + d*x**2)/(3*d**2) + 2*a*b*x**2*sqrt(c + d*x**2)/(3*d) + 8*b**2*c**2*sqrt(c + d*x**2)/(15*d**3) - 4*b**2*c*x**2*sqrt(c + d*x**2)/(15*d**2) + b**2*x**4*sqrt(c + d*x**2)/(5*d), Ne(d, 0)), ((a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6)/sqrt(c), True))","A",0
640,1,238,0,14.271511," ","integrate((b*x**2+a)**2/(d*x**2+c)**(1/2),x)","a^{2} \left(\begin{cases} \frac{\sqrt{- \frac{c}{d}} \operatorname{asin}{\left(x \sqrt{- \frac{d}{c}} \right)}}{\sqrt{c}} & \text{for}\: c > 0 \wedge d < 0 \\\frac{\sqrt{\frac{c}{d}} \operatorname{asinh}{\left(x \sqrt{\frac{d}{c}} \right)}}{\sqrt{c}} & \text{for}\: c > 0 \wedge d > 0 \\\frac{\sqrt{- \frac{c}{d}} \operatorname{acosh}{\left(x \sqrt{- \frac{d}{c}} \right)}}{\sqrt{- c}} & \text{for}\: d > 0 \wedge c < 0 \end{cases}\right) + \frac{a b \sqrt{c} x \sqrt{1 + \frac{d x^{2}}{c}}}{d} - \frac{a b c \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{d^{\frac{3}{2}}} - \frac{3 b^{2} c^{\frac{3}{2}} x}{8 d^{2} \sqrt{1 + \frac{d x^{2}}{c}}} - \frac{b^{2} \sqrt{c} x^{3}}{8 d \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{3 b^{2} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{8 d^{\frac{5}{2}}} + \frac{b^{2} x^{5}}{4 \sqrt{c} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"a**2*Piecewise((sqrt(-c/d)*asin(x*sqrt(-d/c))/sqrt(c), (c > 0) & (d < 0)), (sqrt(c/d)*asinh(x*sqrt(d/c))/sqrt(c), (c > 0) & (d > 0)), (sqrt(-c/d)*acosh(x*sqrt(-d/c))/sqrt(-c), (d > 0) & (c < 0))) + a*b*sqrt(c)*x*sqrt(1 + d*x**2/c)/d - a*b*c*asinh(sqrt(d)*x/sqrt(c))/d**(3/2) - 3*b**2*c**(3/2)*x/(8*d**2*sqrt(1 + d*x**2/c)) - b**2*sqrt(c)*x**3/(8*d*sqrt(1 + d*x**2/c)) + 3*b**2*c**2*asinh(sqrt(d)*x/sqrt(c))/(8*d**(5/2)) + b**2*x**5/(4*sqrt(c)*sqrt(1 + d*x**2/c))","A",0
641,1,76,0,53.562968," ","integrate((b*x**2+a)**2/x/(d*x**2+c)**(1/2),x)","\frac{a^{2} \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{c}} \sqrt{c + d x^{2}}} \right)}}{c \sqrt{- \frac{1}{c}}} + \frac{b^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}{3 d^{2}} + \frac{b \sqrt{c + d x^{2}} \left(2 a d - b c\right)}{d^{2}}"," ",0,"a**2*atan(1/(sqrt(-1/c)*sqrt(c + d*x**2)))/(c*sqrt(-1/c)) + b**2*(c + d*x**2)**(3/2)/(3*d**2) + b*sqrt(c + d*x**2)*(2*a*d - b*c)/d**2","A",0
642,1,155,0,8.038368," ","integrate((b*x**2+a)**2/x**2/(d*x**2+c)**(1/2),x)","- \frac{a^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{c} + 2 a b \left(\begin{cases} \frac{\sqrt{- \frac{c}{d}} \operatorname{asin}{\left(x \sqrt{- \frac{d}{c}} \right)}}{\sqrt{c}} & \text{for}\: c > 0 \wedge d < 0 \\\frac{\sqrt{\frac{c}{d}} \operatorname{asinh}{\left(x \sqrt{\frac{d}{c}} \right)}}{\sqrt{c}} & \text{for}\: c > 0 \wedge d > 0 \\\frac{\sqrt{- \frac{c}{d}} \operatorname{acosh}{\left(x \sqrt{- \frac{d}{c}} \right)}}{\sqrt{- c}} & \text{for}\: d > 0 \wedge c < 0 \end{cases}\right) + \frac{b^{2} \sqrt{c} x \sqrt{1 + \frac{d x^{2}}{c}}}{2 d} - \frac{b^{2} c \operatorname{asinh}{\left(\frac{\sqrt{d} x}{\sqrt{c}} \right)}}{2 d^{\frac{3}{2}}}"," ",0,"-a**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/c + 2*a*b*Piecewise((sqrt(-c/d)*asin(x*sqrt(-d/c))/sqrt(c), (c > 0) & (d < 0)), (sqrt(c/d)*asinh(x*sqrt(d/c))/sqrt(c), (c > 0) & (d > 0)), (sqrt(-c/d)*acosh(x*sqrt(-d/c))/sqrt(-c), (d > 0) & (c < 0))) + b**2*sqrt(c)*x*sqrt(1 + d*x**2/c)/(2*d) - b**2*c*asinh(sqrt(d)*x/sqrt(c))/(2*d**(3/2))","A",0
643,1,99,0,130.447177," ","integrate((b*x**2+a)**2/x**3/(d*x**2+c)**(1/2),x)","- \frac{a^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{2 c x} + \frac{a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)}}{2 c^{\frac{3}{2}}} - \frac{2 a b \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{d} x} \right)}}{\sqrt{c}} + b^{2} \left(\begin{cases} \frac{x^{2}}{2 \sqrt{c}} & \text{for}\: d = 0 \\\frac{\sqrt{c + d x^{2}}}{d} & \text{otherwise} \end{cases}\right)"," ",0,"-a**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(2*c*x) + a**2*d*asinh(sqrt(c)/(sqrt(d)*x))/(2*c**(3/2)) - 2*a*b*asinh(sqrt(c)/(sqrt(d)*x))/sqrt(c) + b**2*Piecewise((x**2/(2*sqrt(c)), Eq(d, 0)), (sqrt(c + d*x**2)/d, True))","A",0
644,1,158,0,5.416200," ","integrate((b*x**2+a)**2/x**4/(d*x**2+c)**(1/2),x)","- \frac{a^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 c x^{2}} + \frac{2 a^{2} d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3 c^{2}} - \frac{2 a b \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{c} + b^{2} \left(\begin{cases} \frac{\sqrt{- \frac{c}{d}} \operatorname{asin}{\left(x \sqrt{- \frac{d}{c}} \right)}}{\sqrt{c}} & \text{for}\: c > 0 \wedge d < 0 \\\frac{\sqrt{\frac{c}{d}} \operatorname{asinh}{\left(x \sqrt{\frac{d}{c}} \right)}}{\sqrt{c}} & \text{for}\: c > 0 \wedge d > 0 \\\frac{\sqrt{- \frac{c}{d}} \operatorname{acosh}{\left(x \sqrt{- \frac{d}{c}} \right)}}{\sqrt{- c}} & \text{for}\: d > 0 \wedge c < 0 \end{cases}\right)"," ",0,"-a**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*c*x**2) + 2*a**2*d**(3/2)*sqrt(c/(d*x**2) + 1)/(3*c**2) - 2*a*b*sqrt(d)*sqrt(c/(d*x**2) + 1)/c + b**2*Piecewise((sqrt(-c/d)*asin(x*sqrt(-d/c))/sqrt(c), (c > 0) & (d < 0)), (sqrt(c/d)*asinh(x*sqrt(d/c))/sqrt(c), (c > 0) & (d > 0)), (sqrt(-c/d)*acosh(x*sqrt(-d/c))/sqrt(-c), (d > 0) & (c < 0)))","A",0
645,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**5/(d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,1,391,0,7.484415," ","integrate((b*x**2+a)**2/x**6/(d*x**2+c)**(1/2),x)","- \frac{3 a^{2} c^{4} d^{\frac{9}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{5} d^{4} x^{4} + 30 c^{4} d^{5} x^{6} + 15 c^{3} d^{6} x^{8}} - \frac{2 a^{2} c^{3} d^{\frac{11}{2}} x^{2} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{5} d^{4} x^{4} + 30 c^{4} d^{5} x^{6} + 15 c^{3} d^{6} x^{8}} - \frac{3 a^{2} c^{2} d^{\frac{13}{2}} x^{4} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{5} d^{4} x^{4} + 30 c^{4} d^{5} x^{6} + 15 c^{3} d^{6} x^{8}} - \frac{12 a^{2} c d^{\frac{15}{2}} x^{6} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{5} d^{4} x^{4} + 30 c^{4} d^{5} x^{6} + 15 c^{3} d^{6} x^{8}} - \frac{8 a^{2} d^{\frac{17}{2}} x^{8} \sqrt{\frac{c}{d x^{2}} + 1}}{15 c^{5} d^{4} x^{4} + 30 c^{4} d^{5} x^{6} + 15 c^{3} d^{6} x^{8}} - \frac{2 a b \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{3 c x^{2}} + \frac{4 a b d^{\frac{3}{2}} \sqrt{\frac{c}{d x^{2}} + 1}}{3 c^{2}} - \frac{b^{2} \sqrt{d} \sqrt{\frac{c}{d x^{2}} + 1}}{c}"," ",0,"-3*a**2*c**4*d**(9/2)*sqrt(c/(d*x**2) + 1)/(15*c**5*d**4*x**4 + 30*c**4*d**5*x**6 + 15*c**3*d**6*x**8) - 2*a**2*c**3*d**(11/2)*x**2*sqrt(c/(d*x**2) + 1)/(15*c**5*d**4*x**4 + 30*c**4*d**5*x**6 + 15*c**3*d**6*x**8) - 3*a**2*c**2*d**(13/2)*x**4*sqrt(c/(d*x**2) + 1)/(15*c**5*d**4*x**4 + 30*c**4*d**5*x**6 + 15*c**3*d**6*x**8) - 12*a**2*c*d**(15/2)*x**6*sqrt(c/(d*x**2) + 1)/(15*c**5*d**4*x**4 + 30*c**4*d**5*x**6 + 15*c**3*d**6*x**8) - 8*a**2*d**(17/2)*x**8*sqrt(c/(d*x**2) + 1)/(15*c**5*d**4*x**4 + 30*c**4*d**5*x**6 + 15*c**3*d**6*x**8) - 2*a*b*sqrt(d)*sqrt(c/(d*x**2) + 1)/(3*c*x**2) + 4*a*b*d**(3/2)*sqrt(c/(d*x**2) + 1)/(3*c**2) - b**2*sqrt(d)*sqrt(c/(d*x**2) + 1)/c","B",0
647,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**7/(d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,0,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{x^{4} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4*(a + b*x**2)**2/(c + d*x**2)**(3/2), x)","F",0
649,1,236,0,1.990681," ","integrate(x**3*(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\begin{cases} \frac{2 a^{2} c}{d^{2} \sqrt{c + d x^{2}}} + \frac{a^{2} x^{2}}{d \sqrt{c + d x^{2}}} - \frac{16 a b c^{2}}{3 d^{3} \sqrt{c + d x^{2}}} - \frac{8 a b c x^{2}}{3 d^{2} \sqrt{c + d x^{2}}} + \frac{2 a b x^{4}}{3 d \sqrt{c + d x^{2}}} + \frac{16 b^{2} c^{3}}{5 d^{4} \sqrt{c + d x^{2}}} + \frac{8 b^{2} c^{2} x^{2}}{5 d^{3} \sqrt{c + d x^{2}}} - \frac{2 b^{2} c x^{4}}{5 d^{2} \sqrt{c + d x^{2}}} + \frac{b^{2} x^{6}}{5 d \sqrt{c + d x^{2}}} & \text{for}\: d \neq 0 \\\frac{\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}}{c^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*c/(d**2*sqrt(c + d*x**2)) + a**2*x**2/(d*sqrt(c + d*x**2)) - 16*a*b*c**2/(3*d**3*sqrt(c + d*x**2)) - 8*a*b*c*x**2/(3*d**2*sqrt(c + d*x**2)) + 2*a*b*x**4/(3*d*sqrt(c + d*x**2)) + 16*b**2*c**3/(5*d**4*sqrt(c + d*x**2)) + 8*b**2*c**2*x**2/(5*d**3*sqrt(c + d*x**2)) - 2*b**2*c*x**4/(5*d**2*sqrt(c + d*x**2)) + b**2*x**6/(5*d*sqrt(c + d*x**2)), Ne(d, 0)), ((a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8)/c**(3/2), True))","A",0
650,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{x^{2} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x**2)**2/(c + d*x**2)**(3/2), x)","F",0
651,1,155,0,1.290836," ","integrate(x*(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\begin{cases} - \frac{a^{2}}{d \sqrt{c + d x^{2}}} + \frac{4 a b c}{d^{2} \sqrt{c + d x^{2}}} + \frac{2 a b x^{2}}{d \sqrt{c + d x^{2}}} - \frac{8 b^{2} c^{2}}{3 d^{3} \sqrt{c + d x^{2}}} - \frac{4 b^{2} c x^{2}}{3 d^{2} \sqrt{c + d x^{2}}} + \frac{b^{2} x^{4}}{3 d \sqrt{c + d x^{2}}} & \text{for}\: d \neq 0 \\\frac{\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}}{c^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(d*sqrt(c + d*x**2)) + 4*a*b*c/(d**2*sqrt(c + d*x**2)) + 2*a*b*x**2/(d*sqrt(c + d*x**2)) - 8*b**2*c**2/(3*d**3*sqrt(c + d*x**2)) - 4*b**2*c*x**2/(3*d**2*sqrt(c + d*x**2)) + b**2*x**4/(3*d*sqrt(c + d*x**2)), Ne(d, 0)), ((a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6)/c**(3/2), True))","A",0
652,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(c + d*x**2)**(3/2), x)","F",0
653,1,70,0,36.045833," ","integrate((b*x**2+a)**2/x/(d*x**2+c)**(3/2),x)","\frac{a^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{c \sqrt{- c}} + \frac{b^{2} \sqrt{c + d x^{2}}}{d^{2}} + \frac{\left(a d - b c\right)^{2}}{c d^{2} \sqrt{c + d x^{2}}}"," ",0,"a**2*atan(sqrt(c + d*x**2)/sqrt(-c))/(c*sqrt(-c)) + b**2*sqrt(c + d*x**2)/d**2 + (a*d - b*c)**2/(c*d**2*sqrt(c + d*x**2))","A",0
654,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**2/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**2*(c + d*x**2)**(3/2)), x)","F",0
655,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**3/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{3} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**3*(c + d*x**2)**(3/2)), x)","F",0
656,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**4/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{4} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**4*(c + d*x**2)**(3/2)), x)","F",0
657,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**5/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{5} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**5*(c + d*x**2)**(3/2)), x)","F",0
658,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**6/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{6} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**6*(c + d*x**2)**(3/2)), x)","F",0
659,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/x**7/(d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
660,0,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{x^{4} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*(a + b*x**2)**2/(c + d*x**2)**(5/2), x)","F",0
661,1,454,0,2.945697," ","integrate(x**3*(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\begin{cases} - \frac{2 a^{2} c d^{2}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} - \frac{3 a^{2} d^{3} x^{2}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} + \frac{16 a b c^{2} d}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} + \frac{24 a b c d^{2} x^{2}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} + \frac{6 a b d^{3} x^{4}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} - \frac{16 b^{2} c^{3}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} - \frac{24 b^{2} c^{2} d x^{2}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} - \frac{6 b^{2} c d^{2} x^{4}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} + \frac{b^{2} d^{3} x^{6}}{3 c d^{4} \sqrt{c + d x^{2}} + 3 d^{5} x^{2} \sqrt{c + d x^{2}}} & \text{for}\: d \neq 0 \\\frac{\frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8}}{c^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*c*d**2/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) - 3*a**2*d**3*x**2/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) + 16*a*b*c**2*d/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) + 24*a*b*c*d**2*x**2/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) + 6*a*b*d**3*x**4/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) - 16*b**2*c**3/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) - 24*b**2*c**2*d*x**2/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) - 6*b**2*c*d**2*x**4/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)) + b**2*d**3*x**6/(3*c*d**4*sqrt(c + d*x**2) + 3*d**5*x**2*sqrt(c + d*x**2)), Ne(d, 0)), ((a**2*x**4/4 + a*b*x**6/3 + b**2*x**8/8)/c**(5/2), True))","A",0
662,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{x^{2} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x**2)**2/(c + d*x**2)**(5/2), x)","F",0
663,1,303,0,1.377146," ","integrate(x*(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\begin{cases} - \frac{a^{2} d^{2}}{3 c d^{3} \sqrt{c + d x^{2}} + 3 d^{4} x^{2} \sqrt{c + d x^{2}}} - \frac{4 a b c d}{3 c d^{3} \sqrt{c + d x^{2}} + 3 d^{4} x^{2} \sqrt{c + d x^{2}}} - \frac{6 a b d^{2} x^{2}}{3 c d^{3} \sqrt{c + d x^{2}} + 3 d^{4} x^{2} \sqrt{c + d x^{2}}} + \frac{8 b^{2} c^{2}}{3 c d^{3} \sqrt{c + d x^{2}} + 3 d^{4} x^{2} \sqrt{c + d x^{2}}} + \frac{12 b^{2} c d x^{2}}{3 c d^{3} \sqrt{c + d x^{2}} + 3 d^{4} x^{2} \sqrt{c + d x^{2}}} + \frac{3 b^{2} d^{2} x^{4}}{3 c d^{3} \sqrt{c + d x^{2}} + 3 d^{4} x^{2} \sqrt{c + d x^{2}}} & \text{for}\: d \neq 0 \\\frac{\frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6}}{c^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*d**2/(3*c*d**3*sqrt(c + d*x**2) + 3*d**4*x**2*sqrt(c + d*x**2)) - 4*a*b*c*d/(3*c*d**3*sqrt(c + d*x**2) + 3*d**4*x**2*sqrt(c + d*x**2)) - 6*a*b*d**2*x**2/(3*c*d**3*sqrt(c + d*x**2) + 3*d**4*x**2*sqrt(c + d*x**2)) + 8*b**2*c**2/(3*c*d**3*sqrt(c + d*x**2) + 3*d**4*x**2*sqrt(c + d*x**2)) + 12*b**2*c*d*x**2/(3*c*d**3*sqrt(c + d*x**2) + 3*d**4*x**2*sqrt(c + d*x**2)) + 3*b**2*d**2*x**4/(3*c*d**3*sqrt(c + d*x**2) + 3*d**4*x**2*sqrt(c + d*x**2)), Ne(d, 0)), ((a**2*x**2/2 + a*b*x**4/2 + b**2*x**6/6)/c**(5/2), True))","A",0
664,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(c + d*x**2)**(5/2), x)","F",0
665,1,87,0,44.361447," ","integrate((b*x**2+a)**2/x/(d*x**2+c)**(5/2),x)","\frac{a^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{c^{2} \sqrt{- c}} + \frac{\left(a d - b c\right)^{2}}{3 c d^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}} + \frac{\left(a d - b c\right) \left(a d + b c\right)}{c^{2} d^{2} \sqrt{c + d x^{2}}}"," ",0,"a**2*atan(sqrt(c + d*x**2)/sqrt(-c))/(c**2*sqrt(-c)) + (a*d - b*c)**2/(3*c*d**2*(c + d*x**2)**(3/2)) + (a*d - b*c)*(a*d + b*c)/(c**2*d**2*sqrt(c + d*x**2))","A",0
666,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**2/(d*x**2+c)**(5/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**2*(c + d*x**2)**(5/2)), x)","F",0
667,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**3/(d*x**2+c)**(5/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{3} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**3*(c + d*x**2)**(5/2)), x)","F",0
668,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**4/(d*x**2+c)**(5/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{4} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**4*(c + d*x**2)**(5/2)), x)","F",0
669,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**5/(d*x**2+c)**(5/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{5} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**5*(c + d*x**2)**(5/2)), x)","F",0
670,0,0,0,0.000000," ","integrate((b*x**2+a)**2/x**6/(d*x**2+c)**(5/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{x^{6} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(x**6*(c + d*x**2)**(5/2)), x)","F",0
671,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a)/(d*x**2)**(1/2),x)","\int \frac{x^{5}}{\sqrt{d x^{2}} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(x**5/(sqrt(d*x**2)*(a + b*x**2)), x)","F",0
672,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)/(d*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{d x^{2}} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(x**3/(sqrt(d*x**2)*(a + b*x**2)), x)","F",0
673,0,0,0,0.000000," ","integrate(x/(b*x**2+a)/(d*x**2)**(1/2),x)","\int \frac{x}{\sqrt{d x^{2}} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(x/(sqrt(d*x**2)*(a + b*x**2)), x)","F",0
674,0,0,0,0.000000," ","integrate(1/x/(b*x**2+a)/(d*x**2)**(1/2),x)","\int \frac{1}{x \sqrt{d x^{2}} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(1/(x*sqrt(d*x**2)*(a + b*x**2)), x)","F",0
675,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)/(d*x**2)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{d x^{2}} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(1/(x**3*sqrt(d*x**2)*(a + b*x**2)), x)","F",0
676,0,0,0,0.000000," ","integrate(x**4*(d*x**2+c)**(1/2)/(b*x**2+a),x)","\int \frac{x^{4} \sqrt{c + d x^{2}}}{a + b x^{2}}\, dx"," ",0,"Integral(x**4*sqrt(c + d*x**2)/(a + b*x**2), x)","F",0
677,1,87,0,7.230139," ","integrate(x**3*(d*x**2+c)**(1/2)/(b*x**2+a),x)","\frac{2 \left(- \frac{a d^{2} \sqrt{c + d x^{2}}}{2 b^{2}} + \frac{a d^{2} \left(a d - b c\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{2 b^{3} \sqrt{\frac{a d - b c}{b}}} + \frac{d \left(c + d x^{2}\right)^{\frac{3}{2}}}{6 b}\right)}{d^{2}}"," ",0,"2*(-a*d**2*sqrt(c + d*x**2)/(2*b**2) + a*d**2*(a*d - b*c)*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(2*b**3*sqrt((a*d - b*c)/b)) + d*(c + d*x**2)**(3/2)/(6*b))/d**2","A",0
678,0,0,0,0.000000," ","integrate(x**2*(d*x**2+c)**(1/2)/(b*x**2+a),x)","\int \frac{x^{2} \sqrt{c + d x^{2}}}{a + b x^{2}}\, dx"," ",0,"Integral(x**2*sqrt(c + d*x**2)/(a + b*x**2), x)","F",0
679,1,61,0,4.886989," ","integrate(x*(d*x**2+c)**(1/2)/(b*x**2+a),x)","\frac{2 \left(\frac{d \sqrt{c + d x^{2}}}{2 b} - \frac{d \left(a d - b c\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{2 b^{2} \sqrt{\frac{a d - b c}{b}}}\right)}{d}"," ",0,"2*(d*sqrt(c + d*x**2)/(2*b) - d*(a*d - b*c)*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(2*b**2*sqrt((a*d - b*c)/b)))/d","A",0
680,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a),x)","\int \frac{\sqrt{c + d x^{2}}}{a + b x^{2}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(a + b*x**2), x)","F",0
681,1,78,0,9.585903," ","integrate((d*x**2+c)**(1/2)/x/(b*x**2+a),x)","\frac{2 \left(\frac{c d \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{2 a \sqrt{- c}} + \frac{d \left(a d - b c\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{2 a b \sqrt{\frac{a d - b c}{b}}}\right)}{d}"," ",0,"2*(c*d*atan(sqrt(c + d*x**2)/sqrt(-c))/(2*a*sqrt(-c)) + d*(a*d - b*c)*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(2*a*b*sqrt((a*d - b*c)/b)))/d","A",0
682,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/x**2/(b*x**2+a),x)","\int \frac{\sqrt{c + d x^{2}}}{x^{2} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(x**2*(a + b*x**2)), x)","F",0
683,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/x**3/(b*x**2+a),x)","\int \frac{\sqrt{c + d x^{2}}}{x^{3} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(x**3*(a + b*x**2)), x)","F",0
684,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/x**4/(b*x**2+a),x)","\int \frac{\sqrt{c + d x^{2}}}{x^{4} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(x**4*(a + b*x**2)), x)","F",0
685,0,0,0,0.000000," ","integrate(x**4*(d*x**2+c)**(3/2)/(b*x**2+a),x)","\int \frac{x^{4} \left(c + d x^{2}\right)^{\frac{3}{2}}}{a + b x^{2}}\, dx"," ",0,"Integral(x**4*(c + d*x**2)**(3/2)/(a + b*x**2), x)","F",0
686,1,104,0,46.419695," ","integrate(x**3*(d*x**2+c)**(3/2)/(b*x**2+a),x)","- \frac{a \left(c + d x^{2}\right)^{\frac{3}{2}}}{3 b^{2}} - \frac{a \left(a d - b c\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{4} \sqrt{\frac{a d - b c}{b}}} + \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{5 b d} + \frac{\sqrt{c + d x^{2}} \left(a^{2} d - a b c\right)}{b^{3}}"," ",0,"-a*(c + d*x**2)**(3/2)/(3*b**2) - a*(a*d - b*c)**2*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(b**4*sqrt((a*d - b*c)/b)) + (c + d*x**2)**(5/2)/(5*b*d) + sqrt(c + d*x**2)*(a**2*d - a*b*c)/b**3","A",0
687,0,0,0,0.000000," ","integrate(x**2*(d*x**2+c)**(3/2)/(b*x**2+a),x)","\int \frac{x^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}{a + b x^{2}}\, dx"," ",0,"Integral(x**2*(c + d*x**2)**(3/2)/(a + b*x**2), x)","F",0
688,1,80,0,33.908895," ","integrate(x*(d*x**2+c)**(3/2)/(b*x**2+a),x)","\frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{3 b} + \frac{\sqrt{c + d x^{2}} \left(- a d + b c\right)}{b^{2}} + \frac{\left(a d - b c\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{3} \sqrt{\frac{a d - b c}{b}}}"," ",0,"(c + d*x**2)**(3/2)/(3*b) + sqrt(c + d*x**2)*(-a*d + b*c)/b**2 + (a*d - b*c)**2*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(b**3*sqrt((a*d - b*c)/b))","A",0
689,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{a + b x^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(a + b*x**2), x)","F",0
690,1,92,0,29.872222," ","integrate((d*x**2+c)**(3/2)/x/(b*x**2+a),x)","\frac{d \sqrt{c + d x^{2}}}{b} + \frac{c^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{a \sqrt{- c}} - \frac{\left(a d - b c\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{a b^{2} \sqrt{\frac{a d - b c}{b}}}"," ",0,"d*sqrt(c + d*x**2)/b + c**2*atan(sqrt(c + d*x**2)/sqrt(-c))/(a*sqrt(-c)) - (a*d - b*c)**2*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(a*b**2*sqrt((a*d - b*c)/b))","A",0
691,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/x**2/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{x^{2} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(x**2*(a + b*x**2)), x)","F",0
692,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/x**3/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{x^{3} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(x**3*(a + b*x**2)), x)","F",0
693,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/x**4/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{x^{4} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(x**4*(a + b*x**2)), x)","F",0
694,0,0,0,0.000000," ","integrate(x**4*(d*x**2+c)**(5/2)/(b*x**2+a),x)","\int \frac{x^{4} \left(c + d x^{2}\right)^{\frac{5}{2}}}{a + b x^{2}}\, dx"," ",0,"Integral(x**4*(c + d*x**2)**(5/2)/(a + b*x**2), x)","F",0
695,1,144,0,84.634112," ","integrate(x**3*(d*x**2+c)**(5/2)/(b*x**2+a),x)","- \frac{a \left(c + d x^{2}\right)^{\frac{5}{2}}}{5 b^{2}} + \frac{a \left(a d - b c\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{5} \sqrt{\frac{a d - b c}{b}}} + \frac{\left(c + d x^{2}\right)^{\frac{7}{2}}}{7 b d} + \frac{\left(c + d x^{2}\right)^{\frac{3}{2}} \left(a^{2} d - a b c\right)}{3 b^{3}} + \frac{\sqrt{c + d x^{2}} \left(- a^{3} d^{2} + 2 a^{2} b c d - a b^{2} c^{2}\right)}{b^{4}}"," ",0,"-a*(c + d*x**2)**(5/2)/(5*b**2) + a*(a*d - b*c)**3*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(b**5*sqrt((a*d - b*c)/b)) + (c + d*x**2)**(7/2)/(7*b*d) + (c + d*x**2)**(3/2)*(a**2*d - a*b*c)/(3*b**3) + sqrt(c + d*x**2)*(-a**3*d**2 + 2*a**2*b*c*d - a*b**2*c**2)/b**4","A",0
696,0,0,0,0.000000," ","integrate(x**2*(d*x**2+c)**(5/2)/(b*x**2+a),x)","\int \frac{x^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}{a + b x^{2}}\, dx"," ",0,"Integral(x**2*(c + d*x**2)**(5/2)/(a + b*x**2), x)","F",0
697,1,117,0,50.764364," ","integrate(x*(d*x**2+c)**(5/2)/(b*x**2+a),x)","\frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{5 b} + \frac{\left(c + d x^{2}\right)^{\frac{3}{2}} \left(- a d + b c\right)}{3 b^{2}} + \frac{\sqrt{c + d x^{2}} \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{b^{3}} - \frac{\left(a d - b c\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{4} \sqrt{\frac{a d - b c}{b}}}"," ",0,"(c + d*x**2)**(5/2)/(5*b) + (c + d*x**2)**(3/2)*(-a*d + b*c)/(3*b**2) + sqrt(c + d*x**2)*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/b**3 - (a*d - b*c)**3*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(b**4*sqrt((a*d - b*c)/b))","A",0
698,0,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{a + b x^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(5/2)/(a + b*x**2), x)","F",0
699,1,119,0,67.140237," ","integrate((d*x**2+c)**(5/2)/x/(b*x**2+a),x)","\frac{d \left(c + d x^{2}\right)^{\frac{3}{2}}}{3 b} + \frac{\sqrt{c + d x^{2}} \left(- a d^{2} + 2 b c d\right)}{b^{2}} + \frac{c^{3} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{a \sqrt{- c}} + \frac{\left(a d - b c\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{a b^{3} \sqrt{\frac{a d - b c}{b}}}"," ",0,"d*(c + d*x**2)**(3/2)/(3*b) + sqrt(c + d*x**2)*(-a*d**2 + 2*b*c*d)/b**2 + c**3*atan(sqrt(c + d*x**2)/sqrt(-c))/(a*sqrt(-c)) + (a*d - b*c)**3*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(a*b**3*sqrt((a*d - b*c)/b))","A",0
700,0,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/x**2/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{x^{2} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral((c + d*x**2)**(5/2)/(x**2*(a + b*x**2)), x)","F",0
701,0,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/x**3/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{x^{3} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral((c + d*x**2)**(5/2)/(x**3*(a + b*x**2)), x)","F",0
702,0,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/x**4/(b*x**2+a),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{x^{4} \left(a + b x^{2}\right)}\, dx"," ",0,"Integral((c + d*x**2)**(5/2)/(x**4*(a + b*x**2)), x)","F",0
703,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5}}{\left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
704,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3}}{\left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
705,1,36,0,6.894857," ","integrate(x/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\frac{\operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b \sqrt{\frac{a d - b c}{b}}}"," ",0,"atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(b*sqrt((a*d - b*c)/b))","A",0
706,1,63,0,14.307884," ","integrate(1/x/(b*x**2+a)/(d*x**2+c)**(1/2),x)","- \frac{\operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{a \sqrt{\frac{a d - b c}{b}}} + \frac{\operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{a \sqrt{- c}}"," ",0,"-atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(a*sqrt((a*d - b*c)/b)) + atan(sqrt(c + d*x**2)/sqrt(-c))/(a*sqrt(-c))","A",0
707,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{3} \left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
708,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{x^{4}}{\left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
709,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{x^{2}}{\left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
710,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
711,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{2} \left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
712,0,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{4} \left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**4*(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
713,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{x^{4}}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
714,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{x^{3}}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
715,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{x^{2}}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
716,1,61,0,19.962278," ","integrate(x/(b*x**2+a)/(d*x**2+c)**(3/2),x)","- \frac{1}{\sqrt{c + d x^{2}} \left(a d - b c\right)} - \frac{\operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{\sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)}"," ",0,"-1/(sqrt(c + d*x**2)*(a*d - b*c)) - atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(sqrt((a*d - b*c)/b)*(a*d - b*c))","A",0
717,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
718,1,94,0,21.003481," ","integrate(1/x/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\frac{d}{c \sqrt{c + d x^{2}} \left(a d - b c\right)} + \frac{b \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{a \sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)} + \frac{\operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{a c \sqrt{- c}}"," ",0,"d/(c*sqrt(c + d*x**2)*(a*d - b*c)) + b*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(a*sqrt((a*d - b*c)/b)*(a*d - b*c)) + atan(sqrt(c + d*x**2)/sqrt(-c))/(a*c*sqrt(-c))","A",0
719,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{1}{x^{2} \left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
720,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{1}{x^{3} \left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
721,0,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{1}{x^{4} \left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*(a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
722,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\int \frac{x^{4}}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)*(c + d*x**2)**(5/2)), x)","F",0
723,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\int \frac{x^{3}}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)*(c + d*x**2)**(5/2)), x)","F",0
724,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\int \frac{x^{2}}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)*(c + d*x**2)**(5/2)), x)","F",0
725,1,85,0,25.052538," ","integrate(x/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\frac{b}{\sqrt{c + d x^{2}} \left(a d - b c\right)^{2}} + \frac{b \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{\sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)^{2}} - \frac{1}{3 \left(c + d x^{2}\right)^{\frac{3}{2}} \left(a d - b c\right)}"," ",0,"b/(sqrt(c + d*x**2)*(a*d - b*c)**2) + b*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(sqrt((a*d - b*c)/b)*(a*d - b*c)**2) - 1/(3*(c + d*x**2)**(3/2)*(a*d - b*c))","A",0
726,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)*(c + d*x**2)**(5/2)), x)","F",0
727,1,133,0,26.339862," ","integrate(1/x/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\frac{d}{3 c \left(c + d x^{2}\right)^{\frac{3}{2}} \left(a d - b c\right)} + \frac{d \left(a d - 2 b c\right)}{c^{2} \sqrt{c + d x^{2}} \left(a d - b c\right)^{2}} - \frac{b^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{a \sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)^{2}} + \frac{\operatorname{atan}{\left(\frac{\sqrt{c + d x^{2}}}{\sqrt{- c}} \right)}}{a c^{2} \sqrt{- c}}"," ",0,"d/(3*c*(c + d*x**2)**(3/2)*(a*d - b*c)) + d*(a*d - 2*b*c)/(c**2*sqrt(c + d*x**2)*(a*d - b*c)**2) - b**2*atan(sqrt(c + d*x**2)/sqrt((a*d - b*c)/b))/(a*sqrt((a*d - b*c)/b)*(a*d - b*c)**2) + atan(sqrt(c + d*x**2)/sqrt(-c))/(a*c**2*sqrt(-c))","A",0
728,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\int \frac{1}{x^{2} \left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**2)*(c + d*x**2)**(5/2)), x)","F",0
729,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\int \frac{1}{x^{3} \left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**2)*(c + d*x**2)**(5/2)), x)","F",0
730,0,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)/(d*x**2+c)**(5/2),x)","\int \frac{1}{x^{4} \left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**4*(a + b*x**2)*(c + d*x**2)**(5/2)), x)","F",0
731,0,0,0,0.000000," ","integrate(x**4*(d*x**2+c)**(1/2)/(b*x**2+a)**2,x)","\int \frac{x^{4} \sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**4*sqrt(c + d*x**2)/(a + b*x**2)**2, x)","F",0
732,-1,0,0,0.000000," ","integrate(x**3*(d*x**2+c)**(1/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,0,0,0,0.000000," ","integrate(x**2*(d*x**2+c)**(1/2)/(b*x**2+a)**2,x)","\int \frac{x^{2} \sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**2*sqrt(c + d*x**2)/(a + b*x**2)**2, x)","F",0
734,0,0,0,0.000000," ","integrate(x*(d*x**2+c)**(1/2)/(b*x**2+a)**2,x)","\int \frac{x \sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x*sqrt(c + d*x**2)/(a + b*x**2)**2, x)","F",0
735,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a)**2,x)","\int \frac{\sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(a + b*x**2)**2, x)","F",0
736,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/x/(b*x**2+a)**2,x)","\int \frac{\sqrt{c + d x^{2}}}{x \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(x*(a + b*x**2)**2), x)","F",0
737,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/x**2/(b*x**2+a)**2,x)","\int \frac{\sqrt{c + d x^{2}}}{x^{2} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(x**2*(a + b*x**2)**2), x)","F",0
738,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/x**3/(b*x**2+a)**2,x)","\int \frac{\sqrt{c + d x^{2}}}{x^{3} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(x**3*(a + b*x**2)**2), x)","F",0
739,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/x**4/(b*x**2+a)**2,x)","\int \frac{\sqrt{c + d x^{2}}}{x^{4} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(x**4*(a + b*x**2)**2), x)","F",0
740,0,0,0,0.000000," ","integrate(x**4*(d*x**2+c)**(3/2)/(b*x**2+a)**2,x)","\int \frac{x^{4} \left(c + d x^{2}\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**4*(c + d*x**2)**(3/2)/(a + b*x**2)**2, x)","F",0
741,-1,0,0,0.000000," ","integrate(x**3*(d*x**2+c)**(3/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,0,0,0,0.000000," ","integrate(x**2*(d*x**2+c)**(3/2)/(b*x**2+a)**2,x)","\int \frac{x^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**2*(c + d*x**2)**(3/2)/(a + b*x**2)**2, x)","F",0
743,-1,0,0,0.000000," ","integrate(x*(d*x**2+c)**(3/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/(b*x**2+a)**2,x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(a + b*x**2)**2, x)","F",0
745,-1,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/x/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/x**2/(b*x**2+a)**2,x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{x^{2} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(x**2*(a + b*x**2)**2), x)","F",0
747,-1,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/x**3/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/x**4/(b*x**2+a)**2,x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{x^{4} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(x**4*(a + b*x**2)**2), x)","F",0
749,0,0,0,0.000000," ","integrate(x**4*(d*x**2+c)**(5/2)/(b*x**2+a)**2,x)","\int \frac{x^{4} \left(c + d x^{2}\right)^{\frac{5}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**4*(c + d*x**2)**(5/2)/(a + b*x**2)**2, x)","F",0
750,-1,0,0,0.000000," ","integrate(x**3*(d*x**2+c)**(5/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,0,0,0,0.000000," ","integrate(x**2*(d*x**2+c)**(5/2)/(b*x**2+a)**2,x)","\int \frac{x^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**2*(c + d*x**2)**(5/2)/(a + b*x**2)**2, x)","F",0
752,-1,0,0,0.000000," ","integrate(x*(d*x**2+c)**(5/2)/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,0,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/(b*x**2+a)**2,x)","\int \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{\left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(5/2)/(a + b*x**2)**2, x)","F",0
754,-1,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/x/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,0,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/x**2/(b*x**2+a)**2,x)","\int \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{x^{2} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(5/2)/(x**2*(a + b*x**2)**2), x)","F",0
756,-1,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/x**3/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,0,0,0,0.000000," ","integrate((d*x**2+c)**(5/2)/x**4/(b*x**2+a)**2,x)","\int \frac{\left(c + d x^{2}\right)^{\frac{5}{2}}}{x^{4} \left(a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((c + d*x**2)**(5/2)/(x**4*(a + b*x**2)**2), x)","F",0
758,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{x^{4}}{\left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
759,-1,0,0,0.000000," ","integrate(x**3/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{x^{2}}{\left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
761,0,0,0,0.000000," ","integrate(x/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{x}{\left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x/((a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
762,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
763,0,0,0,0.000000," ","integrate(1/x/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{1}{x \left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
764,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{2} \left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
765,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{3} \left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
766,0,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{4} \left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**4*(a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
767,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{x^{4}}{\left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)**2*(c + d*x**2)**(3/2)), x)","F",0
768,-1,0,0,0.000000," ","integrate(x**3/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{x^{2}}{\left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**2*(c + d*x**2)**(3/2)), x)","F",0
770,-1,0,0,0.000000," ","integrate(x/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
771,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**2*(c + d*x**2)**(3/2)), x)","F",0
772,0,0,0,0.000000," ","integrate(1/x/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{1}{x \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*x**2)**2*(c + d*x**2)**(3/2)), x)","F",0
773,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{1}{x^{2} \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**2)**2*(c + d*x**2)**(3/2)), x)","F",0
774,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{1}{x^{3} \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**2)**2*(c + d*x**2)**(3/2)), x)","F",0
775,0,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{1}{x^{4} \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**4*(a + b*x**2)**2*(c + d*x**2)**(3/2)), x)","F",0
776,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{x^{4}}{\left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4/((a + b*x**2)**2*(c + d*x**2)**(5/2)), x)","F",0
777,-1,0,0,0.000000," ","integrate(x**3/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
778,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{x^{2}}{\left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**2*(c + d*x**2)**(5/2)), x)","F",0
779,-1,0,0,0.000000," ","integrate(x/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
780,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**2*(c + d*x**2)**(5/2)), x)","F",0
781,0,0,0,0.000000," ","integrate(1/x/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{1}{x \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*(a + b*x**2)**2*(c + d*x**2)**(5/2)), x)","F",0
782,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{1}{x^{2} \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*(a + b*x**2)**2*(c + d*x**2)**(5/2)), x)","F",0
783,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{1}{x^{3} \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**3*(a + b*x**2)**2*(c + d*x**2)**(5/2)), x)","F",0
784,0,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\int \frac{1}{x^{4} \left(a + b x^{2}\right)^{2} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**4*(a + b*x**2)**2*(c + d*x**2)**(5/2)), x)","F",0
785,1,97,0,10.435045," ","integrate((e*x)**(3/2)*(B*x**2+A)*(b*x**2+a)**(1/2),x)","\frac{A \sqrt{a} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{B \sqrt{a} e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*sqrt(a)*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4)) + B*sqrt(a)*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4))","C",0
786,1,95,0,3.754126," ","integrate((B*x**2+A)*(e*x)**(1/2)*(b*x**2+a)**(1/2),x)","\frac{A \sqrt{a} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{a} \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{3} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*sqrt(a)*(e*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*e*gamma(7/4)) + B*sqrt(a)*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**3*gamma(11/4))","C",0
787,1,97,0,3.746471," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/(e*x)**(1/2),x)","\frac{A \sqrt{a} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B \sqrt{a} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*sqrt(a)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(5/4)) + B*sqrt(a)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(9/4))","C",0
788,1,100,0,3.974106," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/(e*x)**(3/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B \sqrt{a} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*sqrt(x)*gamma(3/4)) + B*sqrt(a)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(7/4))","C",0
789,1,100,0,7.456667," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/(e*x)**(5/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B \sqrt{a} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*x**(3/2)*gamma(1/4)) + B*sqrt(a)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(5/4))","C",0
790,1,107,0,22.336546," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/(e*x)**(7/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B \sqrt{a} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(5/2)*gamma(-1/4)) + B*sqrt(a)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*sqrt(x)*gamma(3/4))","C",0
791,1,97,0,21.303165," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**(9/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)} + \frac{B \sqrt{a} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**2*exp_polar(I*pi)/a)/(2*x**(7/2)*gamma(-3/4)) + B*sqrt(a)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*x**(3/2)*gamma(1/4))","C",0
792,1,100,0,53.119658," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**(11/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 x^{\frac{9}{2}} \Gamma\left(- \frac{5}{4}\right)} + \frac{B \sqrt{a} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), b*x**2*exp_polar(I*pi)/a)/(2*x**(9/2)*gamma(-5/4)) + B*sqrt(a)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*x**(5/2)*gamma(-1/4))","C",0
793,1,100,0,135.645948," ","integrate((B*x**2+A)*(b*x**2+a)**(1/2)/x**(13/2),x)","\frac{A \sqrt{a} \Gamma\left(- \frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{4}, - \frac{1}{2} \\ - \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 x^{\frac{11}{2}} \Gamma\left(- \frac{7}{4}\right)} + \frac{B \sqrt{a} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)}"," ",0,"A*sqrt(a)*gamma(-11/4)*hyper((-11/4, -1/2), (-7/4,), b*x**2*exp_polar(I*pi)/a)/(2*x**(11/2)*gamma(-7/4)) + B*sqrt(a)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), b*x**2*exp_polar(I*pi)/a)/(2*x**(7/2)*gamma(-3/4))","C",0
794,1,199,0,27.140366," ","integrate((e*x)**(3/2)*(b*x**2+a)**(3/2)*(B*x**2+A),x)","\frac{A a^{\frac{3}{2}} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{A \sqrt{a} b e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)} + \frac{B a^{\frac{3}{2}} e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)} + \frac{B \sqrt{a} b e^{\frac{3}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{17}{4}\right)}"," ",0,"A*a**(3/2)*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(9/4)) + A*sqrt(a)*b*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4)) + B*a**(3/2)*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(13/4)) + B*sqrt(a)*b*e**(3/2)*x**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), b*x**2*exp_polar(I*pi)/a)/(2*gamma(17/4))","C",0
795,1,197,0,8.909599," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)*(e*x)**(1/2),x)","\frac{A a^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e \Gamma\left(\frac{7}{4}\right)} + \frac{A \sqrt{a} b \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{B a^{\frac{3}{2}} \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{B \sqrt{a} b \left(e x\right)^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{5} \Gamma\left(\frac{15}{4}\right)}"," ",0,"A*a**(3/2)*(e*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*e*gamma(7/4)) + A*sqrt(a)*b*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**3*gamma(11/4)) + B*a**(3/2)*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**3*gamma(11/4)) + B*sqrt(a)*b*(e*x)**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**5*gamma(15/4))","C",0
796,1,199,0,10.410592," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/(e*x)**(1/2),x)","\frac{A a^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{A \sqrt{a} b x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{B a^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{B \sqrt{a} b x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*a**(3/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(5/4)) + A*sqrt(a)*b*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(9/4)) + B*a**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(9/4)) + B*sqrt(a)*b*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(e)*gamma(13/4))","C",0
797,1,202,0,10.486071," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/(e*x)**(3/2),x)","\frac{A a^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{A \sqrt{a} b x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B a^{\frac{3}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{a} b x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*a**(3/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*sqrt(x)*gamma(3/4)) + A*sqrt(a)*b*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(7/4)) + B*a**(3/2)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(7/4)) + B*sqrt(a)*b*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(3/2)*gamma(11/4))","C",0
798,1,202,0,14.667149," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/(e*x)**(5/2),x)","\frac{A a^{\frac{3}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{A \sqrt{a} b \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{B a^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{B \sqrt{a} b x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*a**(3/2)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*x**(3/2)*gamma(1/4)) + A*sqrt(a)*b*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(5/4)) + B*a**(3/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(5/4)) + B*sqrt(a)*b*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(5/2)*gamma(9/4))","C",0
799,1,212,0,39.743093," ","integrate((b*x**2+a)**(3/2)*(B*x**2+A)/(e*x)**(7/2),x)","\frac{A a^{\frac{3}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{A \sqrt{a} b \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B a^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B \sqrt{a} b x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 e^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*a**(3/2)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*x**(5/2)*gamma(-1/4)) + A*sqrt(a)*b*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*sqrt(x)*gamma(3/4)) + B*a**(3/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*sqrt(x)*gamma(3/4)) + B*sqrt(a)*b*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*e**(7/2)*gamma(7/4))","C",0
800,1,94,0,25.887478," ","integrate((e*x)**(5/2)*(B*x**2+A)/(b*x**2+a)**(1/2),x)","\frac{A e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{11}{4}\right)} + \frac{B e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{15}{4}\right)}"," ",0,"A*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(11/4)) + B*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((1/2, 11/4), (15/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(15/4))","C",0
801,1,94,0,8.274301," ","integrate((e*x)**(3/2)*(B*x**2+A)/(b*x**2+a)**(1/2),x)","\frac{A e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{9}{4}\right)} + \frac{B e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(9/4)) + B*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((1/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*gamma(13/4))","C",0
802,1,92,0,3.960827," ","integrate((B*x**2+A)*(e*x)**(1/2)/(b*x**2+a)**(1/2),x)","\frac{A \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e \Gamma\left(\frac{7}{4}\right)} + \frac{B \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{3} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*(e*x)**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e*gamma(7/4)) + B*(e*x)**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**3*gamma(11/4))","C",0
803,1,94,0,2.841507," ","integrate((B*x**2+A)/(e*x)**(1/2)/(b*x**2+a)**(1/2),x)","\frac{A \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} \sqrt{e} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*sqrt(e)*gamma(5/4)) + B*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*sqrt(e)*gamma(9/4))","C",0
804,1,97,0,4.148259," ","integrate((B*x**2+A)/(e*x)**(3/2)/(b*x**2+a)**(1/2),x)","\frac{A \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(3/2)*sqrt(x)*gamma(3/4)) + B*x**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(3/2)*gamma(7/4))","C",0
805,1,97,0,9.412937," ","integrate((B*x**2+A)/(e*x)**(5/2)/(b*x**2+a)**(1/2),x)","\frac{A \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"A*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(5/2)*x**(3/2)*gamma(1/4)) + B*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(5/2)*gamma(5/4))","C",0
806,1,104,0,30.891416," ","integrate((B*x**2+A)/(e*x)**(7/2)/(b*x**2+a)**(1/2),x)","\frac{A \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 \sqrt{a} e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"A*gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(7/2)*x**(5/2)*gamma(-1/4)) + B*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*sqrt(a)*e**(7/2)*sqrt(x)*gamma(3/4))","C",0
807,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(B*x**2+A)/(b*x**2+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(B*x**2+A)/(b*x**2+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,1,94,0,38.481218," ","integrate((e*x)**(3/2)*(B*x**2+A)/(b*x**2+a)**(3/2),x)","\frac{A e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{B e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"A*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(9/4)) + B*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((3/2, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(13/4))","C",0
810,1,94,0,12.473699," ","integrate((B*x**2+A)*(e*x)**(1/2)/(b*x**2+a)**(3/2),x)","\frac{A \sqrt{e} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{e} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*sqrt(e)*x**(3/2)*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(7/4)) + B*sqrt(e)*x**(7/2)*gamma(7/4)*hyper((3/2, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(11/4))","C",0
811,1,94,0,14.060853," ","integrate((B*x**2+A)/(b*x**2+a)**(3/2)/(e*x)**(1/2),x)","\frac{A \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \sqrt{e} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*sqrt(x)*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*sqrt(e)*gamma(5/4)) + B*x**(5/2)*gamma(5/4)*hyper((5/4, 3/2), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*sqrt(e)*gamma(9/4))","C",0
812,1,97,0,24.790169," ","integrate((B*x**2+A)/(e*x)**(3/2)/(b*x**2+a)**(3/2),x)","\frac{A \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{B x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"A*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(3/2)*sqrt(x)*gamma(3/4)) + B*x**(3/2)*gamma(3/4)*hyper((3/4, 3/2), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(3/2)*gamma(7/4))","C",0
813,1,97,0,55.999864," ","integrate((B*x**2+A)/(e*x)**(5/2)/(b*x**2+a)**(3/2),x)","\frac{A \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{B \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"A*gamma(-3/4)*hyper((-3/4, 3/2), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(5/2)*x**(3/2)*gamma(1/4)) + B*sqrt(x)*gamma(1/4)*hyper((1/4, 3/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(5/2)*gamma(5/4))","C",0
814,1,104,0,132.170400," ","integrate((B*x**2+A)/(e*x)**(7/2)/(b*x**2+a)**(3/2),x)","\frac{A \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{3}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{B \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"A*gamma(-5/4)*hyper((-5/4, 3/2), (-1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(7/2)*x**(5/2)*gamma(-1/4)) + B*gamma(-1/4)*hyper((-1/4, 3/2), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/2)*e**(7/2)*sqrt(x)*gamma(3/4))","C",0
815,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate((e*x)**(3/2)*(B*x**2+A)/(b*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,1,94,0,65.674824," ","integrate((B*x**2+A)*(e*x)**(1/2)/(b*x**2+a)**(5/2),x)","\frac{A \sqrt{e} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{B \sqrt{e} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, \frac{5}{2} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"A*sqrt(e)*x**(3/2)*gamma(3/4)*hyper((3/4, 5/2), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(7/4)) + B*sqrt(e)*x**(7/2)*gamma(7/4)*hyper((7/4, 5/2), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*gamma(11/4))","C",0
819,1,94,0,119.020774," ","integrate((B*x**2+A)/(b*x**2+a)**(5/2)/(e*x)**(1/2),x)","\frac{A \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{5}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{B x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{2}} \sqrt{e} \Gamma\left(\frac{9}{4}\right)}"," ",0,"A*sqrt(x)*gamma(1/4)*hyper((1/4, 5/2), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*sqrt(e)*gamma(5/4)) + B*x**(5/2)*gamma(5/4)*hyper((5/4, 5/2), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/2)*sqrt(e)*gamma(9/4))","C",0
820,-1,0,0,0.000000," ","integrate((B*x**2+A)/(e*x)**(3/2)/(b*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate((B*x**2+A)/(e*x)**(5/2)/(b*x**2+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,1,150,0,21.696725," ","integrate((e*x)**(3/2)*(b*x**2+a)**2*(d*x**2+c)**(1/2),x)","\frac{a^{2} \sqrt{c} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{a b \sqrt{c} e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\Gamma\left(\frac{13}{4}\right)} + \frac{b^{2} \sqrt{c} e^{\frac{3}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{17}{4}\right)}"," ",0,"a**2*sqrt(c)*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(9/4)) + a*b*sqrt(c)*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/gamma(13/4) + b**2*sqrt(c)*e**(3/2)*x**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(17/4))","C",0
823,1,148,0,5.983359," ","integrate((b*x**2+a)**2*(e*x)**(1/2)*(d*x**2+c)**(1/2),x)","\frac{a^{2} \sqrt{c} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e \Gamma\left(\frac{7}{4}\right)} + \frac{a b \sqrt{c} \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{b^{2} \sqrt{c} \left(e x\right)^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{5} \Gamma\left(\frac{15}{4}\right)}"," ",0,"a**2*sqrt(c)*(e*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(2*e*gamma(7/4)) + a*b*sqrt(c)*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(e**3*gamma(11/4)) + b**2*sqrt(c)*(e*x)**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**5*gamma(15/4))","C",0
824,1,150,0,6.415304," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/(e*x)**(1/2),x)","\frac{a^{2} \sqrt{c} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{a b \sqrt{c} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{b^{2} \sqrt{c} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**2*sqrt(c)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(e)*gamma(5/4)) + a*b*sqrt(c)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(e)*gamma(9/4)) + b**2*sqrt(c)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(e)*gamma(13/4))","C",0
825,1,153,0,6.650151," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/(e*x)**(3/2),x)","\frac{a^{2} \sqrt{c} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{a b \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{b^{2} \sqrt{c} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**2*sqrt(c)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(3/2)*sqrt(x)*gamma(3/4)) + a*b*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(e**(3/2)*gamma(7/4)) + b**2*sqrt(c)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(3/2)*gamma(11/4))","C",0
826,1,153,0,9.908483," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/(e*x)**(5/2),x)","\frac{a^{2} \sqrt{c} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{a b \sqrt{c} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{b^{2} \sqrt{c} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**2*sqrt(c)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(5/2)*x**(3/2)*gamma(1/4)) + a*b*sqrt(c)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), d*x**2*exp_polar(I*pi)/c)/(e**(5/2)*gamma(5/4)) + b**2*sqrt(c)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(5/2)*gamma(9/4))","C",0
827,1,160,0,30.178690," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/(e*x)**(7/2),x)","\frac{a^{2} \sqrt{c} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{a b \sqrt{c} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{b^{2} \sqrt{c} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**2*sqrt(c)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(7/2)*x**(5/2)*gamma(-1/4)) + a*b*sqrt(c)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), d*x**2*exp_polar(I*pi)/c)/(e**(7/2)*sqrt(x)*gamma(3/4)) + b**2*sqrt(c)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(7/2)*gamma(7/4))","C",0
828,1,144,0,22.099321," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**(9/2),x)","\frac{a^{2} \sqrt{c} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)} + \frac{a b \sqrt{c} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{b^{2} \sqrt{c} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**2*sqrt(c)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), d*x**2*exp_polar(I*pi)/c)/(2*x**(7/2)*gamma(-3/4)) + a*b*sqrt(c)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), d*x**2*exp_polar(I*pi)/c)/(x**(3/2)*gamma(1/4)) + b**2*sqrt(c)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(5/4))","C",0
829,1,151,0,54.021382," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**(11/2),x)","\frac{a^{2} \sqrt{c} \Gamma\left(- \frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{9}{4}, - \frac{1}{2} \\ - \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 x^{\frac{9}{2}} \Gamma\left(- \frac{5}{4}\right)} + \frac{a b \sqrt{c} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{b^{2} \sqrt{c} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"a**2*sqrt(c)*gamma(-9/4)*hyper((-9/4, -1/2), (-5/4,), d*x**2*exp_polar(I*pi)/c)/(2*x**(9/2)*gamma(-5/4)) + a*b*sqrt(c)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), d*x**2*exp_polar(I*pi)/c)/(x**(5/2)*gamma(-1/4)) + b**2*sqrt(c)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(x)*gamma(3/4))","C",0
830,1,151,0,132.817530," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**(13/2),x)","\frac{a^{2} \sqrt{c} \Gamma\left(- \frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{11}{4}, - \frac{1}{2} \\ - \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 x^{\frac{11}{2}} \Gamma\left(- \frac{7}{4}\right)} + \frac{a b \sqrt{c} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, - \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)} + \frac{b^{2} \sqrt{c} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"a**2*sqrt(c)*gamma(-11/4)*hyper((-11/4, -1/2), (-7/4,), d*x**2*exp_polar(I*pi)/c)/(2*x**(11/2)*gamma(-7/4)) + a*b*sqrt(c)*gamma(-7/4)*hyper((-7/4, -1/2), (-3/4,), d*x**2*exp_polar(I*pi)/c)/(x**(7/2)*gamma(-3/4)) + b**2*sqrt(c)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), d*x**2*exp_polar(I*pi)/c)/(2*x**(3/2)*gamma(1/4))","C",0
831,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(d*x**2+c)**(1/2)/x**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,1,306,0,148.823557," ","integrate((e*x)**(5/2)*(b*x**2+a)**2*(d*x**2+c)**(3/2),x)","\frac{a^{2} c^{\frac{3}{2}} e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{11}{4}\right)} + \frac{a^{2} \sqrt{c} d e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{15}{4}\right)} + \frac{a b c^{\frac{3}{2}} e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\Gamma\left(\frac{15}{4}\right)} + \frac{a b \sqrt{c} d e^{\frac{5}{2}} x^{\frac{15}{2}} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\Gamma\left(\frac{19}{4}\right)} + \frac{b^{2} c^{\frac{3}{2}} e^{\frac{5}{2}} x^{\frac{15}{2}} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{19}{4}\right)} + \frac{b^{2} \sqrt{c} d e^{\frac{5}{2}} x^{\frac{19}{2}} \Gamma\left(\frac{19}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{19}{4} \\ \frac{23}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{23}{4}\right)}"," ",0,"a**2*c**(3/2)*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(11/4)) + a**2*sqrt(c)*d*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(15/4)) + a*b*c**(3/2)*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/gamma(15/4) + a*b*sqrt(c)*d*e**(5/2)*x**(15/2)*gamma(15/4)*hyper((-1/2, 15/4), (19/4,), d*x**2*exp_polar(I*pi)/c)/gamma(19/4) + b**2*c**(3/2)*e**(5/2)*x**(15/2)*gamma(15/4)*hyper((-1/2, 15/4), (19/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(19/4)) + b**2*sqrt(c)*d*e**(5/2)*x**(19/2)*gamma(19/4)*hyper((-1/2, 19/4), (23/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(23/4))","C",0
833,1,306,0,51.736607," ","integrate((e*x)**(3/2)*(b*x**2+a)**2*(d*x**2+c)**(3/2),x)","\frac{a^{2} c^{\frac{3}{2}} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{9}{4}\right)} + \frac{a^{2} \sqrt{c} d e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{13}{4}\right)} + \frac{a b c^{\frac{3}{2}} e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\Gamma\left(\frac{13}{4}\right)} + \frac{a b \sqrt{c} d e^{\frac{3}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\Gamma\left(\frac{17}{4}\right)} + \frac{b^{2} c^{\frac{3}{2}} e^{\frac{3}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{17}{4}\right)} + \frac{b^{2} \sqrt{c} d e^{\frac{3}{2}} x^{\frac{17}{2}} \Gamma\left(\frac{17}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{17}{4} \\ \frac{21}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \Gamma\left(\frac{21}{4}\right)}"," ",0,"a**2*c**(3/2)*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(9/4)) + a**2*sqrt(c)*d*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(13/4)) + a*b*c**(3/2)*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/gamma(13/4) + a*b*sqrt(c)*d*e**(3/2)*x**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), d*x**2*exp_polar(I*pi)/c)/gamma(17/4) + b**2*c**(3/2)*e**(3/2)*x**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(17/4)) + b**2*sqrt(c)*d*e**(3/2)*x**(17/2)*gamma(17/4)*hyper((-1/2, 17/4), (21/4,), d*x**2*exp_polar(I*pi)/c)/(2*gamma(21/4))","C",0
834,1,304,0,13.433764," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)*(e*x)**(1/2),x)","\frac{a^{2} c^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e \Gamma\left(\frac{7}{4}\right)} + \frac{a^{2} \sqrt{c} d \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{a b c^{\frac{3}{2}} \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{a b \sqrt{c} d \left(e x\right)^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{5} \Gamma\left(\frac{15}{4}\right)} + \frac{b^{2} c^{\frac{3}{2}} \left(e x\right)^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{5} \Gamma\left(\frac{15}{4}\right)} + \frac{b^{2} \sqrt{c} d \left(e x\right)^{\frac{15}{2}} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{7} \Gamma\left(\frac{19}{4}\right)}"," ",0,"a**2*c**(3/2)*(e*x)**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(2*e*gamma(7/4)) + a**2*sqrt(c)*d*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**3*gamma(11/4)) + a*b*c**(3/2)*(e*x)**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(e**3*gamma(11/4)) + a*b*sqrt(c)*d*(e*x)**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/(e**5*gamma(15/4)) + b**2*c**(3/2)*(e*x)**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**5*gamma(15/4)) + b**2*sqrt(c)*d*(e*x)**(15/2)*gamma(15/4)*hyper((-1/2, 15/4), (19/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**7*gamma(19/4))","C",0
835,1,306,0,18.152709," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/(e*x)**(1/2),x)","\frac{a^{2} c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{a^{2} \sqrt{c} d x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{a b c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{a b \sqrt{c} d x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{e} \Gamma\left(\frac{13}{4}\right)} + \frac{b^{2} c^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{13}{4}\right)} + \frac{b^{2} \sqrt{c} d x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{e} \Gamma\left(\frac{17}{4}\right)}"," ",0,"a**2*c**(3/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(e)*gamma(5/4)) + a**2*sqrt(c)*d*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(e)*gamma(9/4)) + a*b*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(e)*gamma(9/4)) + a*b*sqrt(c)*d*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(e)*gamma(13/4)) + b**2*c**(3/2)*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(e)*gamma(13/4)) + b**2*sqrt(c)*d*x**(13/2)*gamma(13/4)*hyper((-1/2, 13/4), (17/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(e)*gamma(17/4))","C",0
836,1,309,0,18.543666," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/(e*x)**(3/2),x)","\frac{a^{2} c^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{a^{2} \sqrt{c} d x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{a b c^{\frac{3}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{a b \sqrt{c} d x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)} + \frac{b^{2} c^{\frac{3}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)} + \frac{b^{2} \sqrt{c} d x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{3}{2}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"a**2*c**(3/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(3/2)*sqrt(x)*gamma(3/4)) + a**2*sqrt(c)*d*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(3/2)*gamma(7/4)) + a*b*c**(3/2)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(e**(3/2)*gamma(7/4)) + a*b*sqrt(c)*d*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(e**(3/2)*gamma(11/4)) + b**2*c**(3/2)*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(3/2)*gamma(11/4)) + b**2*sqrt(c)*d*x**(11/2)*gamma(11/4)*hyper((-1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(3/2)*gamma(15/4))","C",0
837,1,309,0,24.585871," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/(e*x)**(5/2),x)","\frac{a^{2} c^{\frac{3}{2}} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, - \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{a^{2} \sqrt{c} d \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{a b c^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{a b \sqrt{c} d x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{b^{2} c^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{b^{2} \sqrt{c} d x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{5}{2}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**2*c**(3/2)*gamma(-3/4)*hyper((-3/4, -1/2), (1/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(5/2)*x**(3/2)*gamma(1/4)) + a**2*sqrt(c)*d*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(5/2)*gamma(5/4)) + a*b*c**(3/2)*sqrt(x)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), d*x**2*exp_polar(I*pi)/c)/(e**(5/2)*gamma(5/4)) + a*b*sqrt(c)*d*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(e**(5/2)*gamma(9/4)) + b**2*c**(3/2)*x**(5/2)*gamma(5/4)*hyper((-1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(5/2)*gamma(9/4)) + b**2*sqrt(c)*d*x**(9/2)*gamma(9/4)*hyper((-1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(5/2)*gamma(13/4))","C",0
838,1,320,0,53.380611," ","integrate((b*x**2+a)**2*(d*x**2+c)**(3/2)/(e*x)**(7/2),x)","\frac{a^{2} c^{\frac{3}{2}} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, - \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{a^{2} \sqrt{c} d \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{a b c^{\frac{3}{2}} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{a b \sqrt{c} d x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{e^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{b^{2} c^{\frac{3}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{b^{2} \sqrt{c} d x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 e^{\frac{7}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**2*c**(3/2)*gamma(-5/4)*hyper((-5/4, -1/2), (-1/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(7/2)*x**(5/2)*gamma(-1/4)) + a**2*sqrt(c)*d*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(7/2)*sqrt(x)*gamma(3/4)) + a*b*c**(3/2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), d*x**2*exp_polar(I*pi)/c)/(e**(7/2)*sqrt(x)*gamma(3/4)) + a*b*sqrt(c)*d*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(e**(7/2)*gamma(7/4)) + b**2*c**(3/2)*x**(3/2)*gamma(3/4)*hyper((-1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(7/2)*gamma(7/4)) + b**2*sqrt(c)*d*x**(7/2)*gamma(7/4)*hyper((-1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(2*e**(7/2)*gamma(11/4))","C",0
839,1,144,0,49.387547," ","integrate((e*x)**(5/2)*(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\frac{a^{2} e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{11}{4}\right)} + \frac{a b e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} \Gamma\left(\frac{15}{4}\right)} + \frac{b^{2} e^{\frac{5}{2}} x^{\frac{15}{2}} \Gamma\left(\frac{15}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{15}{4} \\ \frac{19}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{19}{4}\right)}"," ",0,"a**2*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*gamma(11/4)) + a*b*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*gamma(15/4)) + b**2*e**(5/2)*x**(15/2)*gamma(15/4)*hyper((1/2, 15/4), (19/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*gamma(19/4))","C",0
840,1,144,0,16.253501," ","integrate((e*x)**(3/2)*(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\frac{a^{2} e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{9}{4}\right)} + \frac{a b e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} \Gamma\left(\frac{13}{4}\right)} + \frac{b^{2} e^{\frac{3}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} \Gamma\left(\frac{17}{4}\right)}"," ",0,"a**2*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*gamma(9/4)) + a*b*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*gamma(13/4)) + b**2*e**(3/2)*x**(13/2)*gamma(13/4)*hyper((1/2, 13/4), (17/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*gamma(17/4))","C",0
841,1,143,0,5.690754," ","integrate((b*x**2+a)**2*(e*x)**(1/2)/(d*x**2+c)**(1/2),x)","\frac{a^{2} \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e \Gamma\left(\frac{7}{4}\right)} + \frac{a b \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} e^{3} \Gamma\left(\frac{11}{4}\right)} + \frac{b^{2} \left(e x\right)^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{5} \Gamma\left(\frac{15}{4}\right)}"," ",0,"a**2*(e*x)**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e*gamma(7/4)) + a*b*(e*x)**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*e**3*gamma(11/4)) + b**2*(e*x)**(11/2)*gamma(11/4)*hyper((1/2, 11/4), (15/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**5*gamma(15/4))","C",0
842,1,144,0,5.310304," ","integrate((b*x**2+a)**2/(e*x)**(1/2)/(d*x**2+c)**(1/2),x)","\frac{a^{2} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} \sqrt{e} \Gamma\left(\frac{5}{4}\right)} + \frac{a b x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} \sqrt{e} \Gamma\left(\frac{9}{4}\right)} + \frac{b^{2} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} \sqrt{e} \Gamma\left(\frac{13}{4}\right)}"," ",0,"a**2*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*sqrt(e)*gamma(5/4)) + a*b*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*sqrt(e)*gamma(9/4)) + b**2*x**(9/2)*gamma(9/4)*hyper((1/2, 9/4), (13/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*sqrt(e)*gamma(13/4))","C",0
843,1,148,0,6.061399," ","integrate((b*x**2+a)**2/(e*x)**(3/2)/(d*x**2+c)**(1/2),x)","\frac{a^{2} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{a b x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{b^{2} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{3}{2}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"a**2*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(3/2)*sqrt(x)*gamma(3/4)) + a*b*x**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*e**(3/2)*gamma(7/4)) + b**2*x**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(3/2)*gamma(11/4))","C",0
844,1,148,0,12.596027," ","integrate((b*x**2+a)**2/(e*x)**(5/2)/(d*x**2+c)**(1/2),x)","\frac{a^{2} \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{a b \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{b^{2} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{5}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"a**2*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(5/2)*x**(3/2)*gamma(1/4)) + a*b*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*e**(5/2)*gamma(5/4)) + b**2*x**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(5/2)*gamma(9/4))","C",0
845,1,155,0,40.791891," ","integrate((b*x**2+a)**2/(e*x)**(7/2)/(d*x**2+c)**(1/2),x)","\frac{a^{2} \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{7}{2}} x^{\frac{5}{2}} \Gamma\left(- \frac{1}{4}\right)} + \frac{a b \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)} + \frac{b^{2} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"a**2*gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(7/2)*x**(5/2)*gamma(-1/4)) + a*b*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*e**(7/2)*sqrt(x)*gamma(3/4)) + b**2*x**(3/2)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(7/2)*gamma(7/4))","C",0
846,1,155,0,162.255233," ","integrate((b*x**2+a)**2/(e*x)**(9/2)/(d*x**2+c)**(1/2),x)","\frac{a^{2} \Gamma\left(- \frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{9}{2}} x^{\frac{7}{2}} \Gamma\left(- \frac{3}{4}\right)} + \frac{a b \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{\sqrt{c} e^{\frac{9}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{b^{2} \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{d x^{2} e^{i \pi}}{c}} \right)}}{2 \sqrt{c} e^{\frac{9}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"a**2*gamma(-7/4)*hyper((-7/4, 1/2), (-3/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(9/2)*x**(7/2)*gamma(-3/4)) + a*b*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), d*x**2*exp_polar(I*pi)/c)/(sqrt(c)*e**(9/2)*x**(3/2)*gamma(1/4)) + b**2*sqrt(x)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), d*x**2*exp_polar(I*pi)/c)/(2*sqrt(c)*e**(9/2)*gamma(5/4))","C",0
847,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(11/2)/(d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(13/2)/(d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,0,0,0,0.000000," ","integrate((e*x)**(3/2)*(b*x**2+a)**2/(d*x**2+c)**(3/2),x)","\int \frac{\left(e x\right)^{\frac{3}{2}} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((e*x)**(3/2)*(a + b*x**2)**2/(c + d*x**2)**(3/2), x)","F",0
852,0,0,0,0.000000," ","integrate((b*x**2+a)**2*(e*x)**(1/2)/(d*x**2+c)**(3/2),x)","\int \frac{\sqrt{e x} \left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(e*x)*(a + b*x**2)**2/(c + d*x**2)**(3/2), x)","F",0
853,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(d*x**2+c)**(3/2)/(e*x)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\sqrt{e x} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(sqrt(e*x)*(c + d*x**2)**(3/2)), x)","F",0
854,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(3/2)/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\left(e x\right)^{\frac{3}{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/((e*x)**(3/2)*(c + d*x**2)**(3/2)), x)","F",0
855,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(5/2)/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\left(e x\right)^{\frac{5}{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/((e*x)**(5/2)*(c + d*x**2)**(3/2)), x)","F",0
856,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(7/2)/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\left(e x\right)^{\frac{7}{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/((e*x)**(7/2)*(c + d*x**2)**(3/2)), x)","F",0
857,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate((e*x)**(3/2)*(b*x**2+a)**2/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate((b*x**2+a)**2*(e*x)**(1/2)/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(d*x**2+c)**(5/2)/(e*x)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\sqrt{e x} \left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(sqrt(e*x)*(c + d*x**2)**(5/2)), x)","F",0
862,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(3/2)/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
863,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(5/2)/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
864,-1,0,0,0.000000," ","integrate((b*x**2+a)**2/(e*x)**(7/2)/(d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,0,0,0,0.000000," ","integrate((e*x)**(3/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a),x)","- \int \frac{\left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}}}{- a + b x^{2}}\, dx"," ",0,"-Integral((e*x)**(3/2)*sqrt(c - d*x**2)/(-a + b*x**2), x)","F",0
868,0,0,0,0.000000," ","integrate((e*x)**(1/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a),x)","- \int \frac{\sqrt{e x} \sqrt{c - d x^{2}}}{- a + b x^{2}}\, dx"," ",0,"-Integral(sqrt(e*x)*sqrt(c - d*x**2)/(-a + b*x**2), x)","F",0
869,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(-b*x**2+a)/(e*x)**(1/2),x)","- \int \frac{\sqrt{c - d x^{2}}}{- a \sqrt{e x} + b x^{2} \sqrt{e x}}\, dx"," ",0,"-Integral(sqrt(c - d*x**2)/(-a*sqrt(e*x) + b*x**2*sqrt(e*x)), x)","F",0
870,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(e*x)**(3/2)/(-b*x**2+a),x)","- \int \frac{\sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{3}{2}} + b x^{2} \left(e x\right)^{\frac{3}{2}}}\, dx"," ",0,"-Integral(sqrt(c - d*x**2)/(-a*(e*x)**(3/2) + b*x**2*(e*x)**(3/2)), x)","F",0
871,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(e*x)**(5/2)/(-b*x**2+a),x)","- \int \frac{\sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{5}{2}} + b x^{2} \left(e x\right)^{\frac{5}{2}}}\, dx"," ",0,"-Integral(sqrt(c - d*x**2)/(-a*(e*x)**(5/2) + b*x**2*(e*x)**(5/2)), x)","F",0
872,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(e*x)**(7/2)/(-b*x**2+a),x)","- \int \frac{\sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{7}{2}} + b x^{2} \left(e x\right)^{\frac{7}{2}}}\, dx"," ",0,"-Integral(sqrt(c - d*x**2)/(-a*(e*x)**(7/2) + b*x**2*(e*x)**(7/2)), x)","F",0
873,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(-d*x**2+c)**(3/2)/(-b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,0,0,0,0.000000," ","integrate((e*x)**(3/2)*(-d*x**2+c)**(3/2)/(-b*x**2+a),x)","- \int \frac{c \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}}}{- a + b x^{2}}\, dx - \int \left(- \frac{d x^{2} \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}}}{- a + b x^{2}}\right)\, dx"," ",0,"-Integral(c*(e*x)**(3/2)*sqrt(c - d*x**2)/(-a + b*x**2), x) - Integral(-d*x**2*(e*x)**(3/2)*sqrt(c - d*x**2)/(-a + b*x**2), x)","F",0
875,0,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)*(e*x)**(1/2)/(-b*x**2+a),x)","- \int \frac{c \sqrt{e x} \sqrt{c - d x^{2}}}{- a + b x^{2}}\, dx - \int \left(- \frac{d x^{2} \sqrt{e x} \sqrt{c - d x^{2}}}{- a + b x^{2}}\right)\, dx"," ",0,"-Integral(c*sqrt(e*x)*sqrt(c - d*x**2)/(-a + b*x**2), x) - Integral(-d*x**2*sqrt(e*x)*sqrt(c - d*x**2)/(-a + b*x**2), x)","F",0
876,0,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)/(-b*x**2+a)/(e*x)**(1/2),x)","- \int \frac{c \sqrt{c - d x^{2}}}{- a \sqrt{e x} + b x^{2} \sqrt{e x}}\, dx - \int \left(- \frac{d x^{2} \sqrt{c - d x^{2}}}{- a \sqrt{e x} + b x^{2} \sqrt{e x}}\right)\, dx"," ",0,"-Integral(c*sqrt(c - d*x**2)/(-a*sqrt(e*x) + b*x**2*sqrt(e*x)), x) - Integral(-d*x**2*sqrt(c - d*x**2)/(-a*sqrt(e*x) + b*x**2*sqrt(e*x)), x)","F",0
877,0,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)/(e*x)**(3/2)/(-b*x**2+a),x)","- \int \frac{c \sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{3}{2}} + b x^{2} \left(e x\right)^{\frac{3}{2}}}\, dx - \int \left(- \frac{d x^{2} \sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{3}{2}} + b x^{2} \left(e x\right)^{\frac{3}{2}}}\right)\, dx"," ",0,"-Integral(c*sqrt(c - d*x**2)/(-a*(e*x)**(3/2) + b*x**2*(e*x)**(3/2)), x) - Integral(-d*x**2*sqrt(c - d*x**2)/(-a*(e*x)**(3/2) + b*x**2*(e*x)**(3/2)), x)","F",0
878,0,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)/(e*x)**(5/2)/(-b*x**2+a),x)","- \int \frac{c \sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{5}{2}} + b x^{2} \left(e x\right)^{\frac{5}{2}}}\, dx - \int \left(- \frac{d x^{2} \sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{5}{2}} + b x^{2} \left(e x\right)^{\frac{5}{2}}}\right)\, dx"," ",0,"-Integral(c*sqrt(c - d*x**2)/(-a*(e*x)**(5/2) + b*x**2*(e*x)**(5/2)), x) - Integral(-d*x**2*sqrt(c - d*x**2)/(-a*(e*x)**(5/2) + b*x**2*(e*x)**(5/2)), x)","F",0
879,0,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)/(e*x)**(7/2)/(-b*x**2+a),x)","- \int \frac{c \sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{7}{2}} + b x^{2} \left(e x\right)^{\frac{7}{2}}}\, dx - \int \left(- \frac{d x^{2} \sqrt{c - d x^{2}}}{- a \left(e x\right)^{\frac{7}{2}} + b x^{2} \left(e x\right)^{\frac{7}{2}}}\right)\, dx"," ",0,"-Integral(c*sqrt(c - d*x**2)/(-a*(e*x)**(7/2) + b*x**2*(e*x)**(7/2)), x) - Integral(-d*x**2*sqrt(c - d*x**2)/(-a*(e*x)**(7/2) + b*x**2*(e*x)**(7/2)), x)","F",0
880,-1,0,0,0.000000," ","integrate((e*x)**(7/2)/(-b*x**2+a)/(-d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,0,0,0,0.000000," ","integrate((e*x)**(5/2)/(-b*x**2+a)/(-d*x**2+c)**(1/2),x)","- \int \frac{\left(e x\right)^{\frac{5}{2}}}{- a \sqrt{c - d x^{2}} + b x^{2} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral((e*x)**(5/2)/(-a*sqrt(c - d*x**2) + b*x**2*sqrt(c - d*x**2)), x)","F",0
882,0,0,0,0.000000," ","integrate((e*x)**(3/2)/(-b*x**2+a)/(-d*x**2+c)**(1/2),x)","- \int \frac{\left(e x\right)^{\frac{3}{2}}}{- a \sqrt{c - d x^{2}} + b x^{2} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral((e*x)**(3/2)/(-a*sqrt(c - d*x**2) + b*x**2*sqrt(c - d*x**2)), x)","F",0
883,0,0,0,0.000000," ","integrate((e*x)**(1/2)/(-b*x**2+a)/(-d*x**2+c)**(1/2),x)","- \int \frac{\sqrt{e x}}{- a \sqrt{c - d x^{2}} + b x^{2} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(sqrt(e*x)/(-a*sqrt(c - d*x**2) + b*x**2*sqrt(c - d*x**2)), x)","F",0
884,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)/(e*x)**(1/2)/(-d*x**2+c)**(1/2),x)","- \int \frac{1}{- a \sqrt{e x} \sqrt{c - d x^{2}} + b x^{2} \sqrt{e x} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(1/(-a*sqrt(e*x)*sqrt(c - d*x**2) + b*x**2*sqrt(e*x)*sqrt(c - d*x**2)), x)","F",0
885,0,0,0,0.000000," ","integrate(1/(e*x)**(3/2)/(-b*x**2+a)/(-d*x**2+c)**(1/2),x)","- \int \frac{1}{- a \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}} + b x^{2} \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(1/(-a*(e*x)**(3/2)*sqrt(c - d*x**2) + b*x**2*(e*x)**(3/2)*sqrt(c - d*x**2)), x)","F",0
886,0,0,0,0.000000," ","integrate(1/(e*x)**(5/2)/(-b*x**2+a)/(-d*x**2+c)**(1/2),x)","- \int \frac{1}{- a \left(e x\right)^{\frac{5}{2}} \sqrt{c - d x^{2}} + b x^{2} \left(e x\right)^{\frac{5}{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(1/(-a*(e*x)**(5/2)*sqrt(c - d*x**2) + b*x**2*(e*x)**(5/2)*sqrt(c - d*x**2)), x)","F",0
887,0,0,0,0.000000," ","integrate(1/(e*x)**(7/2)/(-b*x**2+a)/(-d*x**2+c)**(1/2),x)","- \int \frac{1}{- a \left(e x\right)^{\frac{7}{2}} \sqrt{c - d x^{2}} + b x^{2} \left(e x\right)^{\frac{7}{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(1/(-a*(e*x)**(7/2)*sqrt(c - d*x**2) + b*x**2*(e*x)**(7/2)*sqrt(c - d*x**2)), x)","F",0
888,-1,0,0,0.000000," ","integrate((e*x)**(9/2)/(-b*x**2+a)/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate((e*x)**(7/2)/(-b*x**2+a)/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,0,0,0,0.000000," ","integrate((e*x)**(5/2)/(-b*x**2+a)/(-d*x**2+c)**(3/2),x)","- \int \frac{\left(e x\right)^{\frac{5}{2}}}{- a c \sqrt{c - d x^{2}} + a d x^{2} \sqrt{c - d x^{2}} + b c x^{2} \sqrt{c - d x^{2}} - b d x^{4} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral((e*x)**(5/2)/(-a*c*sqrt(c - d*x**2) + a*d*x**2*sqrt(c - d*x**2) + b*c*x**2*sqrt(c - d*x**2) - b*d*x**4*sqrt(c - d*x**2)), x)","F",0
891,0,0,0,0.000000," ","integrate((e*x)**(3/2)/(-b*x**2+a)/(-d*x**2+c)**(3/2),x)","- \int \frac{\left(e x\right)^{\frac{3}{2}}}{- a c \sqrt{c - d x^{2}} + a d x^{2} \sqrt{c - d x^{2}} + b c x^{2} \sqrt{c - d x^{2}} - b d x^{4} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral((e*x)**(3/2)/(-a*c*sqrt(c - d*x**2) + a*d*x**2*sqrt(c - d*x**2) + b*c*x**2*sqrt(c - d*x**2) - b*d*x**4*sqrt(c - d*x**2)), x)","F",0
892,0,0,0,0.000000," ","integrate((e*x)**(1/2)/(-b*x**2+a)/(-d*x**2+c)**(3/2),x)","- \int \frac{\sqrt{e x}}{- a c \sqrt{c - d x^{2}} + a d x^{2} \sqrt{c - d x^{2}} + b c x^{2} \sqrt{c - d x^{2}} - b d x^{4} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(sqrt(e*x)/(-a*c*sqrt(c - d*x**2) + a*d*x**2*sqrt(c - d*x**2) + b*c*x**2*sqrt(c - d*x**2) - b*d*x**4*sqrt(c - d*x**2)), x)","F",0
893,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)/(-d*x**2+c)**(3/2)/(e*x)**(1/2),x)","- \int \frac{1}{- a c \sqrt{e x} \sqrt{c - d x^{2}} + a d x^{2} \sqrt{e x} \sqrt{c - d x^{2}} + b c x^{2} \sqrt{e x} \sqrt{c - d x^{2}} - b d x^{4} \sqrt{e x} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(1/(-a*c*sqrt(e*x)*sqrt(c - d*x**2) + a*d*x**2*sqrt(e*x)*sqrt(c - d*x**2) + b*c*x**2*sqrt(e*x)*sqrt(c - d*x**2) - b*d*x**4*sqrt(e*x)*sqrt(c - d*x**2)), x)","F",0
894,0,0,0,0.000000," ","integrate(1/(e*x)**(3/2)/(-b*x**2+a)/(-d*x**2+c)**(3/2),x)","- \int \frac{1}{- a c \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}} + a d x^{2} \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}} + b c x^{2} \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}} - b d x^{4} \left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(1/(-a*c*(e*x)**(3/2)*sqrt(c - d*x**2) + a*d*x**2*(e*x)**(3/2)*sqrt(c - d*x**2) + b*c*x**2*(e*x)**(3/2)*sqrt(c - d*x**2) - b*d*x**4*(e*x)**(3/2)*sqrt(c - d*x**2)), x)","F",0
895,0,0,0,0.000000," ","integrate(1/(e*x)**(5/2)/(-b*x**2+a)/(-d*x**2+c)**(3/2),x)","- \int \frac{1}{- a c \left(e x\right)^{\frac{5}{2}} \sqrt{c - d x^{2}} + a d x^{2} \left(e x\right)^{\frac{5}{2}} \sqrt{c - d x^{2}} + b c x^{2} \left(e x\right)^{\frac{5}{2}} \sqrt{c - d x^{2}} - b d x^{4} \left(e x\right)^{\frac{5}{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"-Integral(1/(-a*c*(e*x)**(5/2)*sqrt(c - d*x**2) + a*d*x**2*(e*x)**(5/2)*sqrt(c - d*x**2) + b*c*x**2*(e*x)**(5/2)*sqrt(c - d*x**2) - b*d*x**4*(e*x)**(5/2)*sqrt(c - d*x**2)), x)","F",0
896,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,0,0,0,0.000000," ","integrate((e*x)**(3/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a)**2,x)","\int \frac{\left(e x\right)^{\frac{3}{2}} \sqrt{c - d x^{2}}}{\left(- a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((e*x)**(3/2)*sqrt(c - d*x**2)/(-a + b*x**2)**2, x)","F",0
899,0,0,0,0.000000," ","integrate((e*x)**(1/2)*(-d*x**2+c)**(1/2)/(-b*x**2+a)**2,x)","\int \frac{\sqrt{e x} \sqrt{c - d x^{2}}}{\left(- a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(e*x)*sqrt(c - d*x**2)/(-a + b*x**2)**2, x)","F",0
900,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(e*x)**(1/2)/(-b*x**2+a)**2,x)","\int \frac{\sqrt{c - d x^{2}}}{\sqrt{e x} \left(- a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c - d*x**2)/(sqrt(e*x)*(-a + b*x**2)**2), x)","F",0
901,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(e*x)**(3/2)/(-b*x**2+a)**2,x)","\int \frac{\sqrt{c - d x^{2}}}{\left(e x\right)^{\frac{3}{2}} \left(- a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c - d*x**2)/((e*x)**(3/2)*(-a + b*x**2)**2), x)","F",0
902,-1,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(e*x)**(5/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(-d*x**2+c)**(3/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(-d*x**2+c)**(3/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,-1,0,0,0.000000," ","integrate((e*x)**(3/2)*(-d*x**2+c)**(3/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,0,0,0,0.000000," ","integrate((e*x)**(1/2)*(-d*x**2+c)**(3/2)/(-b*x**2+a)**2,x)","\int \frac{\sqrt{e x} \left(c - d x^{2}\right)^{\frac{3}{2}}}{\left(- a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(e*x)*(c - d*x**2)**(3/2)/(-a + b*x**2)**2, x)","F",0
907,0,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)/(e*x)**(1/2)/(-b*x**2+a)**2,x)","\int \frac{\left(c - d x^{2}\right)^{\frac{3}{2}}}{\sqrt{e x} \left(- a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((c - d*x**2)**(3/2)/(sqrt(e*x)*(-a + b*x**2)**2), x)","F",0
908,-1,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)/(e*x)**(3/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,-1,0,0,0.000000," ","integrate((-d*x**2+c)**(3/2)/(e*x)**(5/2)/(-b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,-1,0,0,0.000000," ","integrate((e*x)**(9/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,-1,0,0,0.000000," ","integrate((e*x)**(7/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
912,-1,0,0,0.000000," ","integrate((e*x)**(5/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
913,0,0,0,0.000000," ","integrate((e*x)**(3/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\int \frac{\left(e x\right)^{\frac{3}{2}}}{\left(- a + b x^{2}\right)^{2} \sqrt{c - d x^{2}}}\, dx"," ",0,"Integral((e*x)**(3/2)/((-a + b*x**2)**2*sqrt(c - d*x**2)), x)","F",0
914,0,0,0,0.000000," ","integrate((e*x)**(1/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\int \frac{\sqrt{e x}}{\left(- a + b x^{2}\right)^{2} \sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(e*x)/((-a + b*x**2)**2*sqrt(c - d*x**2)), x)","F",0
915,0,0,0,0.000000," ","integrate(1/(e*x)**(1/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{e x} \left(- a + b x^{2}\right)^{2} \sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(e*x)*(-a + b*x**2)**2*sqrt(c - d*x**2)), x)","F",0
916,0,0,0,0.000000," ","integrate(1/(e*x)**(3/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\int \frac{1}{\left(e x\right)^{\frac{3}{2}} \left(- a + b x^{2}\right)^{2} \sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(1/((e*x)**(3/2)*(-a + b*x**2)**2*sqrt(c - d*x**2)), x)","F",0
917,-1,0,0,0.000000," ","integrate(1/(e*x)**(5/2)/(-b*x**2+a)**2/(-d*x**2+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
918,-1,0,0,0.000000," ","integrate((e*x)**(9/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,-1,0,0,0.000000," ","integrate((e*x)**(7/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,-1,0,0,0.000000," ","integrate((e*x)**(5/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
921,-1,0,0,0.000000," ","integrate((e*x)**(3/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
922,-1,0,0,0.000000," ","integrate((e*x)**(1/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
923,-1,0,0,0.000000," ","integrate(1/(e*x)**(1/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
924,-1,0,0,0.000000," ","integrate(1/(e*x)**(3/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
925,-1,0,0,0.000000," ","integrate(1/(e*x)**(5/2)/(-b*x**2+a)**2/(-d*x**2+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate((e*x)**(9/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,-1,0,0,0.000000," ","integrate((e*x)**(7/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
928,-1,0,0,0.000000," ","integrate((e*x)**(5/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
929,-1,0,0,0.000000," ","integrate((e*x)**(3/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
930,-1,0,0,0.000000," ","integrate((e*x)**(1/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
931,-1,0,0,0.000000," ","integrate(1/(e*x)**(1/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
932,-1,0,0,0.000000," ","integrate(1/(e*x)**(3/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
933,-1,0,0,0.000000," ","integrate(1/(e*x)**(5/2)/(-b*x**2+a)**2/(-d*x**2+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
934,0,0,0,0.000000," ","integrate(x**5*(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5} \sqrt{a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5*sqrt(a + b*x**2)/sqrt(c + d*x**2), x)","F",0
935,0,0,0,0.000000," ","integrate(x**3*(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3} \sqrt{a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3*sqrt(a + b*x**2)/sqrt(c + d*x**2), x)","F",0
936,0,0,0,0.000000," ","integrate(x*(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x \sqrt{a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x*sqrt(a + b*x**2)/sqrt(c + d*x**2), x)","F",0
937,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/x/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{x \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(x*sqrt(c + d*x**2)), x)","F",0
938,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/x**3/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{x^{3} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(x**3*sqrt(c + d*x**2)), x)","F",0
939,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/x**5/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{x^{5} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(x**5*sqrt(c + d*x**2)), x)","F",0
940,0,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{4} \sqrt{a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**4*sqrt(a + b*x**2)/sqrt(c + d*x**2), x)","F",0
941,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{2} \sqrt{a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*x**2)/sqrt(c + d*x**2), x)","F",0
942,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/x**2/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{x^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(x**2*sqrt(c + d*x**2)), x)","F",0
943,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/x**4/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{x^{4} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(x**4*sqrt(c + d*x**2)), x)","F",0
944,0,0,0,0.000000," ","integrate(x**5*(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5} \left(a + b x^{2}\right)^{\frac{3}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5*(a + b*x**2)**(3/2)/sqrt(c + d*x**2), x)","F",0
945,0,0,0,0.000000," ","integrate(x**3*(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3} \left(a + b x^{2}\right)^{\frac{3}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3*(a + b*x**2)**(3/2)/sqrt(c + d*x**2), x)","F",0
946,0,0,0,0.000000," ","integrate(x*(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x \left(a + b x^{2}\right)^{\frac{3}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x*(a + b*x**2)**(3/2)/sqrt(c + d*x**2), x)","F",0
947,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/x/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{x \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(x*sqrt(c + d*x**2)), x)","F",0
948,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/x**3/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{x^{3} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(x**3*sqrt(c + d*x**2)), x)","F",0
949,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/x**5/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{x^{5} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(x**5*sqrt(c + d*x**2)), x)","F",0
950,0,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{4} \left(a + b x^{2}\right)^{\frac{3}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**4*(a + b*x**2)**(3/2)/sqrt(c + d*x**2), x)","F",0
951,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{2} \left(a + b x^{2}\right)^{\frac{3}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x**2)**(3/2)/sqrt(c + d*x**2), x)","F",0
952,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/x**2/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{x^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(x**2*sqrt(c + d*x**2)), x)","F",0
953,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/x**4/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{x^{4} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(x**4*sqrt(c + d*x**2)), x)","F",0
954,0,0,0,0.000000," ","integrate(x**5*(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5} \left(a + b x^{2}\right)^{\frac{5}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5*(a + b*x**2)**(5/2)/sqrt(c + d*x**2), x)","F",0
955,0,0,0,0.000000," ","integrate(x**3*(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3} \left(a + b x^{2}\right)^{\frac{5}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3*(a + b*x**2)**(5/2)/sqrt(c + d*x**2), x)","F",0
956,0,0,0,0.000000," ","integrate(x*(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x \left(a + b x^{2}\right)^{\frac{5}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x*(a + b*x**2)**(5/2)/sqrt(c + d*x**2), x)","F",0
957,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/x/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{x \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(x*sqrt(c + d*x**2)), x)","F",0
958,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/x**3/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{x^{3} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(x**3*sqrt(c + d*x**2)), x)","F",0
959,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/x**5/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{x^{5} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(x**5*sqrt(c + d*x**2)), x)","F",0
960,0,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{4} \left(a + b x^{2}\right)^{\frac{5}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**4*(a + b*x**2)**(5/2)/sqrt(c + d*x**2), x)","F",0
961,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{2} \left(a + b x^{2}\right)^{\frac{5}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x**2)**(5/2)/sqrt(c + d*x**2), x)","F",0
962,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/x**2/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{x^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(x**2*sqrt(c + d*x**2)), x)","F",0
963,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/x**4/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{x^{4} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(x**4*sqrt(c + d*x**2)), x)","F",0
964,0,0,0,0.000000," ","integrate(x**4*(3*x**2-1)**(1/2)/(-3*x**2+2)**(1/2),x)","\int \frac{x^{4} \sqrt{3 x^{2} - 1}}{\sqrt{2 - 3 x^{2}}}\, dx"," ",0,"Integral(x**4*sqrt(3*x**2 - 1)/sqrt(2 - 3*x**2), x)","F",0
965,0,0,0,0.000000," ","integrate(x**3*(3*x**2-1)**(1/2)/(-3*x**2+2)**(1/2),x)","\int \frac{x^{3} \sqrt{3 x^{2} - 1}}{\sqrt{2 - 3 x^{2}}}\, dx"," ",0,"Integral(x**3*sqrt(3*x**2 - 1)/sqrt(2 - 3*x**2), x)","F",0
966,0,0,0,0.000000," ","integrate(x**2*(3*x**2-1)**(1/2)/(-3*x**2+2)**(1/2),x)","\int \frac{x^{2} \sqrt{3 x^{2} - 1}}{\sqrt{2 - 3 x^{2}}}\, dx"," ",0,"Integral(x**2*sqrt(3*x**2 - 1)/sqrt(2 - 3*x**2), x)","F",0
967,1,66,0,6.109197," ","integrate(x*(3*x**2-1)**(1/2)/(-3*x**2+2)**(1/2),x)","\frac{\begin{cases} - \frac{\sqrt{2 - 3 x^{2}} \sqrt{3 x^{2} - 1}}{2} + \frac{\operatorname{asin}{\left(\sqrt{3 x^{2} - 1} \right)}}{2} & \text{for}\: \left(x \geq \frac{\sqrt{3}}{3} \wedge x < \frac{\sqrt{6}}{3}\right) \vee \left(x \leq - \frac{\sqrt{3}}{3} \wedge x > - \frac{\sqrt{6}}{3}\right) \end{cases}}{3}"," ",0,"Piecewise((-sqrt(2 - 3*x**2)*sqrt(3*x**2 - 1)/2 + asin(sqrt(3*x**2 - 1))/2, ((x >= sqrt(3)/3) & (x < sqrt(6)/3)) | ((x <= -sqrt(3)/3) & (x > -sqrt(6)/3))))/3","A",0
968,0,0,0,0.000000," ","integrate(x**2*(b*x**2+2)**(1/2)/(d*x**2+3)**(1/2),x)","\int \frac{x^{2} \sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}\, dx"," ",0,"Integral(x**2*sqrt(b*x**2 + 2)/sqrt(d*x**2 + 3), x)","F",0
969,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5}}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
970,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
971,0,0,0,0.000000," ","integrate(x/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
972,0,0,0,0.000000," ","integrate(1/x/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x \sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x*sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
973,0,0,0,0.000000," ","integrate(1/x**3/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
974,0,0,0,0.000000," ","integrate(1/x**5/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{5} \sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**5*sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
975,0,0,0,0.000000," ","integrate(x**6/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{6}}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**6/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
976,0,0,0,0.000000," ","integrate(x**4/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{4}}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**4/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
977,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**2/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
978,0,0,0,0.000000," ","integrate(1/x**2/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
979,0,0,0,0.000000," ","integrate(1/x**4/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{x^{4} \sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(x**4*sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
980,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5}}{\left(a + b x^{2}\right)^{\frac{3}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**2)**(3/2)*sqrt(c + d*x**2)), x)","F",0
981,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3}}{\left(a + b x^{2}\right)^{\frac{3}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)**(3/2)*sqrt(c + d*x**2)), x)","F",0
982,0,0,0,0.000000," ","integrate(x/(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{x}{\left(a + b x^{2}\right)^{\frac{3}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x/((a + b*x**2)**(3/2)*sqrt(c + d*x**2)), x)","F",0
983,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5}}{\left(a + b x^{2}\right)^{\frac{5}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**2)**(5/2)*sqrt(c + d*x**2)), x)","F",0
984,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3}}{\left(a + b x^{2}\right)^{\frac{5}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)**(5/2)*sqrt(c + d*x**2)), x)","F",0
985,0,0,0,0.000000," ","integrate(x/(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{x}{\left(a + b x^{2}\right)^{\frac{5}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x/((a + b*x**2)**(5/2)*sqrt(c + d*x**2)), x)","F",0
986,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a)**(7/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5}}{\left(a + b x^{2}\right)^{\frac{7}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**2)**(7/2)*sqrt(c + d*x**2)), x)","F",0
987,0,0,0,0.000000," ","integrate(x**3/(b*x**2+a)**(7/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{3}}{\left(a + b x^{2}\right)^{\frac{7}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**3/((a + b*x**2)**(7/2)*sqrt(c + d*x**2)), x)","F",0
988,0,0,0,0.000000," ","integrate(x/(b*x**2+a)**(7/2)/(d*x**2+c)**(1/2),x)","\int \frac{x}{\left(a + b x^{2}\right)^{\frac{7}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x/((a + b*x**2)**(7/2)*sqrt(c + d*x**2)), x)","F",0
989,0,0,0,0.000000," ","integrate(x**5/(b*x**2+a)**(9/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{5}}{\left(a + b x^{2}\right)^{\frac{9}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**5/((a + b*x**2)**(9/2)*sqrt(c + d*x**2)), x)","F",0
990,0,0,0,0.000000," ","integrate(x/(-b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{a - b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x/(sqrt(a - b*x**2)*sqrt(c + d*x**2)), x)","F",0
991,0,0,0,0.000000," ","integrate(x/(-b*x**2+a)**(1/2)/(-d*x**2+c)**(1/2),x)","\int \frac{x}{\sqrt{a - b x^{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(x/(sqrt(a - b*x**2)*sqrt(c - d*x**2)), x)","F",0
992,0,0,0,0.000000," ","integrate(x**2/(b*x**2+2)**(1/2)/(d*x**2+3)**(1/2),x)","\int \frac{x^{2}}{\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}}\, dx"," ",0,"Integral(x**2/(sqrt(b*x**2 + 2)*sqrt(d*x**2 + 3)), x)","F",0
993,0,0,0,0.000000," ","integrate(x**2/(-x**2+4)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(x - 2\right) \left(x + 2\right)} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(x**2/(sqrt(-(x - 2)*(x + 2))*sqrt(c + d*x**2)), x)","F",0
994,0,0,0,0.000000," ","integrate(x**2/(x**2+4)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{x^{2}}{\sqrt{c + d x^{2}} \sqrt{x^{2} + 4}}\, dx"," ",0,"Integral(x**2/(sqrt(c + d*x**2)*sqrt(x**2 + 4)), x)","F",0
995,0,0,0,0.000000," ","integrate(x**2/(-x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(x**2/(sqrt(-(x - 1)*(x + 1))*sqrt(3*x**2 + 2)), x)","F",0
996,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(1/2)/(-x**2+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \sqrt{2 - 3 x^{2}}}\, dx"," ",0,"Integral(x**2/(sqrt(-(x - 1)*(x + 1))*sqrt(2 - 3*x**2)), x)","F",0
997,0,0,0,0.000000," ","integrate(x**2/(-x**2+4)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(x - 2\right) \left(x + 2\right)} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(x**2/(sqrt(-(x - 2)*(x + 2))*sqrt(3*x**2 + 2)), x)","F",0
998,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(1/2)/(-x**2+4)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(x - 2\right) \left(x + 2\right)} \sqrt{2 - 3 x^{2}}}\, dx"," ",0,"Integral(x**2/(sqrt(-(x - 2)*(x + 2))*sqrt(2 - 3*x**2)), x)","F",0
999,0,0,0,0.000000," ","integrate(x**2/(-4*x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(2 x - 1\right) \left(2 x + 1\right)} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(x**2/(sqrt(-(2*x - 1)*(2*x + 1))*sqrt(3*x**2 + 2)), x)","F",0
1000,0,0,0,0.000000," ","integrate(x**2/(-4*x**2+1)**(1/2)/(-3*x**2+2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(2 x - 1\right) \left(2 x + 1\right)} \sqrt{2 - 3 x^{2}}}\, dx"," ",0,"Integral(x**2/(sqrt(-(2*x - 1)*(2*x + 1))*sqrt(2 - 3*x**2)), x)","F",0
1001,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{2 - 3 x^{2}} \sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(x**2/(sqrt(2 - 3*x**2)*sqrt(x**2 + 1)), x)","F",0
1002,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(1/2)/(x**2+4)**(1/2),x)","\int \frac{x^{2}}{\sqrt{2 - 3 x^{2}} \sqrt{x^{2} + 4}}\, dx"," ",0,"Integral(x**2/(sqrt(2 - 3*x**2)*sqrt(x**2 + 4)), x)","F",0
1003,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(1/2)/(4*x**2+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{2 - 3 x^{2}} \sqrt{4 x^{2} + 1}}\, dx"," ",0,"Integral(x**2/(sqrt(2 - 3*x**2)*sqrt(4*x**2 + 1)), x)","F",0
1004,0,0,0,0.000000," ","integrate(x**2/(x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{x^{2} + 1} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(x**2/(sqrt(x**2 + 1)*sqrt(3*x**2 + 2)), x)","F",0
1005,0,0,0,0.000000," ","integrate(x**2/(x**2+4)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{x^{2} + 4} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(x**2/(sqrt(x**2 + 4)*sqrt(3*x**2 + 2)), x)","F",0
1006,0,0,0,0.000000," ","integrate(x**2/(3*x**2+2)**(1/2)/(4*x**2+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{3 x^{2} + 2} \sqrt{4 x^{2} + 1}}\, dx"," ",0,"Integral(x**2/(sqrt(3*x**2 + 2)*sqrt(4*x**2 + 1)), x)","F",0
1007,0,0,0,0.000000," ","integrate(x**2/(-x**2+1)**(1/2)/(2*x**2-1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \sqrt{2 x^{2} - 1}}\, dx"," ",0,"Integral(x**2/(sqrt(-(x - 1)*(x + 1))*sqrt(2*x**2 - 1)), x)","F",0
1008,0,0,0,0.000000," ","integrate(x**5/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{x^{5}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(x**5/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1009,0,0,0,0.000000," ","integrate(x**3/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{x^{3}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(x**3/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1010,0,0,0,0.000000," ","integrate(x/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{x}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(x/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1011,0,0,0,0.000000," ","integrate(1/x/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{x \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/(x*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1012,0,0,0,0.000000," ","integrate(1/x**3/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{x^{3} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/(x**3*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1013,0,0,0,0.000000," ","integrate(1/x**5/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{x^{5} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/(x**5*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1014,0,0,0,0.000000," ","integrate(x**4/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{x^{4}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(x**4/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1015,0,0,0,0.000000," ","integrate(x**2/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{x^{2}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(x**2/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1016,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1017,0,0,0,0.000000," ","integrate(1/x**2/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{x^{2} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/(x**2*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1018,0,0,0,0.000000," ","integrate(1/x**4/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{x^{4} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/(x**4*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
1019,0,0,0,0.000000," ","integrate(x**7/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{x^{7}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(x**7/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1020,0,0,0,0.000000," ","integrate(x**5/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{x^{5}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(x**5/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1021,0,0,0,0.000000," ","integrate(x**3/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{x^{3}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(x**3/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1022,0,0,0,0.000000," ","integrate(x/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{x}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(x/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1023,0,0,0,0.000000," ","integrate(1/x/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{1}{x \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(1/(x*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1024,0,0,0,0.000000," ","integrate(1/x**3/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{1}{x^{3} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(1/(x**3*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1025,0,0,0,0.000000," ","integrate(1/x**5/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{1}{x^{5} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(1/(x**5*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1026,0,0,0,0.000000," ","integrate(x**4/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{x^{4}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(x**4/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1027,0,0,0,0.000000," ","integrate(x**2/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{x^{2}}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(x**2/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1028,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{1}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(1/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1029,0,0,0,0.000000," ","integrate(1/x**2/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{1}{x^{2} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1030,0,0,0,0.000000," ","integrate(1/x**4/(-x**2+1)**(1/3)/(x**2+3)**2,x)","\int \frac{1}{x^{4} \sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)^{2}}\, dx"," ",0,"Integral(1/(x**4*(-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)**2), x)","F",0
1031,0,0,0,0.000000," ","integrate(x**7/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{x^{7}}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(x**7/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
1032,0,0,0,0.000000," ","integrate(x**5/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{x^{5}}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(x**5/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
1033,0,0,0,0.000000," ","integrate(x**3/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{x^{3}}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(x**3/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
1034,0,0,0,0.000000," ","integrate(x/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{x}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(x/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
1035,0,0,0,0.000000," ","integrate(1/x/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{3} \sqrt[4]{2 - 3 x^{2}} - 4 x \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(3*x**3*(2 - 3*x**2)**(1/4) - 4*x*(2 - 3*x**2)**(1/4)), x)","F",0
1036,0,0,0,0.000000," ","integrate(1/x**3/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{5} \sqrt[4]{2 - 3 x^{2}} - 4 x^{3} \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(3*x**5*(2 - 3*x**2)**(1/4) - 4*x**3*(2 - 3*x**2)**(1/4)), x)","F",0
1037,0,0,0,0.000000," ","integrate(x**4/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{x^{4}}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(x**4/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
1038,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{x^{2}}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(x**2/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
1039,0,0,0,0.000000," ","integrate(1/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
1040,0,0,0,0.000000," ","integrate(1/x**2/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{4} \sqrt[4]{2 - 3 x^{2}} - 4 x^{2} \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(3*x**4*(2 - 3*x**2)**(1/4) - 4*x**2*(2 - 3*x**2)**(1/4)), x)","F",0
1041,0,0,0,0.000000," ","integrate(1/x**4/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{6} \sqrt[4]{2 - 3 x^{2}} - 4 x^{4} \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(3*x**6*(2 - 3*x**2)**(1/4) - 4*x**4*(2 - 3*x**2)**(1/4)), x)","F",0
1042,1,88,0,24.081872," ","integrate(x**7/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\frac{2 \left(3 x^{2} - 1\right)^{\frac{11}{4}}}{891} + \frac{8 \left(3 x^{2} - 1\right)^{\frac{7}{4}}}{567} + \frac{14 \left(3 x^{2} - 1\right)^{\frac{3}{4}}}{243} + \frac{4 \log{\left(\sqrt[4]{3 x^{2} - 1} - 1 \right)}}{81} - \frac{4 \log{\left(\sqrt[4]{3 x^{2} - 1} + 1 \right)}}{81} + \frac{8 \operatorname{atan}{\left(\sqrt[4]{3 x^{2} - 1} \right)}}{81}"," ",0,"2*(3*x**2 - 1)**(11/4)/891 + 8*(3*x**2 - 1)**(7/4)/567 + 14*(3*x**2 - 1)**(3/4)/243 + 4*log((3*x**2 - 1)**(1/4) - 1)/81 - 4*log((3*x**2 - 1)**(1/4) + 1)/81 + 8*atan((3*x**2 - 1)**(1/4))/81","A",0
1043,1,75,0,18.983029," ","integrate(x**5/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\frac{2 \left(3 x^{2} - 1\right)^{\frac{7}{4}}}{189} + \frac{2 \left(3 x^{2} - 1\right)^{\frac{3}{4}}}{27} + \frac{2 \log{\left(\sqrt[4]{3 x^{2} - 1} - 1 \right)}}{27} - \frac{2 \log{\left(\sqrt[4]{3 x^{2} - 1} + 1 \right)}}{27} + \frac{4 \operatorname{atan}{\left(\sqrt[4]{3 x^{2} - 1} \right)}}{27}"," ",0,"2*(3*x**2 - 1)**(7/4)/189 + 2*(3*x**2 - 1)**(3/4)/27 + 2*log((3*x**2 - 1)**(1/4) - 1)/27 - 2*log((3*x**2 - 1)**(1/4) + 1)/27 + 4*atan((3*x**2 - 1)**(1/4))/27","A",0
1044,1,58,0,14.208147," ","integrate(x**3/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\frac{2 \left(3 x^{2} - 1\right)^{\frac{3}{4}}}{27} + \frac{\log{\left(\sqrt[4]{3 x^{2} - 1} - 1 \right)}}{9} - \frac{\log{\left(\sqrt[4]{3 x^{2} - 1} + 1 \right)}}{9} + \frac{2 \operatorname{atan}{\left(\sqrt[4]{3 x^{2} - 1} \right)}}{9}"," ",0,"2*(3*x**2 - 1)**(3/4)/27 + log((3*x**2 - 1)**(1/4) - 1)/9 - log((3*x**2 - 1)**(1/4) + 1)/9 + 2*atan((3*x**2 - 1)**(1/4))/9","A",0
1045,1,42,0,8.986176," ","integrate(x/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\frac{\log{\left(\sqrt[4]{3 x^{2} - 1} - 1 \right)}}{6} - \frac{\log{\left(\sqrt[4]{3 x^{2} - 1} + 1 \right)}}{6} + \frac{\operatorname{atan}{\left(\sqrt[4]{3 x^{2} - 1} \right)}}{3}"," ",0,"log((3*x**2 - 1)**(1/4) - 1)/6 - log((3*x**2 - 1)**(1/4) + 1)/6 + atan((3*x**2 - 1)**(1/4))/3","A",0
1046,0,0,0,0.000000," ","integrate(1/x/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{1}{x \left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(1/(x*(3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
1047,0,0,0,0.000000," ","integrate(1/x**3/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{1}{x^{3} \left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(1/(x**3*(3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
1048,0,0,0,0.000000," ","integrate(x**4/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{x^{4}}{\left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(x**4/((3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
1049,0,0,0,0.000000," ","integrate(x**2/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{x^{2}}{\left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(x**2/((3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
1050,0,0,0,0.000000," ","integrate(1/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{1}{\left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(1/((3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
1051,0,0,0,0.000000," ","integrate(1/x**2/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{1}{x^{2} \left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(1/(x**2*(3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
1052,0,0,0,0.000000," ","integrate(1/x**4/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{1}{x^{4} \left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(1/(x**4*(3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
1053,0,0,0,0.000000," ","integrate(x**2/(3*x**2+2)**(3/4)/(3*x**2+4),x)","\int \frac{x^{2}}{\left(3 x^{2} + 2\right)^{\frac{3}{4}} \left(3 x^{2} + 4\right)}\, dx"," ",0,"Integral(x**2/((3*x**2 + 2)**(3/4)*(3*x**2 + 4)), x)","F",0
1054,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x^{2}}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1055,0,0,0,0.000000," ","integrate(x**2/(b*x**2+2)**(3/4)/(b*x**2+4),x)","\int \frac{x^{2}}{\left(b x^{2} + 2\right)^{\frac{3}{4}} \left(b x^{2} + 4\right)}\, dx"," ",0,"Integral(x**2/((b*x**2 + 2)**(3/4)*(b*x**2 + 4)), x)","F",0
1056,0,0,0,0.000000," ","integrate(x**2/(-b*x**2+2)**(3/4)/(-b*x**2+4),x)","- \int \frac{x^{2}}{b x^{2} \left(- b x^{2} + 2\right)^{\frac{3}{4}} - 4 \left(- b x^{2} + 2\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(b*x**2*(-b*x**2 + 2)**(3/4) - 4*(-b*x**2 + 2)**(3/4)), x)","F",0
1057,0,0,0,0.000000," ","integrate(x**2/(3*x**2+a)**(3/4)/(3*x**2+2*a),x)","\int \frac{x^{2}}{\left(a + 3 x^{2}\right)^{\frac{3}{4}} \left(2 a + 3 x^{2}\right)}\, dx"," ",0,"Integral(x**2/((a + 3*x**2)**(3/4)*(2*a + 3*x**2)), x)","F",0
1058,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+a)**(3/4)/(-3*x**2+2*a),x)","- \int \frac{x^{2}}{- 2 a \left(a - 3 x^{2}\right)^{\frac{3}{4}} + 3 x^{2} \left(a - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(-2*a*(a - 3*x**2)**(3/4) + 3*x**2*(a - 3*x**2)**(3/4)), x)","F",0
1059,0,0,0,0.000000," ","integrate(x**2/(b*x**2+a)**(3/4)/(b*x**2+2*a),x)","\int \frac{x^{2}}{\left(a + b x^{2}\right)^{\frac{3}{4}} \left(2 a + b x^{2}\right)}\, dx"," ",0,"Integral(x**2/((a + b*x**2)**(3/4)*(2*a + b*x**2)), x)","F",0
1060,0,0,0,0.000000," ","integrate(x**2/(-b*x**2+a)**(3/4)/(-b*x**2+2*a),x)","- \int \frac{x^{2}}{- 2 a \left(a - b x^{2}\right)^{\frac{3}{4}} + b x^{2} \left(a - b x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(-2*a*(a - b*x**2)**(3/4) + b*x**2*(a - b*x**2)**(3/4)), x)","F",0
1061,0,0,0,0.000000," ","integrate(x**7/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x^{7}}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**7/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1062,0,0,0,0.000000," ","integrate(x**5/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x^{5}}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**5/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1063,0,0,0,0.000000," ","integrate(x**3/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x^{3}}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**3/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1064,0,0,0,0.000000," ","integrate(x/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1065,0,0,0,0.000000," ","integrate(1/x/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{3} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 x \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(1/(3*x**3*(2 - 3*x**2)**(3/4) - 4*x*(2 - 3*x**2)**(3/4)), x)","F",0
1066,0,0,0,0.000000," ","integrate(1/x**3/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{5} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 x^{3} \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(1/(3*x**5*(2 - 3*x**2)**(3/4) - 4*x**3*(2 - 3*x**2)**(3/4)), x)","F",0
1067,0,0,0,0.000000," ","integrate(x**6/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x^{6}}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**6/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1068,0,0,0,0.000000," ","integrate(x**4/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x^{4}}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**4/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1069,0,0,0,0.000000," ","integrate(x**2/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{x^{2}}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1070,0,0,0,0.000000," ","integrate(1/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(1/(3*x**2*(2 - 3*x**2)**(3/4) - 4*(2 - 3*x**2)**(3/4)), x)","F",0
1071,0,0,0,0.000000," ","integrate(1/x**2/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{4} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 x^{2} \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(1/(3*x**4*(2 - 3*x**2)**(3/4) - 4*x**2*(2 - 3*x**2)**(3/4)), x)","F",0
1072,0,0,0,0.000000," ","integrate(1/x**4/(-3*x**2+2)**(3/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{6} \left(2 - 3 x^{2}\right)^{\frac{3}{4}} - 4 x^{4} \left(2 - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(1/(3*x**6*(2 - 3*x**2)**(3/4) - 4*x**4*(2 - 3*x**2)**(3/4)), x)","F",0
1073,0,0,0,0.000000," ","integrate(x**2/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{x^{2}}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**2/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1074,0,0,0,0.000000," ","integrate(x**2/(-3*x**2-2)/(-3*x**2-1)**(3/4),x)","- \int \frac{x^{2}}{3 x^{2} \left(- 3 x^{2} - 1\right)^{\frac{3}{4}} + 2 \left(- 3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(3*x**2*(-3*x**2 - 1)**(3/4) + 2*(-3*x**2 - 1)**(3/4)), x)","F",0
1075,0,0,0,0.000000," ","integrate(x**2/(b*x**2-2)/(b*x**2-1)**(3/4),x)","\int \frac{x^{2}}{\left(b x^{2} - 2\right) \left(b x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**2/((b*x**2 - 2)*(b*x**2 - 1)**(3/4)), x)","F",0
1076,0,0,0,0.000000," ","integrate(x**2/(-b*x**2-2)/(-b*x**2-1)**(3/4),x)","- \int \frac{x^{2}}{b x^{2} \left(- b x^{2} - 1\right)^{\frac{3}{4}} + 2 \left(- b x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(b*x**2*(-b*x**2 - 1)**(3/4) + 2*(-b*x**2 - 1)**(3/4)), x)","F",0
1077,0,0,0,0.000000," ","integrate(x**2/(3*x**2-2*a)/(3*x**2-a)**(3/4),x)","\int \frac{x^{2}}{\left(- 2 a + 3 x^{2}\right) \left(- a + 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**2/((-2*a + 3*x**2)*(-a + 3*x**2)**(3/4)), x)","F",0
1078,0,0,0,0.000000," ","integrate(x**2/(-3*x**2-2*a)/(-3*x**2-a)**(3/4),x)","- \int \frac{x^{2}}{2 a \left(- a - 3 x^{2}\right)^{\frac{3}{4}} + 3 x^{2} \left(- a - 3 x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(2*a*(-a - 3*x**2)**(3/4) + 3*x**2*(-a - 3*x**2)**(3/4)), x)","F",0
1079,0,0,0,0.000000," ","integrate(x**2/(b*x**2-2*a)/(b*x**2-a)**(3/4),x)","\int \frac{x^{2}}{\left(- 2 a + b x^{2}\right) \left(- a + b x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**2/((-2*a + b*x**2)*(-a + b*x**2)**(3/4)), x)","F",0
1080,0,0,0,0.000000," ","integrate(x**2/(-b*x**2-2*a)/(-b*x**2-a)**(3/4),x)","- \int \frac{x^{2}}{2 a \left(- a - b x^{2}\right)^{\frac{3}{4}} + b x^{2} \left(- a - b x^{2}\right)^{\frac{3}{4}}}\, dx"," ",0,"-Integral(x**2/(2*a*(-a - b*x**2)**(3/4) + b*x**2*(-a - b*x**2)**(3/4)), x)","F",0
1081,0,0,0,0.000000," ","integrate(x**7/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{x^{7}}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**7/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1082,0,0,0,0.000000," ","integrate(x**5/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{x^{5}}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**5/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1083,0,0,0,0.000000," ","integrate(x**3/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{x^{3}}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**3/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1084,1,42,0,9.730703," ","integrate(x/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\frac{\log{\left(\sqrt[4]{3 x^{2} - 1} - 1 \right)}}{6} - \frac{\log{\left(\sqrt[4]{3 x^{2} - 1} + 1 \right)}}{6} - \frac{\operatorname{atan}{\left(\sqrt[4]{3 x^{2} - 1} \right)}}{3}"," ",0,"log((3*x**2 - 1)**(1/4) - 1)/6 - log((3*x**2 - 1)**(1/4) + 1)/6 - atan((3*x**2 - 1)**(1/4))/3","A",0
1085,0,0,0,0.000000," ","integrate(1/x/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{1}{x \left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x*(3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1086,0,0,0,0.000000," ","integrate(1/x**3/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{1}{x^{3} \left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x**3*(3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1087,0,0,0,0.000000," ","integrate(x**6/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{x^{6}}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**6/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1088,0,0,0,0.000000," ","integrate(x**4/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{x^{4}}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**4/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1089,0,0,0,0.000000," ","integrate(x**2/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{x^{2}}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(x**2/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1090,0,0,0,0.000000," ","integrate(1/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{1}{\left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1091,0,0,0,0.000000," ","integrate(1/x**2/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{1}{x^{2} \left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x**2*(3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1092,0,0,0,0.000000," ","integrate(1/x**4/(3*x**2-2)/(3*x**2-1)**(3/4),x)","\int \frac{1}{x^{4} \left(3 x^{2} - 2\right) \left(3 x^{2} - 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(x**4*(3*x**2 - 2)*(3*x**2 - 1)**(3/4)), x)","F",0
1093,1,94,0,41.582108," ","integrate((e*x)**(5/2)*(d*x**2+c)/(b*x**2+a)**(3/4),x)","\frac{c e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{11}{4}\right)} + \frac{d e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"c*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((3/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(11/4)) + d*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((3/4, 11/4), (15/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(15/4))","C",0
1094,1,92,0,5.830666," ","integrate((e*x)**(1/2)*(d*x**2+c)/(b*x**2+a)**(3/4),x)","\frac{c \left(e x\right)^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} e \Gamma\left(\frac{7}{4}\right)} + \frac{d \left(e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} e^{3} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c*(e*x)**(3/2)*gamma(3/4)*hyper((3/4, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*e*gamma(7/4)) + d*(e*x)**(7/2)*gamma(7/4)*hyper((3/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*e**3*gamma(11/4))","C",0
1095,1,85,0,10.423377," ","integrate((d*x**2+c)/(e*x)**(3/2)/(b*x**2+a)**(3/4),x)","\frac{\sqrt[4]{b} c \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{1}{4}\right)}{2 a e^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)} + \frac{d x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} e^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"b**(1/4)*c*(a/(b*x**2) + 1)**(1/4)*gamma(-1/4)/(2*a*e**(3/2)*gamma(3/4)) + d*x**(3/2)*gamma(3/4)*hyper((3/4, 3/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*e**(3/2)*gamma(7/4))","C",0
1096,1,121,0,59.813413," ","integrate((d*x**2+c)/(e*x)**(7/2)/(b*x**2+a)**(3/4),x)","- \frac{\sqrt[4]{b} c \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{8 a e^{\frac{7}{2}} x^{2} \Gamma\left(\frac{3}{4}\right)} + \frac{\sqrt[4]{b} d \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{1}{4}\right)}{2 a e^{\frac{7}{2}} \Gamma\left(\frac{3}{4}\right)} + \frac{b^{\frac{5}{4}} c \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(- \frac{5}{4}\right)}{2 a^{2} e^{\frac{7}{2}} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-b**(1/4)*c*(a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(8*a*e**(7/2)*x**2*gamma(3/4)) + b**(1/4)*d*(a/(b*x**2) + 1)**(1/4)*gamma(-1/4)/(2*a*e**(7/2)*gamma(3/4)) + b**(5/4)*c*(a/(b*x**2) + 1)**(1/4)*gamma(-5/4)/(2*a**2*e**(7/2)*gamma(3/4))","B",0
1097,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(11/2)/(b*x**2+a)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1098,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(15/2)/(b*x**2+a)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1099,1,94,0,111.056103," ","integrate((e*x)**(7/2)*(d*x**2+c)/(b*x**2+a)**(3/4),x)","\frac{c e^{\frac{7}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{13}{4}\right)} + \frac{d e^{\frac{7}{2}} x^{\frac{13}{2}} \Gamma\left(\frac{13}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{13}{4} \\ \frac{17}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{17}{4}\right)}"," ",0,"c*e**(7/2)*x**(9/2)*gamma(9/4)*hyper((3/4, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(13/4)) + d*e**(7/2)*x**(13/2)*gamma(13/4)*hyper((3/4, 13/4), (17/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(17/4))","C",0
1100,1,94,0,12.737790," ","integrate((e*x)**(3/2)*(d*x**2+c)/(b*x**2+a)**(3/4),x)","\frac{c e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{9}{4}\right)} + \frac{d e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((3/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(9/4)) + d*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((3/4, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*gamma(13/4))","C",0
1101,1,78,0,6.295579," ","integrate((d*x**2+c)/(e*x)**(1/2)/(b*x**2+a)**(3/4),x)","- \frac{c {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{b^{\frac{3}{4}} \sqrt{e} x} + \frac{d x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} \sqrt{e} \Gamma\left(\frac{9}{4}\right)}"," ",0,"-c*hyper((1/2, 3/4), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(b**(3/4)*sqrt(e)*x) + d*x**(5/2)*gamma(5/4)*hyper((3/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*sqrt(e)*gamma(9/4))","C",0
1102,1,82,0,24.540825," ","integrate((d*x**2+c)/(e*x)**(5/2)/(b*x**2+a)**(3/4),x)","- \frac{d {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{b^{\frac{3}{4}} e^{\frac{5}{2}} x} + \frac{c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-d*hyper((1/2, 3/4), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(b**(3/4)*e**(5/2)*x) + c*gamma(-3/4)*hyper((-3/4, 3/4), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*e**(5/2)*x**(3/2)*gamma(1/4))","C",0
1103,1,85,0,170.508705," ","integrate((d*x**2+c)/(e*x)**(9/2)/(b*x**2+a)**(3/4),x)","- \frac{c {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{5 b^{\frac{3}{4}} e^{\frac{9}{2}} x^{5}} + \frac{d \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{3}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{4}} e^{\frac{9}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-c*hyper((3/4, 5/2), (7/2,), a*exp_polar(I*pi)/(b*x**2))/(5*b**(3/4)*e**(9/2)*x**5) + d*gamma(-3/4)*hyper((-3/4, 3/4), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(3/4)*e**(9/2)*x**(3/2)*gamma(1/4))","C",0
1104,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(13/2)/(b*x**2+a)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1105,1,94,0,32.825341," ","integrate((e*x)**(3/2)*(d*x**2+c)/(b*x**2+a)**(5/4),x)","\frac{c e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{9}{4}\right)} + \frac{d e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(9/4)) + d*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((5/4, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(13/4))","C",0
1106,1,83,0,16.057258," ","integrate((d*x**2+c)/(e*x)**(1/2)/(b*x**2+a)**(5/4),x)","\frac{c \Gamma\left(\frac{1}{4}\right)}{2 a \sqrt[4]{b} \sqrt{e} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{5}{4}\right)} + \frac{d x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \sqrt{e} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c*gamma(1/4)/(2*a*b**(1/4)*sqrt(e)*(a/(b*x**2) + 1)**(1/4)*gamma(5/4)) + d*x**(5/2)*gamma(5/4)*hyper((5/4, 5/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*sqrt(e)*gamma(9/4))","C",0
1107,1,117,0,64.285130," ","integrate((d*x**2+c)/(e*x)**(5/2)/(b*x**2+a)**(5/4),x)","c \left(\frac{\Gamma\left(- \frac{3}{4}\right)}{8 a \sqrt[4]{b} e^{\frac{5}{2}} x^{2} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{5}{4}\right)} + \frac{b^{\frac{3}{4}} \Gamma\left(- \frac{3}{4}\right)}{2 a^{2} e^{\frac{5}{2}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{5}{4}\right)}\right) + \frac{d \Gamma\left(\frac{1}{4}\right)}{2 a \sqrt[4]{b} e^{\frac{5}{2}} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{5}{4}\right)}"," ",0,"c*(gamma(-3/4)/(8*a*b**(1/4)*e**(5/2)*x**2*(a/(b*x**2) + 1)**(1/4)*gamma(5/4)) + b**(3/4)*gamma(-3/4)/(2*a**2*e**(5/2)*(a/(b*x**2) + 1)**(1/4)*gamma(5/4))) + d*gamma(1/4)/(2*a*b**(1/4)*e**(5/2)*(a/(b*x**2) + 1)**(1/4)*gamma(5/4))","A",0
1108,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(9/2)/(b*x**2+a)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1109,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(13/2)/(b*x**2+a)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,-1,0,0,0.000000," ","integrate((e*x)**(9/2)*(d*x**2+c)/(b*x**2+a)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1111,1,94,0,155.666622," ","integrate((e*x)**(5/2)*(d*x**2+c)/(b*x**2+a)**(5/4),x)","\frac{c e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{11}{4}\right)} + \frac{d e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"c*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((5/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(11/4)) + d*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((5/4, 11/4), (15/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(15/4))","C",0
1112,1,94,0,17.351298," ","integrate((e*x)**(1/2)*(d*x**2+c)/(b*x**2+a)**(5/4),x)","\frac{c \sqrt{e} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{7}{4}\right)} + \frac{d \sqrt{e} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c*sqrt(e)*x**(3/2)*gamma(3/4)*hyper((3/4, 5/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(7/4)) + d*sqrt(e)*x**(7/2)*gamma(7/4)*hyper((5/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*gamma(11/4))","C",0
1113,1,82,0,38.276042," ","integrate((d*x**2+c)/(e*x)**(3/2)/(b*x**2+a)**(5/4),x)","- \frac{d {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{b^{\frac{5}{4}} e^{\frac{3}{2}} x} + \frac{c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} e^{\frac{3}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-d*hyper((1/2, 5/4), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(b**(5/4)*e**(3/2)*x) + c*gamma(-1/4)*hyper((-1/4, 5/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*e**(3/2)*sqrt(x)*gamma(3/4))","C",0
1114,1,85,0,169.393537," ","integrate((d*x**2+c)/(e*x)**(7/2)/(b*x**2+a)**(5/4),x)","- \frac{c {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{5 b^{\frac{5}{4}} e^{\frac{7}{2}} x^{5}} + \frac{d \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{5}{4}} e^{\frac{7}{2}} \sqrt{x} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-c*hyper((5/4, 5/2), (7/2,), a*exp_polar(I*pi)/(b*x**2))/(5*b**(5/4)*e**(7/2)*x**5) + d*gamma(-1/4)*hyper((-1/4, 5/4), (3/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(5/4)*e**(7/2)*sqrt(x)*gamma(3/4))","C",0
1115,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(11/2)/(b*x**2+a)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1116,1,94,0,166.391605," ","integrate((e*x)**(5/2)*(d*x**2+c)/(b*x**2+a)**(7/4),x)","\frac{c e^{\frac{5}{2}} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{11}{4}\right)} + \frac{d e^{\frac{5}{2}} x^{\frac{11}{2}} \Gamma\left(\frac{11}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{15}{4}\right)}"," ",0,"c*e**(5/2)*x**(7/2)*gamma(7/4)*hyper((7/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(11/4)) + d*e**(5/2)*x**(11/2)*gamma(11/4)*hyper((7/4, 11/4), (15/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(15/4))","C",0
1117,1,87,0,21.768245," ","integrate((e*x)**(1/2)*(d*x**2+c)/(b*x**2+a)**(7/4),x)","\frac{c \sqrt{e} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)}{2 a^{\frac{7}{4}} \left(1 + \frac{b x^{2}}{a}\right)^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)} + \frac{d \sqrt{e} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c*sqrt(e)*x**(3/2)*gamma(3/4)/(2*a**(7/4)*(1 + b*x**2/a)**(3/4)*gamma(7/4)) + d*sqrt(e)*x**(7/2)*gamma(7/4)*hyper((7/4, 7/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(11/4))","C",0
1118,1,119,0,79.593989," ","integrate((d*x**2+c)/(e*x)**(3/2)/(b*x**2+a)**(7/4),x)","c \left(\frac{3 \Gamma\left(- \frac{1}{4}\right)}{8 a b^{\frac{3}{4}} e^{\frac{3}{2}} x^{2} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)} + \frac{\sqrt[4]{b} \Gamma\left(- \frac{1}{4}\right)}{2 a^{2} e^{\frac{3}{2}} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)}\right) + \frac{d \Gamma\left(\frac{3}{4}\right)}{2 a b^{\frac{3}{4}} e^{\frac{3}{2}} \left(\frac{a}{b x^{2}} + 1\right)^{\frac{3}{4}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"c*(3*gamma(-1/4)/(8*a*b**(3/4)*e**(3/2)*x**2*(a/(b*x**2) + 1)**(3/4)*gamma(7/4)) + b**(1/4)*gamma(-1/4)/(2*a**2*e**(3/2)*(a/(b*x**2) + 1)**(3/4)*gamma(7/4))) + d*gamma(3/4)/(2*a*b**(3/4)*e**(3/2)*(a/(b*x**2) + 1)**(3/4)*gamma(7/4))","A",0
1119,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(7/2)/(b*x**2+a)**(7/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1120,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(11/2)/(b*x**2+a)**(7/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1121,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(d*x**2+c)/(b*x**2+a)**(7/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1122,1,94,0,70.518578," ","integrate((e*x)**(3/2)*(d*x**2+c)/(b*x**2+a)**(7/4),x)","\frac{c e^{\frac{3}{2}} x^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{9}{4}\right)} + \frac{d e^{\frac{3}{2}} x^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \Gamma\left(\frac{13}{4}\right)}"," ",0,"c*e**(3/2)*x**(5/2)*gamma(5/4)*hyper((5/4, 7/4), (9/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(9/4)) + d*e**(3/2)*x**(9/2)*gamma(9/4)*hyper((7/4, 9/4), (13/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*gamma(13/4))","C",0
1123,1,78,0,41.634794," ","integrate((d*x**2+c)/(e*x)**(1/2)/(b*x**2+a)**(7/4),x)","- \frac{d {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{3}{2} \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{b^{\frac{7}{4}} \sqrt{e} x} + \frac{c \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} \sqrt{e} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-d*hyper((1/2, 7/4), (3/2,), a*exp_polar(I*pi)/(b*x**2))/(b**(7/4)*sqrt(e)*x) + c*sqrt(x)*gamma(1/4)*hyper((1/4, 7/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*sqrt(e)*gamma(5/4))","C",0
1124,1,97,0,130.920679," ","integrate((d*x**2+c)/(e*x)**(5/2)/(b*x**2+a)**(7/4),x)","\frac{c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{7}{4} \\ \frac{1}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} e^{\frac{5}{2}} x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right)} + \frac{d \sqrt{x} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{7}{4}} e^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"c*gamma(-3/4)*hyper((-3/4, 7/4), (1/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*e**(5/2)*x**(3/2)*gamma(1/4)) + d*sqrt(x)*gamma(1/4)*hyper((1/4, 7/4), (5/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(7/4)*e**(5/2)*gamma(5/4))","C",0
1125,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(9/2)/(b*x**2+a)**(7/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,-1,0,0,0.000000," ","integrate((e*x)**(7/2)*(d*x**2+c)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1127,-1,0,0,0.000000," ","integrate((e*x)**(3/2)*(d*x**2+c)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1128,1,230,0,165.872063," ","integrate((d*x**2+c)/(e*x)**(1/2)/(b*x**2+a)**(9/4),x)","c \left(\frac{5 a \Gamma\left(\frac{1}{4}\right)}{8 a^{3} \sqrt[4]{b} \sqrt{e} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{9}{4}\right) + 8 a^{2} b^{\frac{5}{4}} \sqrt{e} x^{2} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{9}{4}\right)} + \frac{4 b x^{2} \Gamma\left(\frac{1}{4}\right)}{8 a^{3} \sqrt[4]{b} \sqrt{e} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{9}{4}\right) + 8 a^{2} b^{\frac{5}{4}} \sqrt{e} x^{2} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{9}{4}\right)}\right) + \frac{d \Gamma\left(\frac{5}{4}\right)}{\frac{2 a^{2} \sqrt[4]{b} \sqrt{e} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{9}{4}\right)}{x^{2}} + 2 a b^{\frac{5}{4}} \sqrt{e} \sqrt[4]{\frac{a}{b x^{2}} + 1} \Gamma\left(\frac{9}{4}\right)}"," ",0,"c*(5*a*gamma(1/4)/(8*a**3*b**(1/4)*sqrt(e)*(a/(b*x**2) + 1)**(1/4)*gamma(9/4) + 8*a**2*b**(5/4)*sqrt(e)*x**2*(a/(b*x**2) + 1)**(1/4)*gamma(9/4)) + 4*b*x**2*gamma(1/4)/(8*a**3*b**(1/4)*sqrt(e)*(a/(b*x**2) + 1)**(1/4)*gamma(9/4) + 8*a**2*b**(5/4)*sqrt(e)*x**2*(a/(b*x**2) + 1)**(1/4)*gamma(9/4))) + d*gamma(5/4)/(2*a**2*b**(1/4)*sqrt(e)*(a/(b*x**2) + 1)**(1/4)*gamma(9/4)/x**2 + 2*a*b**(5/4)*sqrt(e)*(a/(b*x**2) + 1)**(1/4)*gamma(9/4))","B",0
1129,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(5/2)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1130,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(9/2)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1131,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(13/2)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1132,-1,0,0,0.000000," ","integrate((e*x)**(13/2)*(d*x**2+c)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1133,-1,0,0,0.000000," ","integrate((e*x)**(9/2)*(d*x**2+c)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1134,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(d*x**2+c)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1135,1,94,0,93.602002," ","integrate((e*x)**(1/2)*(d*x**2+c)/(b*x**2+a)**(9/4),x)","\frac{c \sqrt{e} x^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{4}, \frac{9}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{9}{4}} \Gamma\left(\frac{7}{4}\right)} + \frac{d \sqrt{e} x^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{4}, \frac{9}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{2 a^{\frac{9}{4}} \Gamma\left(\frac{11}{4}\right)}"," ",0,"c*sqrt(e)*x**(3/2)*gamma(3/4)*hyper((3/4, 9/4), (7/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(9/4)*gamma(7/4)) + d*sqrt(e)*x**(7/2)*gamma(7/4)*hyper((7/4, 9/4), (11/4,), b*x**2*exp_polar(I*pi)/a)/(2*a**(9/4)*gamma(11/4))","C",0
1136,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(3/2)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1137,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(7/2)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1138,-1,0,0,0.000000," ","integrate((d*x**2+c)/(e*x)**(11/2)/(b*x**2+a)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1139,-1,0,0,0.000000," ","integrate((e*x)**m*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1140,-1,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1141,-1,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1142,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1143,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1144,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1145,-1,0,0,0.000000," ","integrate(x**5*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1146,-1,0,0,0.000000," ","integrate(x**3*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1147,-1,0,0,0.000000," ","integrate(x*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1148,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1149,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1150,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,-1,0,0,0.000000," ","integrate((e*x)**(5/2)*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1152,-1,0,0,0.000000," ","integrate((e*x)**(3/2)*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1153,-1,0,0,0.000000," ","integrate((e*x)**(1/2)*(b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/(e*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1155,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/(e*x)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1156,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q/(e*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
