1,1,192,0,16.250498," ","integrate(x**3*(B*x+A)*(b*x**2+a)**(1/2),x)","A \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) - \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*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)) - 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))","A",0
2,1,165,0,10.138790," ","integrate(x**2*(B*x+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}}} + B \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,"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*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
3,1,124,0,14.405028," ","integrate(x*(B*x+A)*(b*x**2+a)**(1/2),x)","A \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) + \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*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + 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
4,1,70,0,6.509798," ","integrate((B*x+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}} + 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,"A*sqrt(a)*x*sqrt(1 + b*x**2/a)/2 + A*a*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b)) + B*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True))","A",0
5,1,107,0,8.799631," ","integrate((B*x+A)*(b*x**2+a)**(1/2)/x,x)","- A \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)} + \frac{A a}{\sqrt{b} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A \sqrt{b} x}{\sqrt{\frac{a}{b x^{2}} + 1}} + \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)*asinh(sqrt(a)/(sqrt(b)*x)) + A*a/(sqrt(b)*x*sqrt(a/(b*x**2) + 1)) + A*sqrt(b)*x/sqrt(a/(b*x**2) + 1) + B*sqrt(a)*x*sqrt(1 + b*x**2/a)/2 + B*a*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b))","A",0
6,1,124,0,11.971730," ","integrate((B*x+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}}} - 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(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)*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
7,1,107,0,5.499421," ","integrate((B*x+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}} - \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)/(2*x) - A*b*asinh(sqrt(a)/(sqrt(b)*x))/(2*sqrt(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
8,1,318,0,20.788858," ","integrate(x**3*(B*x+A)*(b*x**2+a)**(3/2),x)","A a \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) + A b \left(\begin{cases} \frac{8 a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) - \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*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*b*Piecewise((8*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + a*x**4*sqrt(a + b*x**2)/(35*b) + x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*x**6/6, True)) - 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))","A",0
9,1,287,0,20.410760," ","integrate(x**2*(B*x+A)*(b*x**2+a)**(3/2),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}}} + B a \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) + B b \left(\begin{cases} \frac{8 a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",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)) + B*a*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)) + B*b*Piecewise((8*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + a*x**4*sqrt(a + b*x**2)/(35*b) + x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
10,1,223,0,22.469231," ","integrate(x*(B*x+A)*(b*x**2+a)**(3/2),x)","A a \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) + A b \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) + \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*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + A*b*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)) + 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))","A",0
11,1,219,0,12.911625," ","integrate((B*x+A)*(b*x**2+a)**(3/2),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}}} + B a \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 \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,"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*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + B*b*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
12,1,218,0,35.492336," ","integrate((B*x+A)*(b*x**2+a)**(3/2)/x,x)","- A a^{\frac{3}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)} + \frac{A a^{2}}{\sqrt{b} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A a \sqrt{b} x}{\sqrt{\frac{a}{b x^{2}} + 1}} + 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) + \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)*asinh(sqrt(a)/(sqrt(b)*x)) + A*a**2/(sqrt(b)*x*sqrt(a/(b*x**2) + 1)) + A*a*sqrt(b)*x/sqrt(a/(b*x**2) + 1) + A*b*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + 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))","A",0
13,1,184,0,13.289866," ","integrate((B*x+A)*(b*x**2+a)**(3/2)/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} - 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,"-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)*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
14,1,182,0,15.566211," ","integrate((B*x+A)*(b*x**2+a)**(3/2)/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}} - \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,"-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)/(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
15,1,469,0,37.442283," ","integrate(x**3*(B*x+A)*(b*x**2+a)**(5/2),x)","A a^{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) + 2 A a b \left(\begin{cases} \frac{8 a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + A b^{2} \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + b x^{2}}}{315 b^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + b x^{2}}}{315 b^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{6} \sqrt{a + b x^{2}}}{63 b} + \frac{x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) - \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,"A*a**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)) + 2*A*a*b*Piecewise((8*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + a*x**4*sqrt(a + b*x**2)/(35*b) + x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + A*b**2*Piecewise((-16*a**4*sqrt(a + b*x**2)/(315*b**4) + 8*a**3*x**2*sqrt(a + b*x**2)/(315*b**3) - 2*a**2*x**4*sqrt(a + b*x**2)/(105*b**2) + a*x**6*sqrt(a + b*x**2)/(63*b) + x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (sqrt(a)*x**8/8, True)) - 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))","A",0
16,1,442,0,61.217308," ","integrate(x**2*(B*x+A)*(b*x**2+a)**(5/2),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}}} + B a^{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) + 2 B a b \left(\begin{cases} \frac{8 a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + B b^{2} \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + b x^{2}}}{315 b^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + b x^{2}}}{315 b^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{6} \sqrt{a + b x^{2}}}{63 b} + \frac{x^{8} \sqrt{a + b x^{2}}}{9} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right)"," ",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)) + B*a**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)) + 2*B*a*b*Piecewise((8*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + a*x**4*sqrt(a + b*x**2)/(35*b) + x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + B*b**2*Piecewise((-16*a**4*sqrt(a + b*x**2)/(315*b**4) + 8*a**3*x**2*sqrt(a + b*x**2)/(315*b**3) - 2*a**2*x**4*sqrt(a + b*x**2)/(105*b**2) + a*x**6*sqrt(a + b*x**2)/(63*b) + x**8*sqrt(a + b*x**2)/9, Ne(b, 0)), (sqrt(a)*x**8/8, True))","A",0
17,1,354,0,26.540447," ","integrate(x*(B*x+A)*(b*x**2+a)**(5/2),x)","A a^{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) + 2 A a b \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) + A b^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \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**2*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + 2*A*a*b*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*b**2*Piecewise((8*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + a*x**4*sqrt(a + b*x**2)/(35*b) + x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*x**6/6, True)) + 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))","A",0
18,1,348,0,26.046468," ","integrate((B*x+A)*(b*x**2+a)**(5/2),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}}} + B a^{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) + 2 B a b \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) + B b^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + b x^{2}}}{105 b^{2}} + \frac{a x^{4} \sqrt{a + b x^{2}}}{35 b} + \frac{x^{6} \sqrt{a + b x^{2}}}{7} & \text{for}\: b \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right)"," ",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)) + B*a**2*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + 2*B*a*b*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)) + B*b**2*Piecewise((8*a**3*sqrt(a + b*x**2)/(105*b**3) - 4*a**2*x**2*sqrt(a + b*x**2)/(105*b**2) + a*x**4*sqrt(a + b*x**2)/(35*b) + x**6*sqrt(a + b*x**2)/7, Ne(b, 0)), (sqrt(a)*x**6/6, True))","A",0
19,1,323,0,40.753402," ","integrate((B*x+A)*(b*x**2+a)**(5/2)/x,x)","- A a^{\frac{5}{2}} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)} + \frac{A a^{3}}{\sqrt{b} x \sqrt{\frac{a}{b x^{2}} + 1}} + \frac{A a^{2} \sqrt{b} x}{\sqrt{\frac{a}{b x^{2}} + 1}} + 2 A 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) + A 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) + \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)*asinh(sqrt(a)/(sqrt(b)*x)) + A*a**3/(sqrt(b)*x*sqrt(a/(b*x**2) + 1)) + A*a**2*sqrt(b)*x/sqrt(a/(b*x**2) + 1) + 2*A*a*b*Piecewise((sqrt(a)*x**2/2, Eq(b, 0)), ((a + b*x**2)**(3/2)/(3*b), True)) + A*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)) + 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))","A",0
20,1,318,0,18.911181," ","integrate((B*x+A)*(b*x**2+a)**(5/2)/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}}} - 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,"-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)*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
21,1,279,0,12.982785," ","integrate((B*x+A)*(b*x**2+a)**(5/2)/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) - \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,"-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)/(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))","A",0
22,1,150,0,7.911986," ","integrate(x**3*(B*x+A)/(b*x**2+a)**(1/2),x)","A \left(\begin{cases} - \frac{2 a \sqrt{a + b x^{2}}}{3 b^{2}} + \frac{x^{2} \sqrt{a + b x^{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) - \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*Piecewise((-2*a*sqrt(a + b*x**2)/(3*b**2) + x**2*sqrt(a + b*x**2)/(3*b), Ne(b, 0)), (x**4/(4*sqrt(a)), True)) - 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
23,1,94,0,6.228118," ","integrate(x**2*(B*x+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}}} + B \left(\begin{cases} - \frac{2 a \sqrt{a + b x^{2}}}{3 b^{2}} + \frac{x^{2} \sqrt{a + b x^{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right)"," ",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)) + B*Piecewise((-2*a*sqrt(a + b*x**2)/(3*b**2) + x**2*sqrt(a + b*x**2)/(3*b), Ne(b, 0)), (x**4/(4*sqrt(a)), True))","A",0
24,1,70,0,6.255126," ","integrate(x*(B*x+A)/(b*x**2+a)**(1/2),x)","A \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{2}}}{b} & \text{otherwise} \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((x**2/(2*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**2)/b, True)) + 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
25,1,102,0,2.641205," ","integrate((B*x+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) + B \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{2}}}{b} & \text{otherwise} \end{cases}\right)"," ",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*Piecewise((x**2/(2*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**2)/b, True))","B",0
26,1,99,0,5.141401," ","integrate((B*x+A)/x/(b*x**2+a)**(1/2),x)","- \frac{A \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{\sqrt{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*asinh(sqrt(a)/(sqrt(b)*x))/sqrt(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
27,1,41,0,2.798630," ","integrate((B*x+A)/x**2/(b*x**2+a)**(1/2),x)","- \frac{A \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{a} - \frac{B \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{\sqrt{a}}"," ",0,"-A*sqrt(b)*sqrt(a/(b*x**2) + 1)/a - B*asinh(sqrt(a)/(sqrt(b)*x))/sqrt(a)","A",0
28,1,66,0,7.056011," ","integrate((B*x+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 \sqrt{b} \sqrt{\frac{a}{b x^{2}} + 1}}{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*sqrt(b)*sqrt(a/(b*x**2) + 1)/a","A",0
29,1,117,0,10.335196," ","integrate(x**3*(B*x+A)/(b*x**2+a)**(3/2),x)","A \left(\begin{cases} \frac{2 a}{b^{2} \sqrt{a + b x^{2}}} + \frac{x^{2}}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\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*Piecewise((2*a/(b**2*sqrt(a + b*x**2)) + x**2/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**4/(4*a**(3/2)), True)) + 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
30,1,83,0,16.607545," ","integrate(x**2*(B*x+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(\begin{cases} \frac{2 a}{b^{2} \sqrt{a + b x^{2}}} + \frac{x^{2}}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*(asinh(sqrt(b)*x/sqrt(a))/b**(3/2) - x/(sqrt(a)*b*sqrt(1 + b*x**2/a))) + B*Piecewise((2*a/(b**2*sqrt(a + b*x**2)) + x**2/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**4/(4*a**(3/2)), True))","A",0
31,1,66,0,15.184585," ","integrate(x*(B*x+A)/(b*x**2+a)**(3/2),x)","A \left(\begin{cases} - \frac{1}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + 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*Piecewise((-1/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(3/2)), True)) + B*(asinh(sqrt(b)*x/sqrt(a))/b**(3/2) - x/(sqrt(a)*b*sqrt(1 + b*x**2/a)))","A",0
32,1,46,0,10.222593," ","integrate((B*x+A)/(b*x**2+a)**(3/2),x)","\frac{A x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}} + B \left(\begin{cases} - \frac{1}{b \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*x/(a**(3/2)*sqrt(1 + b*x**2/a)) + B*Piecewise((-1/(b*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(3/2)), True))","A",0
33,1,206,0,11.293606," ","integrate((B*x+A)/x/(b*x**2+a)**(3/2),x)","A \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) + \frac{B x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"A*(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*x/(a**(3/2)*sqrt(1 + b*x**2/a))","B",0
34,1,235,0,15.825999," ","integrate((B*x+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) + 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/(a*sqrt(b)*x**2*sqrt(a/(b*x**2) + 1)) - 2*sqrt(b)/(a**2*sqrt(a/(b*x**2) + 1))) + 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
35,1,124,0,10.794936," ","integrate((B*x+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{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*(-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*(-1/(a*sqrt(b)*x**2*sqrt(a/(b*x**2) + 1)) - 2*sqrt(b)/(a**2*sqrt(a/(b*x**2) + 1)))","A",0
36,1,400,0,18.322622," ","integrate(x**3*(B*x+A)/(b*x**2+a)**(5/2),x)","A \left(\begin{cases} - \frac{2 a}{3 a b^{2} \sqrt{a + b x^{2}} + 3 b^{3} x^{2} \sqrt{a + b x^{2}}} - \frac{3 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{x^{4}}{4 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right) + 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*Piecewise((-2*a/(3*a*b**2*sqrt(a + b*x**2) + 3*b**3*x**2*sqrt(a + b*x**2)) - 3*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)), (x**4/(4*a**(5/2)), True)) + 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)))","A",0
37,1,141,0,17.324933," ","integrate(x**2*(B*x+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(\begin{cases} - \frac{2 a}{3 a b^{2} \sqrt{a + b x^{2}} + 3 b^{3} x^{2} \sqrt{a + b x^{2}}} - \frac{3 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{x^{4}}{4 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\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*Piecewise((-2*a/(3*a*b**2*sqrt(a + b*x**2) + 3*b**3*x**2*sqrt(a + b*x**2)) - 3*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)), (x**4/(4*a**(5/2)), True))","B",0
38,1,95,0,13.983112," ","integrate(x*(B*x+A)/(b*x**2+a)**(5/2),x)","A \left(\begin{cases} - \frac{1}{3 a b \sqrt{a + b x^{2}} + 3 b^{2} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\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*Piecewise((-1/(3*a*b*sqrt(a + b*x**2) + 3*b**2*x**2*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(5/2)), True)) + 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))","A",0
39,1,146,0,13.203214," ","integrate((B*x+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) + B \left(\begin{cases} - \frac{1}{3 a b \sqrt{a + b x^{2}} + 3 b^{2} x^{2} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)"," ",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*Piecewise((-1/(3*a*b*sqrt(a + b*x**2) + 3*b**2*x**2*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(5/2)), True))","B",0
40,1,840,0,25.923225," ","integrate((B*x+A)/x/(b*x**2+a)**(5/2),x)","A \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) + 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*(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*(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
41,1,910,0,24.182506," ","integrate((B*x+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{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*(-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*(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
42,1,1034,0,24.756461," ","integrate((B*x+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{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*(-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*(-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
43,1,24,0,0.239515," ","integrate((1-x)*x/(-x**2+1)**(1/2),x)","\frac{x \sqrt{1 - x^{2}}}{2} - \sqrt{1 - x^{2}} - \frac{\operatorname{asin}{\left(x \right)}}{2}"," ",0,"x*sqrt(1 - x**2)/2 - sqrt(1 - x**2) - asin(x)/2","A",0
44,1,24,0,0.293955," ","integrate((-x**2+x)/(-x**2+1)**(1/2),x)","\frac{x \sqrt{1 - x^{2}}}{2} - \sqrt{1 - x^{2}} - \frac{\operatorname{asin}{\left(x \right)}}{2}"," ",0,"x*sqrt(1 - x**2)/2 - sqrt(1 - x**2) - asin(x)/2","A",0
45,1,27,0,0.186202," ","integrate((x**2+3)/(x**2-3),x)","x + \sqrt{3} \log{\left(x - \sqrt{3} \right)} - \sqrt{3} \log{\left(x + \sqrt{3} \right)}"," ",0,"x + sqrt(3)*log(x - sqrt(3)) - sqrt(3)*log(x + sqrt(3))","A",0
46,1,5,0,0.153318," ","integrate((x**2-1)/(x**2+1),x)","x - 2 \operatorname{atan}{\left(x \right)}"," ",0,"x - 2*atan(x)","A",0
47,-1,0,0,0.000000," ","integrate(x**7*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(x**6*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate(x**5*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(x**4*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(x**3*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,904,0,118.646148," ","integrate(x**2*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","A \left(\frac{35 a^{5} x^{3}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{63 a^{4} b x^{5}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{36 a^{3} b^{2} x^{7}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{8 a^{2} b^{3} x^{9}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + B \left(\begin{cases} - \frac{2 a}{35 a^{3} b^{2} \sqrt{a + b x^{2}} + 105 a^{2} b^{3} x^{2} \sqrt{a + b x^{2}} + 105 a b^{4} x^{4} \sqrt{a + b x^{2}} + 35 b^{5} x^{6} \sqrt{a + b x^{2}}} - \frac{7 b x^{2}}{35 a^{3} b^{2} \sqrt{a + b x^{2}} + 105 a^{2} b^{3} x^{2} \sqrt{a + b x^{2}} + 105 a b^{4} x^{4} \sqrt{a + b x^{2}} + 35 b^{5} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right) + C \left(\frac{7 a x^{5}}{35 a^{\frac{11}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{9}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{7}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{5}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{7}}{35 a^{\frac{11}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{9}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{7}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{5}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(35*a**5*x**3/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 63*a**4*b*x**5/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 36*a**3*b**2*x**7/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 8*a**2*b**3*x**9/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a))) + B*Piecewise((-2*a/(35*a**3*b**2*sqrt(a + b*x**2) + 105*a**2*b**3*x**2*sqrt(a + b*x**2) + 105*a*b**4*x**4*sqrt(a + b*x**2) + 35*b**5*x**6*sqrt(a + b*x**2)) - 7*b*x**2/(35*a**3*b**2*sqrt(a + b*x**2) + 105*a**2*b**3*x**2*sqrt(a + b*x**2) + 105*a*b**4*x**4*sqrt(a + b*x**2) + 35*b**5*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**4/(4*a**(9/2)), True)) + C*(7*a*x**5/(35*a**(11/2)*sqrt(1 + b*x**2/a) + 105*a**(9/2)*b*x**2*sqrt(1 + b*x**2/a) + 105*a**(7/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 35*a**(5/2)*b**3*x**6*sqrt(1 + b*x**2/a)) + 2*b*x**7/(35*a**(11/2)*sqrt(1 + b*x**2/a) + 105*a**(9/2)*b*x**2*sqrt(1 + b*x**2/a) + 105*a**(7/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 35*a**(5/2)*b**3*x**6*sqrt(1 + b*x**2/a)))","B",0
53,1,796,0,85.296036," ","integrate(x*(C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","A \left(\begin{cases} - \frac{1}{7 a^{3} b \sqrt{a + b x^{2}} + 21 a^{2} b^{2} x^{2} \sqrt{a + b x^{2}} + 21 a b^{3} x^{4} \sqrt{a + b x^{2}} + 7 b^{4} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right) + B \left(\frac{35 a^{5} x^{3}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{63 a^{4} b x^{5}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{36 a^{3} b^{2} x^{7}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{8 a^{2} b^{3} x^{9}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + C \left(\begin{cases} - \frac{2 a}{35 a^{3} b^{2} \sqrt{a + b x^{2}} + 105 a^{2} b^{3} x^{2} \sqrt{a + b x^{2}} + 105 a b^{4} x^{4} \sqrt{a + b x^{2}} + 35 b^{5} x^{6} \sqrt{a + b x^{2}}} - \frac{7 b x^{2}}{35 a^{3} b^{2} \sqrt{a + b x^{2}} + 105 a^{2} b^{3} x^{2} \sqrt{a + b x^{2}} + 105 a b^{4} x^{4} \sqrt{a + b x^{2}} + 35 b^{5} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*Piecewise((-1/(7*a**3*b*sqrt(a + b*x**2) + 21*a**2*b**2*x**2*sqrt(a + b*x**2) + 21*a*b**3*x**4*sqrt(a + b*x**2) + 7*b**4*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(9/2)), True)) + B*(35*a**5*x**3/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 63*a**4*b*x**5/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 36*a**3*b**2*x**7/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 8*a**2*b**3*x**9/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a))) + C*Piecewise((-2*a/(35*a**3*b**2*sqrt(a + b*x**2) + 105*a**2*b**3*x**2*sqrt(a + b*x**2) + 105*a*b**4*x**4*sqrt(a + b*x**2) + 35*b**5*x**6*sqrt(a + b*x**2)) - 7*b*x**2/(35*a**3*b**2*sqrt(a + b*x**2) + 105*a**2*b**3*x**2*sqrt(a + b*x**2) + 105*a*b**4*x**4*sqrt(a + b*x**2) + 35*b**5*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**4/(4*a**(9/2)), True))","A",0
54,1,1880,0,94.217554," ","integrate((C*x**2+B*x+A)/(b*x**2+a)**(9/2),x)","A \left(\frac{35 a^{14} x}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{175 a^{13} b x^{3}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{371 a^{12} b^{2} x^{5}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{429 a^{11} b^{3} x^{7}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{286 a^{10} b^{4} x^{9}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{104 a^{9} b^{5} x^{11}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{16 a^{8} b^{6} x^{13}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + B \left(\begin{cases} - \frac{1}{7 a^{3} b \sqrt{a + b x^{2}} + 21 a^{2} b^{2} x^{2} \sqrt{a + b x^{2}} + 21 a b^{3} x^{4} \sqrt{a + b x^{2}} + 7 b^{4} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right) + C \left(\frac{35 a^{5} x^{3}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{63 a^{4} b x^{5}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{36 a^{3} b^{2} x^{7}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{8 a^{2} b^{3} x^{9}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{17}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 630 a^{\frac{15}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 420 a^{\frac{13}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{11}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(35*a**14*x/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 175*a**13*b*x**3/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 371*a**12*b**2*x**5/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 429*a**11*b**3*x**7/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 286*a**10*b**4*x**9/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 104*a**9*b**5*x**11/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 16*a**8*b**6*x**13/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a))) + B*Piecewise((-1/(7*a**3*b*sqrt(a + b*x**2) + 21*a**2*b**2*x**2*sqrt(a + b*x**2) + 21*a*b**3*x**4*sqrt(a + b*x**2) + 7*b**4*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(9/2)), True)) + C*(35*a**5*x**3/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 63*a**4*b*x**5/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 36*a**3*b**2*x**7/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)) + 8*a**2*b**3*x**9/(105*a**(19/2)*sqrt(1 + b*x**2/a) + 420*a**(17/2)*b*x**2*sqrt(1 + b*x**2/a) + 630*a**(15/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 420*a**(13/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 105*a**(11/2)*b**4*x**8*sqrt(1 + b*x**2/a)))","B",0
55,1,6613,0,107.413620," ","integrate((C*x**2+B*x+A)/x/(b*x**2+a)**(9/2),x)","A \left(\frac{352 a^{32} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{105 a^{32} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{210 a^{32} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{2924 a^{31} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1050 a^{31} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{2100 a^{31} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{10852 a^{30} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{4725 a^{30} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{9450 a^{30} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{23630 a^{29} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{12600 a^{29} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{25200 a^{29} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{33280 a^{28} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{22050 a^{28} b^{4} x^{8} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{44100 a^{28} b^{4} x^{8} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{31442 a^{27} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{26460 a^{27} b^{5} x^{10} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{52920 a^{27} b^{5} x^{10} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{19924 a^{26} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{22050 a^{26} b^{6} x^{12} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{44100 a^{26} b^{6} x^{12} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{8162 a^{25} b^{7} x^{14} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{12600 a^{25} b^{7} x^{14} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{25200 a^{25} b^{7} x^{14} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1960 a^{24} b^{8} x^{16} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{4725 a^{24} b^{8} x^{16} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{9450 a^{24} b^{8} x^{16} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{210 a^{23} b^{9} x^{18} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1050 a^{23} b^{9} x^{18} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{2100 a^{23} b^{9} x^{18} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{105 a^{22} b^{10} x^{20} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{210 a^{22} b^{10} x^{20} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}}\right) + B \left(\frac{35 a^{14} x}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{175 a^{13} b x^{3}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{371 a^{12} b^{2} x^{5}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{429 a^{11} b^{3} x^{7}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{286 a^{10} b^{4} x^{9}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{104 a^{9} b^{5} x^{11}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{16 a^{8} b^{6} x^{13}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + C \left(\begin{cases} - \frac{1}{7 a^{3} b \sqrt{a + b x^{2}} + 21 a^{2} b^{2} x^{2} \sqrt{a + b x^{2}} + 21 a b^{3} x^{4} \sqrt{a + b x^{2}} + 7 b^{4} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"A*(352*a**32*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 105*a**32*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 210*a**32*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 2924*a**31*b*x**2*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1050*a**31*b*x**2*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 2100*a**31*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 10852*a**30*b**2*x**4*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 4725*a**30*b**2*x**4*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 9450*a**30*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 23630*a**29*b**3*x**6*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 12600*a**29*b**3*x**6*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 25200*a**29*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 33280*a**28*b**4*x**8*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 22050*a**28*b**4*x**8*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 44100*a**28*b**4*x**8*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 31442*a**27*b**5*x**10*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 26460*a**27*b**5*x**10*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 52920*a**27*b**5*x**10*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 19924*a**26*b**6*x**12*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 22050*a**26*b**6*x**12*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 44100*a**26*b**6*x**12*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 8162*a**25*b**7*x**14*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 12600*a**25*b**7*x**14*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 25200*a**25*b**7*x**14*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1960*a**24*b**8*x**16*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 4725*a**24*b**8*x**16*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 9450*a**24*b**8*x**16*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 210*a**23*b**9*x**18*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1050*a**23*b**9*x**18*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 2100*a**23*b**9*x**18*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 105*a**22*b**10*x**20*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 210*a**22*b**10*x**20*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20)) + B*(35*a**14*x/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 175*a**13*b*x**3/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 371*a**12*b**2*x**5/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 429*a**11*b**3*x**7/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 286*a**10*b**4*x**9/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 104*a**9*b**5*x**11/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 16*a**8*b**6*x**13/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a))) + C*Piecewise((-1/(7*a**3*b*sqrt(a + b*x**2) + 21*a**2*b**2*x**2*sqrt(a + b*x**2) + 21*a*b**3*x**4*sqrt(a + b*x**2) + 7*b**4*x**6*sqrt(a + b*x**2)), Ne(b, 0)), (x**2/(2*a**(9/2)), True))","B",0
56,1,6922,0,165.701511," ","integrate((C*x**2+B*x+A)/x**2/(b*x**2+a)**(9/2),x)","A \left(- \frac{35 a^{4} b^{\frac{33}{2}} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{280 a^{3} b^{\frac{35}{2}} x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{560 a^{2} b^{\frac{37}{2}} x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{448 a b^{\frac{39}{2}} x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}} - \frac{128 b^{\frac{41}{2}} x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{35 a^{9} b^{16} + 140 a^{8} b^{17} x^{2} + 210 a^{7} b^{18} x^{4} + 140 a^{6} b^{19} x^{6} + 35 a^{5} b^{20} x^{8}}\right) + B \left(\frac{352 a^{32} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{105 a^{32} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{210 a^{32} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{2924 a^{31} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1050 a^{31} b x^{2} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{2100 a^{31} b x^{2} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{10852 a^{30} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{4725 a^{30} b^{2} x^{4} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{9450 a^{30} b^{2} x^{4} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{23630 a^{29} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{12600 a^{29} b^{3} x^{6} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{25200 a^{29} b^{3} x^{6} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{33280 a^{28} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{22050 a^{28} b^{4} x^{8} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{44100 a^{28} b^{4} x^{8} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{31442 a^{27} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{26460 a^{27} b^{5} x^{10} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{52920 a^{27} b^{5} x^{10} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{19924 a^{26} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{22050 a^{26} b^{6} x^{12} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{44100 a^{26} b^{6} x^{12} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{8162 a^{25} b^{7} x^{14} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{12600 a^{25} b^{7} x^{14} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{25200 a^{25} b^{7} x^{14} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1960 a^{24} b^{8} x^{16} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{4725 a^{24} b^{8} x^{16} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{9450 a^{24} b^{8} x^{16} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{210 a^{23} b^{9} x^{18} \sqrt{1 + \frac{b x^{2}}{a}}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{1050 a^{23} b^{9} x^{18} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{2100 a^{23} b^{9} x^{18} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} + \frac{105 a^{22} b^{10} x^{20} \log{\left(\frac{b x^{2}}{a} \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}} - \frac{210 a^{22} b^{10} x^{20} \log{\left(\sqrt{1 + \frac{b x^{2}}{a}} + 1 \right)}}{210 a^{\frac{73}{2}} + 2100 a^{\frac{71}{2}} b x^{2} + 9450 a^{\frac{69}{2}} b^{2} x^{4} + 25200 a^{\frac{67}{2}} b^{3} x^{6} + 44100 a^{\frac{65}{2}} b^{4} x^{8} + 52920 a^{\frac{63}{2}} b^{5} x^{10} + 44100 a^{\frac{61}{2}} b^{6} x^{12} + 25200 a^{\frac{59}{2}} b^{7} x^{14} + 9450 a^{\frac{57}{2}} b^{8} x^{16} + 2100 a^{\frac{55}{2}} b^{9} x^{18} + 210 a^{\frac{53}{2}} b^{10} x^{20}}\right) + C \left(\frac{35 a^{14} x}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{175 a^{13} b x^{3}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{371 a^{12} b^{2} x^{5}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{429 a^{11} b^{3} x^{7}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{286 a^{10} b^{4} x^{9}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{104 a^{9} b^{5} x^{11}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{16 a^{8} b^{6} x^{13}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{35}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{33}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 700 a^{\frac{31}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}} + 525 a^{\frac{29}{2}} b^{4} x^{8} \sqrt{1 + \frac{b x^{2}}{a}} + 210 a^{\frac{27}{2}} b^{5} x^{10} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{25}{2}} b^{6} x^{12} \sqrt{1 + \frac{b x^{2}}{a}}}\right)"," ",0,"A*(-35*a**4*b**(33/2)*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 280*a**3*b**(35/2)*x**2*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 560*a**2*b**(37/2)*x**4*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 448*a*b**(39/2)*x**6*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8) - 128*b**(41/2)*x**8*sqrt(a/(b*x**2) + 1)/(35*a**9*b**16 + 140*a**8*b**17*x**2 + 210*a**7*b**18*x**4 + 140*a**6*b**19*x**6 + 35*a**5*b**20*x**8)) + B*(352*a**32*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 105*a**32*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 210*a**32*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 2924*a**31*b*x**2*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1050*a**31*b*x**2*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 2100*a**31*b*x**2*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 10852*a**30*b**2*x**4*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 4725*a**30*b**2*x**4*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 9450*a**30*b**2*x**4*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 23630*a**29*b**3*x**6*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 12600*a**29*b**3*x**6*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 25200*a**29*b**3*x**6*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 33280*a**28*b**4*x**8*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 22050*a**28*b**4*x**8*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 44100*a**28*b**4*x**8*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 31442*a**27*b**5*x**10*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 26460*a**27*b**5*x**10*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 52920*a**27*b**5*x**10*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 19924*a**26*b**6*x**12*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 22050*a**26*b**6*x**12*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 44100*a**26*b**6*x**12*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 8162*a**25*b**7*x**14*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 12600*a**25*b**7*x**14*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 25200*a**25*b**7*x**14*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1960*a**24*b**8*x**16*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 4725*a**24*b**8*x**16*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 9450*a**24*b**8*x**16*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 210*a**23*b**9*x**18*sqrt(1 + b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 1050*a**23*b**9*x**18*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 2100*a**23*b**9*x**18*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) + 105*a**22*b**10*x**20*log(b*x**2/a)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20) - 210*a**22*b**10*x**20*log(sqrt(1 + b*x**2/a) + 1)/(210*a**(73/2) + 2100*a**(71/2)*b*x**2 + 9450*a**(69/2)*b**2*x**4 + 25200*a**(67/2)*b**3*x**6 + 44100*a**(65/2)*b**4*x**8 + 52920*a**(63/2)*b**5*x**10 + 44100*a**(61/2)*b**6*x**12 + 25200*a**(59/2)*b**7*x**14 + 9450*a**(57/2)*b**8*x**16 + 2100*a**(55/2)*b**9*x**18 + 210*a**(53/2)*b**10*x**20)) + C*(35*a**14*x/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 175*a**13*b*x**3/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 371*a**12*b**2*x**5/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 429*a**11*b**3*x**7/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 286*a**10*b**4*x**9/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 104*a**9*b**5*x**11/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)) + 16*a**8*b**6*x**13/(35*a**(37/2)*sqrt(1 + b*x**2/a) + 210*a**(35/2)*b*x**2*sqrt(1 + b*x**2/a) + 525*a**(33/2)*b**2*x**4*sqrt(1 + b*x**2/a) + 700*a**(31/2)*b**3*x**6*sqrt(1 + b*x**2/a) + 525*a**(29/2)*b**4*x**8*sqrt(1 + b*x**2/a) + 210*a**(27/2)*b**5*x**10*sqrt(1 + b*x**2/a) + 35*a**(25/2)*b**6*x**12*sqrt(1 + b*x**2/a)))","B",0
57,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/x**3/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,1,97,0,1.970090," ","integrate(A*(c*x)**m/(b*x**2+a),x)","A \left(\frac{c^{m} 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^{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)}\right)"," ",0,"A*(c**m*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**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",0
59,1,192,0,6.404281," ","integrate((c*x)**m*(B*x+A)/(b*x**2+a),x)","\frac{A c^{m} 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 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{B c^{m} m x^{2} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{4 a \Gamma\left(\frac{m}{2} + 2\right)} + \frac{B c^{m} x^{2} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{2 a \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"A*c**m*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*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)) + B*c**m*m*x**2*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(4*a*gamma(m/2 + 2)) + B*c**m*x**2*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(2*a*gamma(m/2 + 2))","C",0
60,1,204,0,6.474895," ","integrate((c*x)**m*(C*x**2+A)/(b*x**2+a),x)","\frac{A c^{m} 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 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 c^{m} 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 C c^{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)}"," ",0,"A*c**m*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*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*c**m*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*C*c**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))","C",0
61,1,298,0,7.602369," ","integrate((c*x)**m*(C*x**2+B*x+A)/(b*x**2+a),x)","\frac{A c^{m} 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 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{B c^{m} m x^{2} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{4 a \Gamma\left(\frac{m}{2} + 2\right)} + \frac{B c^{m} x^{2} x^{m} \Phi\left(\frac{b x^{2} e^{i \pi}}{a}, 1, \frac{m}{2} + 1\right) \Gamma\left(\frac{m}{2} + 1\right)}{2 a \Gamma\left(\frac{m}{2} + 2\right)} + \frac{C c^{m} 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 C c^{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)}"," ",0,"A*c**m*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*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)) + B*c**m*m*x**2*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(4*a*gamma(m/2 + 2)) + B*c**m*x**2*x**m*lerchphi(b*x**2*exp_polar(I*pi)/a, 1, m/2 + 1)*gamma(m/2 + 1)/(2*a*gamma(m/2 + 2)) + C*c**m*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*C*c**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))","C",0
62,1,60,0,0.101016," ","integrate(x**3*(b*x**2+a)*(D*x**3+C*x**2+B*x+A),x)","\frac{A a x^{4}}{4} + \frac{B a x^{5}}{5} + \frac{C b x^{8}}{8} + \frac{D b x^{9}}{9} + x^{7} \left(\frac{B b}{7} + \frac{D a}{7}\right) + x^{6} \left(\frac{A b}{6} + \frac{C a}{6}\right)"," ",0,"A*a*x**4/4 + B*a*x**5/5 + C*b*x**8/8 + D*b*x**9/9 + x**7*(B*b/7 + D*a/7) + x**6*(A*b/6 + C*a/6)","A",0
63,1,60,0,0.090565," ","integrate(x**2*(b*x**2+a)*(D*x**3+C*x**2+B*x+A),x)","\frac{A a x^{3}}{3} + \frac{B a x^{4}}{4} + \frac{C b x^{7}}{7} + \frac{D b x^{8}}{8} + x^{6} \left(\frac{B b}{6} + \frac{D a}{6}\right) + x^{5} \left(\frac{A b}{5} + \frac{C a}{5}\right)"," ",0,"A*a*x**3/3 + B*a*x**4/4 + C*b*x**7/7 + D*b*x**8/8 + x**6*(B*b/6 + D*a/6) + x**5*(A*b/5 + C*a/5)","A",0
64,1,60,0,0.136348," ","integrate(x*(b*x**2+a)*(D*x**3+C*x**2+B*x+A),x)","\frac{A a x^{2}}{2} + \frac{B a x^{3}}{3} + \frac{C b x^{6}}{6} + \frac{D b x^{7}}{7} + x^{5} \left(\frac{B b}{5} + \frac{D a}{5}\right) + x^{4} \left(\frac{A b}{4} + \frac{C a}{4}\right)"," ",0,"A*a*x**2/2 + B*a*x**3/3 + C*b*x**6/6 + D*b*x**7/7 + x**5*(B*b/5 + D*a/5) + x**4*(A*b/4 + C*a/4)","A",0
65,1,56,0,0.121263," ","integrate((b*x**2+a)*(D*x**3+C*x**2+B*x+A),x)","A a x + \frac{B a x^{2}}{2} + \frac{C b x^{5}}{5} + \frac{D b x^{6}}{6} + x^{4} \left(\frac{B b}{4} + \frac{D a}{4}\right) + x^{3} \left(\frac{A b}{3} + \frac{C a}{3}\right)"," ",0,"A*a*x + B*a*x**2/2 + C*b*x**5/5 + D*b*x**6/6 + x**4*(B*b/4 + D*a/4) + x**3*(A*b/3 + C*a/3)","A",0
66,1,54,0,0.324690," ","integrate((b*x**2+a)*(D*x**3+C*x**2+B*x+A)/x,x)","A a \log{\left(x \right)} + B a x + \frac{C b x^{4}}{4} + \frac{D b x^{5}}{5} + x^{3} \left(\frac{B b}{3} + \frac{D a}{3}\right) + x^{2} \left(\frac{A b}{2} + \frac{C a}{2}\right)"," ",0,"A*a*log(x) + B*a*x + C*b*x**4/4 + D*b*x**5/5 + x**3*(B*b/3 + D*a/3) + x**2*(A*b/2 + C*a/2)","A",0
67,1,49,0,0.280449," ","integrate((b*x**2+a)*(D*x**3+C*x**2+B*x+A)/x**2,x)","- \frac{A a}{x} + B a \log{\left(x \right)} + \frac{C b x^{3}}{3} + \frac{D b x^{4}}{4} + x^{2} \left(\frac{B b}{2} + \frac{D a}{2}\right) + x \left(A b + C a\right)"," ",0,"-A*a/x + B*a*log(x) + C*b*x**3/3 + D*b*x**4/4 + x**2*(B*b/2 + D*a/2) + x*(A*b + C*a)","A",0
68,1,51,0,0.506602," ","integrate((b*x**2+a)*(D*x**3+C*x**2+B*x+A)/x**3,x)","\frac{C b x^{2}}{2} + \frac{D b x^{3}}{3} + x \left(B b + D a\right) + \left(A b + C a\right) \log{\left(x \right)} + \frac{- A a - 2 B a x}{2 x^{2}}"," ",0,"C*b*x**2/2 + D*b*x**3/3 + x*(B*b + D*a) + (A*b + C*a)*log(x) + (-A*a - 2*B*a*x)/(2*x**2)","A",0
69,1,54,0,1.009733," ","integrate((b*x**2+a)*(D*x**3+C*x**2+B*x+A)/x**4,x)","C b x + \frac{D b x^{2}}{2} + \left(B b + D a\right) \log{\left(x \right)} + \frac{- 2 A a - 3 B a x + x^{2} \left(- 6 A b - 6 C a\right)}{6 x^{3}}"," ",0,"C*b*x + D*b*x**2/2 + (B*b + D*a)*log(x) + (-2*A*a - 3*B*a*x + x**2*(-6*A*b - 6*C*a))/(6*x**3)","A",0
70,1,110,0,0.135488," ","integrate(x**3*(b*x**2+a)**2*(D*x**3+C*x**2+B*x+A),x)","\frac{A a^{2} x^{4}}{4} + \frac{B a^{2} x^{5}}{5} + \frac{C b^{2} x^{10}}{10} + \frac{D b^{2} x^{11}}{11} + x^{9} \left(\frac{B b^{2}}{9} + \frac{2 D a b}{9}\right) + x^{8} \left(\frac{A b^{2}}{8} + \frac{C a b}{4}\right) + x^{7} \left(\frac{2 B a b}{7} + \frac{D a^{2}}{7}\right) + x^{6} \left(\frac{A a b}{3} + \frac{C a^{2}}{6}\right)"," ",0,"A*a**2*x**4/4 + B*a**2*x**5/5 + C*b**2*x**10/10 + D*b**2*x**11/11 + x**9*(B*b**2/9 + 2*D*a*b/9) + x**8*(A*b**2/8 + C*a*b/4) + x**7*(2*B*a*b/7 + D*a**2/7) + x**6*(A*a*b/3 + C*a**2/6)","A",0
71,1,110,0,0.142202," ","integrate(x**2*(b*x**2+a)**2*(D*x**3+C*x**2+B*x+A),x)","\frac{A a^{2} x^{3}}{3} + \frac{B a^{2} x^{4}}{4} + \frac{C b^{2} x^{9}}{9} + \frac{D b^{2} x^{10}}{10} + x^{8} \left(\frac{B b^{2}}{8} + \frac{D a b}{4}\right) + x^{7} \left(\frac{A b^{2}}{7} + \frac{2 C a b}{7}\right) + x^{6} \left(\frac{B a b}{3} + \frac{D a^{2}}{6}\right) + x^{5} \left(\frac{2 A a b}{5} + \frac{C a^{2}}{5}\right)"," ",0,"A*a**2*x**3/3 + B*a**2*x**4/4 + C*b**2*x**9/9 + D*b**2*x**10/10 + x**8*(B*b**2/8 + D*a*b/4) + x**7*(A*b**2/7 + 2*C*a*b/7) + x**6*(B*a*b/3 + D*a**2/6) + x**5*(2*A*a*b/5 + C*a**2/5)","A",0
72,1,110,0,0.087993," ","integrate(x*(b*x**2+a)**2*(D*x**3+C*x**2+B*x+A),x)","\frac{A a^{2} x^{2}}{2} + \frac{B a^{2} x^{3}}{3} + \frac{C b^{2} x^{8}}{8} + \frac{D b^{2} x^{9}}{9} + x^{7} \left(\frac{B b^{2}}{7} + \frac{2 D a b}{7}\right) + x^{6} \left(\frac{A b^{2}}{6} + \frac{C a b}{3}\right) + x^{5} \left(\frac{2 B a b}{5} + \frac{D a^{2}}{5}\right) + x^{4} \left(\frac{A a b}{2} + \frac{C a^{2}}{4}\right)"," ",0,"A*a**2*x**2/2 + B*a**2*x**3/3 + C*b**2*x**8/8 + D*b**2*x**9/9 + x**7*(B*b**2/7 + 2*D*a*b/7) + x**6*(A*b**2/6 + C*a*b/3) + x**5*(2*B*a*b/5 + D*a**2/5) + x**4*(A*a*b/2 + C*a**2/4)","A",0
73,1,107,0,0.088588," ","integrate((b*x**2+a)**2*(D*x**3+C*x**2+B*x+A),x)","A a^{2} x + \frac{B a^{2} x^{2}}{2} + \frac{C b^{2} x^{7}}{7} + \frac{D b^{2} x^{8}}{8} + x^{6} \left(\frac{B b^{2}}{6} + \frac{D a b}{3}\right) + x^{5} \left(\frac{A b^{2}}{5} + \frac{2 C a b}{5}\right) + x^{4} \left(\frac{B a b}{2} + \frac{D a^{2}}{4}\right) + x^{3} \left(\frac{2 A a b}{3} + \frac{C a^{2}}{3}\right)"," ",0,"A*a**2*x + B*a**2*x**2/2 + C*b**2*x**7/7 + D*b**2*x**8/8 + x**6*(B*b**2/6 + D*a*b/3) + x**5*(A*b**2/5 + 2*C*a*b/5) + x**4*(B*a*b/2 + D*a**2/4) + x**3*(2*A*a*b/3 + C*a**2/3)","A",0
74,1,104,0,0.318030," ","integrate((b*x**2+a)**2*(D*x**3+C*x**2+B*x+A)/x,x)","A a^{2} \log{\left(x \right)} + B a^{2} x + \frac{C b^{2} x^{6}}{6} + \frac{D b^{2} x^{7}}{7} + x^{5} \left(\frac{B b^{2}}{5} + \frac{2 D a b}{5}\right) + x^{4} \left(\frac{A b^{2}}{4} + \frac{C a b}{2}\right) + x^{3} \left(\frac{2 B a b}{3} + \frac{D a^{2}}{3}\right) + x^{2} \left(A a b + \frac{C a^{2}}{2}\right)"," ",0,"A*a**2*log(x) + B*a**2*x + C*b**2*x**6/6 + D*b**2*x**7/7 + x**5*(B*b**2/5 + 2*D*a*b/5) + x**4*(A*b**2/4 + C*a*b/2) + x**3*(2*B*a*b/3 + D*a**2/3) + x**2*(A*a*b + C*a**2/2)","A",0
75,1,99,0,0.350830," ","integrate((b*x**2+a)**2*(D*x**3+C*x**2+B*x+A)/x**2,x)","- \frac{A a^{2}}{x} + B a^{2} \log{\left(x \right)} + \frac{C b^{2} x^{5}}{5} + \frac{D b^{2} x^{6}}{6} + x^{4} \left(\frac{B b^{2}}{4} + \frac{D a b}{2}\right) + x^{3} \left(\frac{A b^{2}}{3} + \frac{2 C a b}{3}\right) + x^{2} \left(B a b + \frac{D a^{2}}{2}\right) + x \left(2 A a b + C a^{2}\right)"," ",0,"-A*a**2/x + B*a**2*log(x) + C*b**2*x**5/5 + D*b**2*x**6/6 + x**4*(B*b**2/4 + D*a*b/2) + x**3*(A*b**2/3 + 2*C*a*b/3) + x**2*(B*a*b + D*a**2/2) + x*(2*A*a*b + C*a**2)","A",0
76,1,100,0,0.578361," ","integrate((b*x**2+a)**2*(D*x**3+C*x**2+B*x+A)/x**3,x)","\frac{C b^{2} x^{4}}{4} + \frac{D b^{2} x^{5}}{5} + a \left(2 A b + C a\right) \log{\left(x \right)} + x^{3} \left(\frac{B b^{2}}{3} + \frac{2 D a b}{3}\right) + x^{2} \left(\frac{A b^{2}}{2} + C a b\right) + x \left(2 B a b + D a^{2}\right) + \frac{- A a^{2} - 2 B a^{2} x}{2 x^{2}}"," ",0,"C*b**2*x**4/4 + D*b**2*x**5/5 + a*(2*A*b + C*a)*log(x) + x**3*(B*b**2/3 + 2*D*a*b/3) + x**2*(A*b**2/2 + C*a*b) + x*(2*B*a*b + D*a**2) + (-A*a**2 - 2*B*a**2*x)/(2*x**2)","A",0
77,1,100,0,1.455738," ","integrate((b*x**2+a)**2*(D*x**3+C*x**2+B*x+A)/x**4,x)","\frac{C b^{2} x^{3}}{3} + \frac{D b^{2} x^{4}}{4} + a \left(2 B b + D a\right) \log{\left(x \right)} + x^{2} \left(\frac{B b^{2}}{2} + D a b\right) + x \left(A b^{2} + 2 C a b\right) + \frac{- 2 A a^{2} - 3 B a^{2} x + x^{2} \left(- 12 A a b - 6 C a^{2}\right)}{6 x^{3}}"," ",0,"C*b**2*x**3/3 + D*b**2*x**4/4 + a*(2*B*b + D*a)*log(x) + x**2*(B*b**2/2 + D*a*b) + x*(A*b**2 + 2*C*a*b) + (-2*A*a**2 - 3*B*a**2*x + x**2*(-12*A*a*b - 6*C*a**2))/(6*x**3)","A",0
78,1,163,0,0.166805," ","integrate(x**3*(b*x**2+a)**3*(D*x**3+C*x**2+B*x+A),x)","\frac{A a^{3} x^{4}}{4} + \frac{B a^{3} x^{5}}{5} + \frac{C b^{3} x^{12}}{12} + \frac{D b^{3} x^{13}}{13} + x^{11} \left(\frac{B b^{3}}{11} + \frac{3 D a b^{2}}{11}\right) + x^{10} \left(\frac{A b^{3}}{10} + \frac{3 C a b^{2}}{10}\right) + x^{9} \left(\frac{B a b^{2}}{3} + \frac{D a^{2} b}{3}\right) + x^{8} \left(\frac{3 A a b^{2}}{8} + \frac{3 C a^{2} b}{8}\right) + x^{7} \left(\frac{3 B a^{2} b}{7} + \frac{D a^{3}}{7}\right) + x^{6} \left(\frac{A a^{2} b}{2} + \frac{C a^{3}}{6}\right)"," ",0,"A*a**3*x**4/4 + B*a**3*x**5/5 + C*b**3*x**12/12 + D*b**3*x**13/13 + x**11*(B*b**3/11 + 3*D*a*b**2/11) + x**10*(A*b**3/10 + 3*C*a*b**2/10) + x**9*(B*a*b**2/3 + D*a**2*b/3) + x**8*(3*A*a*b**2/8 + 3*C*a**2*b/8) + x**7*(3*B*a**2*b/7 + D*a**3/7) + x**6*(A*a**2*b/2 + C*a**3/6)","A",0
79,1,165,0,0.137982," ","integrate(x**2*(b*x**2+a)**3*(D*x**3+C*x**2+B*x+A),x)","\frac{A a^{3} x^{3}}{3} + \frac{B a^{3} x^{4}}{4} + \frac{C b^{3} x^{11}}{11} + \frac{D b^{3} x^{12}}{12} + x^{10} \left(\frac{B b^{3}}{10} + \frac{3 D a b^{2}}{10}\right) + x^{9} \left(\frac{A b^{3}}{9} + \frac{C a b^{2}}{3}\right) + x^{8} \left(\frac{3 B a b^{2}}{8} + \frac{3 D a^{2} b}{8}\right) + x^{7} \left(\frac{3 A a b^{2}}{7} + \frac{3 C a^{2} b}{7}\right) + x^{6} \left(\frac{B a^{2} b}{2} + \frac{D a^{3}}{6}\right) + x^{5} \left(\frac{3 A a^{2} b}{5} + \frac{C a^{3}}{5}\right)"," ",0,"A*a**3*x**3/3 + B*a**3*x**4/4 + C*b**3*x**11/11 + D*b**3*x**12/12 + x**10*(B*b**3/10 + 3*D*a*b**2/10) + x**9*(A*b**3/9 + C*a*b**2/3) + x**8*(3*B*a*b**2/8 + 3*D*a**2*b/8) + x**7*(3*A*a*b**2/7 + 3*C*a**2*b/7) + x**6*(B*a**2*b/2 + D*a**3/6) + x**5*(3*A*a**2*b/5 + C*a**3/5)","A",0
80,1,163,0,0.135563," ","integrate(x*(b*x**2+a)**3*(D*x**3+C*x**2+B*x+A),x)","\frac{A a^{3} x^{2}}{2} + \frac{B a^{3} x^{3}}{3} + \frac{C b^{3} x^{10}}{10} + \frac{D b^{3} x^{11}}{11} + x^{9} \left(\frac{B b^{3}}{9} + \frac{D a b^{2}}{3}\right) + x^{8} \left(\frac{A b^{3}}{8} + \frac{3 C a b^{2}}{8}\right) + x^{7} \left(\frac{3 B a b^{2}}{7} + \frac{3 D a^{2} b}{7}\right) + x^{6} \left(\frac{A a b^{2}}{2} + \frac{C a^{2} b}{2}\right) + x^{5} \left(\frac{3 B a^{2} b}{5} + \frac{D a^{3}}{5}\right) + x^{4} \left(\frac{3 A a^{2} b}{4} + \frac{C a^{3}}{4}\right)"," ",0,"A*a**3*x**2/2 + B*a**3*x**3/3 + C*b**3*x**10/10 + D*b**3*x**11/11 + x**9*(B*b**3/9 + D*a*b**2/3) + x**8*(A*b**3/8 + 3*C*a*b**2/8) + x**7*(3*B*a*b**2/7 + 3*D*a**2*b/7) + x**6*(A*a*b**2/2 + C*a**2*b/2) + x**5*(3*B*a**2*b/5 + D*a**3/5) + x**4*(3*A*a**2*b/4 + C*a**3/4)","A",0
81,1,158,0,0.134893," ","integrate((b*x**2+a)**3*(D*x**3+C*x**2+B*x+A),x)","A a^{3} x + \frac{B a^{3} x^{2}}{2} + \frac{C b^{3} x^{9}}{9} + \frac{D b^{3} x^{10}}{10} + x^{8} \left(\frac{B b^{3}}{8} + \frac{3 D a b^{2}}{8}\right) + x^{7} \left(\frac{A b^{3}}{7} + \frac{3 C a b^{2}}{7}\right) + x^{6} \left(\frac{B a b^{2}}{2} + \frac{D a^{2} b}{2}\right) + x^{5} \left(\frac{3 A a b^{2}}{5} + \frac{3 C a^{2} b}{5}\right) + x^{4} \left(\frac{3 B a^{2} b}{4} + \frac{D a^{3}}{4}\right) + x^{3} \left(A a^{2} b + \frac{C a^{3}}{3}\right)"," ",0,"A*a**3*x + B*a**3*x**2/2 + C*b**3*x**9/9 + D*b**3*x**10/10 + x**8*(B*b**3/8 + 3*D*a*b**2/8) + x**7*(A*b**3/7 + 3*C*a*b**2/7) + x**6*(B*a*b**2/2 + D*a**2*b/2) + x**5*(3*A*a*b**2/5 + 3*C*a**2*b/5) + x**4*(3*B*a**2*b/4 + D*a**3/4) + x**3*(A*a**2*b + C*a**3/3)","A",0
82,1,158,0,0.399261," ","integrate((b*x**2+a)**3*(D*x**3+C*x**2+B*x+A)/x,x)","A a^{3} \log{\left(x \right)} + B a^{3} x + \frac{C b^{3} x^{8}}{8} + \frac{D b^{3} x^{9}}{9} + x^{7} \left(\frac{B b^{3}}{7} + \frac{3 D a b^{2}}{7}\right) + x^{6} \left(\frac{A b^{3}}{6} + \frac{C a b^{2}}{2}\right) + x^{5} \left(\frac{3 B a b^{2}}{5} + \frac{3 D a^{2} b}{5}\right) + x^{4} \left(\frac{3 A a b^{2}}{4} + \frac{3 C a^{2} b}{4}\right) + x^{3} \left(B a^{2} b + \frac{D a^{3}}{3}\right) + x^{2} \left(\frac{3 A a^{2} b}{2} + \frac{C a^{3}}{2}\right)"," ",0,"A*a**3*log(x) + B*a**3*x + C*b**3*x**8/8 + D*b**3*x**9/9 + x**7*(B*b**3/7 + 3*D*a*b**2/7) + x**6*(A*b**3/6 + C*a*b**2/2) + x**5*(3*B*a*b**2/5 + 3*D*a**2*b/5) + x**4*(3*A*a*b**2/4 + 3*C*a**2*b/4) + x**3*(B*a**2*b + D*a**3/3) + x**2*(3*A*a**2*b/2 + C*a**3/2)","A",0
83,1,150,0,0.455985," ","integrate((b*x**2+a)**3*(D*x**3+C*x**2+B*x+A)/x**2,x)","- \frac{A a^{3}}{x} + B a^{3} \log{\left(x \right)} + \frac{C b^{3} x^{7}}{7} + \frac{D b^{3} x^{8}}{8} + x^{6} \left(\frac{B b^{3}}{6} + \frac{D a b^{2}}{2}\right) + x^{5} \left(\frac{A b^{3}}{5} + \frac{3 C a b^{2}}{5}\right) + x^{4} \left(\frac{3 B a b^{2}}{4} + \frac{3 D a^{2} b}{4}\right) + x^{3} \left(A a b^{2} + C a^{2} b\right) + x^{2} \left(\frac{3 B a^{2} b}{2} + \frac{D a^{3}}{2}\right) + x \left(3 A a^{2} b + C a^{3}\right)"," ",0,"-A*a**3/x + B*a**3*log(x) + C*b**3*x**7/7 + D*b**3*x**8/8 + x**6*(B*b**3/6 + D*a*b**2/2) + x**5*(A*b**3/5 + 3*C*a*b**2/5) + x**4*(3*B*a*b**2/4 + 3*D*a**2*b/4) + x**3*(A*a*b**2 + C*a**2*b) + x**2*(3*B*a**2*b/2 + D*a**3/2) + x*(3*A*a**2*b + C*a**3)","A",0
84,1,151,0,0.674345," ","integrate((b*x**2+a)**3*(D*x**3+C*x**2+B*x+A)/x**3,x)","\frac{C b^{3} x^{6}}{6} + \frac{D b^{3} x^{7}}{7} + a^{2} \left(3 A b + C a\right) \log{\left(x \right)} + x^{5} \left(\frac{B b^{3}}{5} + \frac{3 D a b^{2}}{5}\right) + x^{4} \left(\frac{A b^{3}}{4} + \frac{3 C a b^{2}}{4}\right) + x^{3} \left(B a b^{2} + D a^{2} b\right) + x^{2} \left(\frac{3 A a b^{2}}{2} + \frac{3 C a^{2} b}{2}\right) + x \left(3 B a^{2} b + D a^{3}\right) + \frac{- A a^{3} - 2 B a^{3} x}{2 x^{2}}"," ",0,"C*b**3*x**6/6 + D*b**3*x**7/7 + a**2*(3*A*b + C*a)*log(x) + x**5*(B*b**3/5 + 3*D*a*b**2/5) + x**4*(A*b**3/4 + 3*C*a*b**2/4) + x**3*(B*a*b**2 + D*a**2*b) + x**2*(3*A*a*b**2/2 + 3*C*a**2*b/2) + x*(3*B*a**2*b + D*a**3) + (-A*a**3 - 2*B*a**3*x)/(2*x**2)","A",0
85,1,155,0,1.085969," ","integrate((b*x**2+a)**3*(D*x**3+C*x**2+B*x+A)/x**4,x)","\frac{C b^{3} x^{5}}{5} + \frac{D b^{3} x^{6}}{6} + a^{2} \left(3 B b + D a\right) \log{\left(x \right)} + x^{4} \left(\frac{B b^{3}}{4} + \frac{3 D a b^{2}}{4}\right) + x^{3} \left(\frac{A b^{3}}{3} + C a b^{2}\right) + x^{2} \left(\frac{3 B a b^{2}}{2} + \frac{3 D a^{2} b}{2}\right) + x \left(3 A a b^{2} + 3 C a^{2} b\right) + \frac{- 2 A a^{3} - 3 B a^{3} x + x^{2} \left(- 18 A a^{2} b - 6 C a^{3}\right)}{6 x^{3}}"," ",0,"C*b**3*x**5/5 + D*b**3*x**6/6 + a**2*(3*B*b + D*a)*log(x) + x**4*(B*b**3/4 + 3*D*a*b**2/4) + x**3*(A*b**3/3 + C*a*b**2) + x**2*(3*B*a*b**2/2 + 3*D*a**2*b/2) + x*(3*A*a*b**2 + 3*C*a**2*b) + (-2*A*a**3 - 3*B*a**3*x + x**2*(-18*A*a**2*b - 6*C*a**3))/(6*x**3)","A",0
86,1,316,0,1.433719," ","integrate(x**4*(D*x**3+C*x**2+B*x+A)/(b*x**2+a),x)","\frac{C x^{5}}{5 b} + \frac{D x^{6}}{6 b} + x^{4} \left(\frac{B}{4 b} - \frac{D a}{4 b^{2}}\right) + x^{3} \left(\frac{A}{3 b} - \frac{C a}{3 b^{2}}\right) + x^{2} \left(- \frac{B a}{2 b^{2}} + \frac{D a^{2}}{2 b^{3}}\right) + x \left(- \frac{A a}{b^{2}} + \frac{C a^{2}}{b^{3}}\right) + \left(- \frac{a^{2} \left(- B b + D a\right)}{2 b^{4}} - \frac{\sqrt{- a^{3} b^{9}} \left(- A b + C a\right)}{2 b^{8}}\right) \log{\left(x + \frac{B a^{2} b - D a^{3} - 2 b^{4} \left(- \frac{a^{2} \left(- B b + D a\right)}{2 b^{4}} - \frac{\sqrt{- a^{3} b^{9}} \left(- A b + C a\right)}{2 b^{8}}\right)}{- A a b^{2} + C a^{2} b} \right)} + \left(- \frac{a^{2} \left(- B b + D a\right)}{2 b^{4}} + \frac{\sqrt{- a^{3} b^{9}} \left(- A b + C a\right)}{2 b^{8}}\right) \log{\left(x + \frac{B a^{2} b - D a^{3} - 2 b^{4} \left(- \frac{a^{2} \left(- B b + D a\right)}{2 b^{4}} + \frac{\sqrt{- a^{3} b^{9}} \left(- A b + C a\right)}{2 b^{8}}\right)}{- A a b^{2} + C a^{2} b} \right)}"," ",0,"C*x**5/(5*b) + D*x**6/(6*b) + x**4*(B/(4*b) - D*a/(4*b**2)) + x**3*(A/(3*b) - C*a/(3*b**2)) + x**2*(-B*a/(2*b**2) + D*a**2/(2*b**3)) + x*(-A*a/b**2 + C*a**2/b**3) + (-a**2*(-B*b + D*a)/(2*b**4) - sqrt(-a**3*b**9)*(-A*b + C*a)/(2*b**8))*log(x + (B*a**2*b - D*a**3 - 2*b**4*(-a**2*(-B*b + D*a)/(2*b**4) - sqrt(-a**3*b**9)*(-A*b + C*a)/(2*b**8)))/(-A*a*b**2 + C*a**2*b)) + (-a**2*(-B*b + D*a)/(2*b**4) + sqrt(-a**3*b**9)*(-A*b + C*a)/(2*b**8))*log(x + (B*a**2*b - D*a**3 - 2*b**4*(-a**2*(-B*b + D*a)/(2*b**4) + sqrt(-a**3*b**9)*(-A*b + C*a)/(2*b**8)))/(-A*a*b**2 + C*a**2*b))","B",0
87,1,274,0,1.348771," ","integrate(x**3*(D*x**3+C*x**2+B*x+A)/(b*x**2+a),x)","\frac{C x^{4}}{4 b} + \frac{D x^{5}}{5 b} + x^{3} \left(\frac{B}{3 b} - \frac{D a}{3 b^{2}}\right) + x^{2} \left(\frac{A}{2 b} - \frac{C a}{2 b^{2}}\right) + x \left(- \frac{B a}{b^{2}} + \frac{D a^{2}}{b^{3}}\right) + \left(\frac{a \left(- A b + C a\right)}{2 b^{3}} - \frac{\sqrt{- a^{3} b^{7}} \left(- B b + D a\right)}{2 b^{7}}\right) \log{\left(x + \frac{- A a b + C a^{2} - 2 b^{3} \left(\frac{a \left(- A b + C a\right)}{2 b^{3}} - \frac{\sqrt{- a^{3} b^{7}} \left(- B b + D a\right)}{2 b^{7}}\right)}{- B a b + D a^{2}} \right)} + \left(\frac{a \left(- A b + C a\right)}{2 b^{3}} + \frac{\sqrt{- a^{3} b^{7}} \left(- B b + D a\right)}{2 b^{7}}\right) \log{\left(x + \frac{- A a b + C a^{2} - 2 b^{3} \left(\frac{a \left(- A b + C a\right)}{2 b^{3}} + \frac{\sqrt{- a^{3} b^{7}} \left(- B b + D a\right)}{2 b^{7}}\right)}{- B a b + D a^{2}} \right)}"," ",0,"C*x**4/(4*b) + D*x**5/(5*b) + x**3*(B/(3*b) - D*a/(3*b**2)) + x**2*(A/(2*b) - C*a/(2*b**2)) + x*(-B*a/b**2 + D*a**2/b**3) + (a*(-A*b + C*a)/(2*b**3) - sqrt(-a**3*b**7)*(-B*b + D*a)/(2*b**7))*log(x + (-A*a*b + C*a**2 - 2*b**3*(a*(-A*b + C*a)/(2*b**3) - sqrt(-a**3*b**7)*(-B*b + D*a)/(2*b**7)))/(-B*a*b + D*a**2)) + (a*(-A*b + C*a)/(2*b**3) + sqrt(-a**3*b**7)*(-B*b + D*a)/(2*b**7))*log(x + (-A*a*b + C*a**2 - 2*b**3*(a*(-A*b + C*a)/(2*b**3) + sqrt(-a**3*b**7)*(-B*b + D*a)/(2*b**7)))/(-B*a*b + D*a**2))","B",0
88,1,245,0,1.646984," ","integrate(x**2*(D*x**3+C*x**2+B*x+A)/(b*x**2+a),x)","\frac{C x^{3}}{3 b} + \frac{D x^{4}}{4 b} + x^{2} \left(\frac{B}{2 b} - \frac{D a}{2 b^{2}}\right) + x \left(\frac{A}{b} - \frac{C a}{b^{2}}\right) + \left(\frac{a \left(- B b + D a\right)}{2 b^{3}} - \frac{\sqrt{- a b^{7}} \left(- A b + C a\right)}{2 b^{6}}\right) \log{\left(x + \frac{B a b - D a^{2} + 2 b^{3} \left(\frac{a \left(- B b + D a\right)}{2 b^{3}} - \frac{\sqrt{- a b^{7}} \left(- A b + C a\right)}{2 b^{6}}\right)}{- A b^{2} + C a b} \right)} + \left(\frac{a \left(- B b + D a\right)}{2 b^{3}} + \frac{\sqrt{- a b^{7}} \left(- A b + C a\right)}{2 b^{6}}\right) \log{\left(x + \frac{B a b - D a^{2} + 2 b^{3} \left(\frac{a \left(- B b + D a\right)}{2 b^{3}} + \frac{\sqrt{- a b^{7}} \left(- A b + C a\right)}{2 b^{6}}\right)}{- A b^{2} + C a b} \right)}"," ",0,"C*x**3/(3*b) + D*x**4/(4*b) + x**2*(B/(2*b) - D*a/(2*b**2)) + x*(A/b - C*a/b**2) + (a*(-B*b + D*a)/(2*b**3) - sqrt(-a*b**7)*(-A*b + C*a)/(2*b**6))*log(x + (B*a*b - D*a**2 + 2*b**3*(a*(-B*b + D*a)/(2*b**3) - sqrt(-a*b**7)*(-A*b + C*a)/(2*b**6)))/(-A*b**2 + C*a*b)) + (a*(-B*b + D*a)/(2*b**3) + sqrt(-a*b**7)*(-A*b + C*a)/(2*b**6))*log(x + (B*a*b - D*a**2 + 2*b**3*(a*(-B*b + D*a)/(2*b**3) + sqrt(-a*b**7)*(-A*b + C*a)/(2*b**6)))/(-A*b**2 + C*a*b))","B",0
89,1,211,0,0.988147," ","integrate(x*(D*x**3+C*x**2+B*x+A)/(b*x**2+a),x)","\frac{C x^{2}}{2 b} + \frac{D x^{3}}{3 b} + x \left(\frac{B}{b} - \frac{D a}{b^{2}}\right) + \left(- \frac{- A b + C a}{2 b^{2}} - \frac{\sqrt{- a b^{5}} \left(- B b + D a\right)}{2 b^{5}}\right) \log{\left(x + \frac{- A b + C a + 2 b^{2} \left(- \frac{- A b + C a}{2 b^{2}} - \frac{\sqrt{- a b^{5}} \left(- B b + D a\right)}{2 b^{5}}\right)}{- B b + D a} \right)} + \left(- \frac{- A b + C a}{2 b^{2}} + \frac{\sqrt{- a b^{5}} \left(- B b + D a\right)}{2 b^{5}}\right) \log{\left(x + \frac{- A b + C a + 2 b^{2} \left(- \frac{- A b + C a}{2 b^{2}} + \frac{\sqrt{- a b^{5}} \left(- B b + D a\right)}{2 b^{5}}\right)}{- B b + D a} \right)}"," ",0,"C*x**2/(2*b) + D*x**3/(3*b) + x*(B/b - D*a/b**2) + (-(-A*b + C*a)/(2*b**2) - sqrt(-a*b**5)*(-B*b + D*a)/(2*b**5))*log(x + (-A*b + C*a + 2*b**2*(-(-A*b + C*a)/(2*b**2) - sqrt(-a*b**5)*(-B*b + D*a)/(2*b**5)))/(-B*b + D*a)) + (-(-A*b + C*a)/(2*b**2) + sqrt(-a*b**5)*(-B*b + D*a)/(2*b**5))*log(x + (-A*b + C*a + 2*b**2*(-(-A*b + C*a)/(2*b**2) + sqrt(-a*b**5)*(-B*b + D*a)/(2*b**5)))/(-B*b + D*a))","B",0
90,1,219,0,0.881007," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x**2+a),x)","\frac{C x}{b} + \frac{D x^{2}}{2 b} + \left(- \frac{- B b + D a}{2 b^{2}} - \frac{\sqrt{- a b^{5}} \left(- A b + C a\right)}{2 a b^{4}}\right) \log{\left(x + \frac{B a b - D a^{2} - 2 a b^{2} \left(- \frac{- B b + D a}{2 b^{2}} - \frac{\sqrt{- a b^{5}} \left(- A b + C a\right)}{2 a b^{4}}\right)}{- A b^{2} + C a b} \right)} + \left(- \frac{- B b + D a}{2 b^{2}} + \frac{\sqrt{- a b^{5}} \left(- A b + C a\right)}{2 a b^{4}}\right) \log{\left(x + \frac{B a b - D a^{2} - 2 a b^{2} \left(- \frac{- B b + D a}{2 b^{2}} + \frac{\sqrt{- a b^{5}} \left(- A b + C a\right)}{2 a b^{4}}\right)}{- A b^{2} + C a b} \right)}"," ",0,"C*x/b + D*x**2/(2*b) + (-(-B*b + D*a)/(2*b**2) - sqrt(-a*b**5)*(-A*b + C*a)/(2*a*b**4))*log(x + (B*a*b - D*a**2 - 2*a*b**2*(-(-B*b + D*a)/(2*b**2) - sqrt(-a*b**5)*(-A*b + C*a)/(2*a*b**4)))/(-A*b**2 + C*a*b)) + (-(-B*b + D*a)/(2*b**2) + sqrt(-a*b**5)*(-A*b + C*a)/(2*a*b**4))*log(x + (B*a*b - D*a**2 - 2*a*b**2*(-(-B*b + D*a)/(2*b**2) + sqrt(-a*b**5)*(-A*b + C*a)/(2*a*b**4)))/(-A*b**2 + C*a*b))","B",0
91,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x**2/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x**3/(b*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,1,335,0,4.769382," ","integrate(x**4*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**2,x)","\frac{C x^{3}}{3 b^{2}} + \frac{D x^{4}}{4 b^{2}} + x^{2} \left(\frac{B}{2 b^{2}} - \frac{D a}{b^{3}}\right) + x \left(\frac{A}{b^{2}} - \frac{2 C a}{b^{3}}\right) + \left(\frac{a \left(- 2 B b + 3 D a\right)}{2 b^{4}} - \frac{\sqrt{- a b^{9}} \left(- 3 A b + 5 C a\right)}{4 b^{8}}\right) \log{\left(x + \frac{4 B a b - 6 D a^{2} + 4 b^{4} \left(\frac{a \left(- 2 B b + 3 D a\right)}{2 b^{4}} - \frac{\sqrt{- a b^{9}} \left(- 3 A b + 5 C a\right)}{4 b^{8}}\right)}{- 3 A b^{2} + 5 C a b} \right)} + \left(\frac{a \left(- 2 B b + 3 D a\right)}{2 b^{4}} + \frac{\sqrt{- a b^{9}} \left(- 3 A b + 5 C a\right)}{4 b^{8}}\right) \log{\left(x + \frac{4 B a b - 6 D a^{2} + 4 b^{4} \left(\frac{a \left(- 2 B b + 3 D a\right)}{2 b^{4}} + \frac{\sqrt{- a b^{9}} \left(- 3 A b + 5 C a\right)}{4 b^{8}}\right)}{- 3 A b^{2} + 5 C a b} \right)} + \frac{- B a^{2} b + D a^{3} + x \left(A a b^{2} - C a^{2} b\right)}{2 a b^{4} + 2 b^{5} x^{2}}"," ",0,"C*x**3/(3*b**2) + D*x**4/(4*b**2) + x**2*(B/(2*b**2) - D*a/b**3) + x*(A/b**2 - 2*C*a/b**3) + (a*(-2*B*b + 3*D*a)/(2*b**4) - sqrt(-a*b**9)*(-3*A*b + 5*C*a)/(4*b**8))*log(x + (4*B*a*b - 6*D*a**2 + 4*b**4*(a*(-2*B*b + 3*D*a)/(2*b**4) - sqrt(-a*b**9)*(-3*A*b + 5*C*a)/(4*b**8)))/(-3*A*b**2 + 5*C*a*b)) + (a*(-2*B*b + 3*D*a)/(2*b**4) + sqrt(-a*b**9)*(-3*A*b + 5*C*a)/(4*b**8))*log(x + (4*B*a*b - 6*D*a**2 + 4*b**4*(a*(-2*B*b + 3*D*a)/(2*b**4) + sqrt(-a*b**9)*(-3*A*b + 5*C*a)/(4*b**8)))/(-3*A*b**2 + 5*C*a*b)) + (-B*a**2*b + D*a**3 + x*(A*a*b**2 - C*a**2*b))/(2*a*b**4 + 2*b**5*x**2)","B",0
95,1,289,0,3.868367," ","integrate(x**3*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**2,x)","\frac{C x^{2}}{2 b^{2}} + \frac{D x^{3}}{3 b^{2}} + x \left(\frac{B}{b^{2}} - \frac{2 D a}{b^{3}}\right) + \left(- \frac{- A b + 2 C a}{2 b^{3}} - \frac{\sqrt{- a b^{7}} \left(- 3 B b + 5 D a\right)}{4 b^{7}}\right) \log{\left(x + \frac{- 2 A b + 4 C a + 4 b^{3} \left(- \frac{- A b + 2 C a}{2 b^{3}} - \frac{\sqrt{- a b^{7}} \left(- 3 B b + 5 D a\right)}{4 b^{7}}\right)}{- 3 B b + 5 D a} \right)} + \left(- \frac{- A b + 2 C a}{2 b^{3}} + \frac{\sqrt{- a b^{7}} \left(- 3 B b + 5 D a\right)}{4 b^{7}}\right) \log{\left(x + \frac{- 2 A b + 4 C a + 4 b^{3} \left(- \frac{- A b + 2 C a}{2 b^{3}} + \frac{\sqrt{- a b^{7}} \left(- 3 B b + 5 D a\right)}{4 b^{7}}\right)}{- 3 B b + 5 D a} \right)} + \frac{A a b - C a^{2} + x \left(B a b - D a^{2}\right)}{2 a b^{3} + 2 b^{4} x^{2}}"," ",0,"C*x**2/(2*b**2) + D*x**3/(3*b**2) + x*(B/b**2 - 2*D*a/b**3) + (-(-A*b + 2*C*a)/(2*b**3) - sqrt(-a*b**7)*(-3*B*b + 5*D*a)/(4*b**7))*log(x + (-2*A*b + 4*C*a + 4*b**3*(-(-A*b + 2*C*a)/(2*b**3) - sqrt(-a*b**7)*(-3*B*b + 5*D*a)/(4*b**7)))/(-3*B*b + 5*D*a)) + (-(-A*b + 2*C*a)/(2*b**3) + sqrt(-a*b**7)*(-3*B*b + 5*D*a)/(4*b**7))*log(x + (-2*A*b + 4*C*a + 4*b**3*(-(-A*b + 2*C*a)/(2*b**3) + sqrt(-a*b**7)*(-3*B*b + 5*D*a)/(4*b**7)))/(-3*B*b + 5*D*a)) + (A*a*b - C*a**2 + x*(B*a*b - D*a**2))/(2*a*b**3 + 2*b**4*x**2)","B",0
96,1,284,0,4.610541," ","integrate(x**2*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**2,x)","\frac{C x}{b^{2}} + \frac{D x^{2}}{2 b^{2}} + \left(- \frac{- B b + 2 D a}{2 b^{3}} - \frac{\sqrt{- a b^{7}} \left(- A b + 3 C a\right)}{4 a b^{6}}\right) \log{\left(x + \frac{2 B a b - 4 D a^{2} - 4 a b^{3} \left(- \frac{- B b + 2 D a}{2 b^{3}} - \frac{\sqrt{- a b^{7}} \left(- A b + 3 C a\right)}{4 a b^{6}}\right)}{- A b^{2} + 3 C a b} \right)} + \left(- \frac{- B b + 2 D a}{2 b^{3}} + \frac{\sqrt{- a b^{7}} \left(- A b + 3 C a\right)}{4 a b^{6}}\right) \log{\left(x + \frac{2 B a b - 4 D a^{2} - 4 a b^{3} \left(- \frac{- B b + 2 D a}{2 b^{3}} + \frac{\sqrt{- a b^{7}} \left(- A b + 3 C a\right)}{4 a b^{6}}\right)}{- A b^{2} + 3 C a b} \right)} + \frac{B a b - D a^{2} + x \left(- A b^{2} + C a b\right)}{2 a b^{3} + 2 b^{4} x^{2}}"," ",0,"C*x/b**2 + D*x**2/(2*b**2) + (-(-B*b + 2*D*a)/(2*b**3) - sqrt(-a*b**7)*(-A*b + 3*C*a)/(4*a*b**6))*log(x + (2*B*a*b - 4*D*a**2 - 4*a*b**3*(-(-B*b + 2*D*a)/(2*b**3) - sqrt(-a*b**7)*(-A*b + 3*C*a)/(4*a*b**6)))/(-A*b**2 + 3*C*a*b)) + (-(-B*b + 2*D*a)/(2*b**3) + sqrt(-a*b**7)*(-A*b + 3*C*a)/(4*a*b**6))*log(x + (2*B*a*b - 4*D*a**2 - 4*a*b**3*(-(-B*b + 2*D*a)/(2*b**3) + sqrt(-a*b**7)*(-A*b + 3*C*a)/(4*a*b**6)))/(-A*b**2 + 3*C*a*b)) + (B*a*b - D*a**2 + x*(-A*b**2 + C*a*b))/(2*a*b**3 + 2*b**4*x**2)","B",0
97,1,212,0,5.762716," ","integrate(x*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**2,x)","\frac{D x}{b^{2}} + \left(\frac{C}{2 b^{2}} - \frac{\sqrt{- a b^{5}} \left(- B b + 3 D a\right)}{4 a b^{5}}\right) \log{\left(x + \frac{2 C a - 4 a b^{2} \left(\frac{C}{2 b^{2}} - \frac{\sqrt{- a b^{5}} \left(- B b + 3 D a\right)}{4 a b^{5}}\right)}{- B b + 3 D a} \right)} + \left(\frac{C}{2 b^{2}} + \frac{\sqrt{- a b^{5}} \left(- B b + 3 D a\right)}{4 a b^{5}}\right) \log{\left(x + \frac{2 C a - 4 a b^{2} \left(\frac{C}{2 b^{2}} + \frac{\sqrt{- a b^{5}} \left(- B b + 3 D a\right)}{4 a b^{5}}\right)}{- B b + 3 D a} \right)} + \frac{- A b + C a + x \left(- B b + D a\right)}{2 a b^{2} + 2 b^{3} x^{2}}"," ",0,"D*x/b**2 + (C/(2*b**2) - sqrt(-a*b**5)*(-B*b + 3*D*a)/(4*a*b**5))*log(x + (2*C*a - 4*a*b**2*(C/(2*b**2) - sqrt(-a*b**5)*(-B*b + 3*D*a)/(4*a*b**5)))/(-B*b + 3*D*a)) + (C/(2*b**2) + sqrt(-a*b**5)*(-B*b + 3*D*a)/(4*a*b**5))*log(x + (2*C*a - 4*a*b**2*(C/(2*b**2) + sqrt(-a*b**5)*(-B*b + 3*D*a)/(4*a*b**5)))/(-B*b + 3*D*a)) + (-A*b + C*a + x*(-B*b + D*a))/(2*a*b**2 + 2*b**3*x**2)","B",0
98,1,233,0,3.093683," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x**2+a)**2,x)","\left(\frac{D}{2 b^{2}} - \frac{\sqrt{- a^{3} b^{5}} \left(A b + C a\right)}{4 a^{3} b^{4}}\right) \log{\left(x + \frac{- 2 D a^{2} + 4 a^{2} b^{2} \left(\frac{D}{2 b^{2}} - \frac{\sqrt{- a^{3} b^{5}} \left(A b + C a\right)}{4 a^{3} b^{4}}\right)}{A b^{2} + C a b} \right)} + \left(\frac{D}{2 b^{2}} + \frac{\sqrt{- a^{3} b^{5}} \left(A b + C a\right)}{4 a^{3} b^{4}}\right) \log{\left(x + \frac{- 2 D a^{2} + 4 a^{2} b^{2} \left(\frac{D}{2 b^{2}} + \frac{\sqrt{- a^{3} b^{5}} \left(A b + C a\right)}{4 a^{3} b^{4}}\right)}{A b^{2} + C a b} \right)} + \frac{- B a b + D a^{2} + x \left(A b^{2} - C a b\right)}{2 a^{2} b^{2} + 2 a b^{3} x^{2}}"," ",0,"(D/(2*b**2) - sqrt(-a**3*b**5)*(A*b + C*a)/(4*a**3*b**4))*log(x + (-2*D*a**2 + 4*a**2*b**2*(D/(2*b**2) - sqrt(-a**3*b**5)*(A*b + C*a)/(4*a**3*b**4)))/(A*b**2 + C*a*b)) + (D/(2*b**2) + sqrt(-a**3*b**5)*(A*b + C*a)/(4*a**3*b**4))*log(x + (-2*D*a**2 + 4*a**2*b**2*(D/(2*b**2) + sqrt(-a**3*b**5)*(A*b + C*a)/(4*a**3*b**4)))/(A*b**2 + C*a*b)) + (-B*a*b + D*a**2 + x*(A*b**2 - C*a*b))/(2*a**2*b**2 + 2*a*b**3*x**2)","B",0
99,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x**2/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x**3/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,1,357,0,29.586959," ","integrate(x**4*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**3,x)","\frac{C x}{b^{3}} + \frac{D x^{2}}{2 b^{3}} + \left(- \frac{- B b + 3 D a}{2 b^{4}} - \frac{3 \sqrt{- a b^{9}} \left(- A b + 5 C a\right)}{16 a b^{8}}\right) \log{\left(x + \frac{8 B a b - 24 D a^{2} - 16 a b^{4} \left(- \frac{- B b + 3 D a}{2 b^{4}} - \frac{3 \sqrt{- a b^{9}} \left(- A b + 5 C a\right)}{16 a b^{8}}\right)}{- 3 A b^{2} + 15 C a b} \right)} + \left(- \frac{- B b + 3 D a}{2 b^{4}} + \frac{3 \sqrt{- a b^{9}} \left(- A b + 5 C a\right)}{16 a b^{8}}\right) \log{\left(x + \frac{8 B a b - 24 D a^{2} - 16 a b^{4} \left(- \frac{- B b + 3 D a}{2 b^{4}} + \frac{3 \sqrt{- a b^{9}} \left(- A b + 5 C a\right)}{16 a b^{8}}\right)}{- 3 A b^{2} + 15 C a b} \right)} + \frac{6 B a^{2} b - 10 D a^{3} + x^{3} \left(- 5 A b^{3} + 9 C a b^{2}\right) + x^{2} \left(8 B a b^{2} - 12 D a^{2} b\right) + x \left(- 3 A a b^{2} + 7 C a^{2} b\right)}{8 a^{2} b^{4} + 16 a b^{5} x^{2} + 8 b^{6} x^{4}}"," ",0,"C*x/b**3 + D*x**2/(2*b**3) + (-(-B*b + 3*D*a)/(2*b**4) - 3*sqrt(-a*b**9)*(-A*b + 5*C*a)/(16*a*b**8))*log(x + (8*B*a*b - 24*D*a**2 - 16*a*b**4*(-(-B*b + 3*D*a)/(2*b**4) - 3*sqrt(-a*b**9)*(-A*b + 5*C*a)/(16*a*b**8)))/(-3*A*b**2 + 15*C*a*b)) + (-(-B*b + 3*D*a)/(2*b**4) + 3*sqrt(-a*b**9)*(-A*b + 5*C*a)/(16*a*b**8))*log(x + (8*B*a*b - 24*D*a**2 - 16*a*b**4*(-(-B*b + 3*D*a)/(2*b**4) + 3*sqrt(-a*b**9)*(-A*b + 5*C*a)/(16*a*b**8)))/(-3*A*b**2 + 15*C*a*b)) + (6*B*a**2*b - 10*D*a**3 + x**3*(-5*A*b**3 + 9*C*a*b**2) + x**2*(8*B*a*b**2 - 12*D*a**2*b) + x*(-3*A*a*b**2 + 7*C*a**2*b))/(8*a**2*b**4 + 16*a*b**5*x**2 + 8*b**6*x**4)","B",0
103,1,282,0,29.728400," ","integrate(x**3*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**3,x)","\frac{D x}{b^{3}} + \left(\frac{C}{2 b^{3}} - \frac{3 \sqrt{- a b^{7}} \left(- B b + 5 D a\right)}{16 a b^{7}}\right) \log{\left(x + \frac{8 C a - 16 a b^{3} \left(\frac{C}{2 b^{3}} - \frac{3 \sqrt{- a b^{7}} \left(- B b + 5 D a\right)}{16 a b^{7}}\right)}{- 3 B b + 15 D a} \right)} + \left(\frac{C}{2 b^{3}} + \frac{3 \sqrt{- a b^{7}} \left(- B b + 5 D a\right)}{16 a b^{7}}\right) \log{\left(x + \frac{8 C a - 16 a b^{3} \left(\frac{C}{2 b^{3}} + \frac{3 \sqrt{- a b^{7}} \left(- B b + 5 D a\right)}{16 a b^{7}}\right)}{- 3 B b + 15 D a} \right)} + \frac{- 2 A a b + 6 C a^{2} + x^{3} \left(- 5 B b^{2} + 9 D a b\right) + x^{2} \left(- 4 A b^{2} + 8 C a b\right) + x \left(- 3 B a b + 7 D a^{2}\right)}{8 a^{2} b^{3} + 16 a b^{4} x^{2} + 8 b^{5} x^{4}}"," ",0,"D*x/b**3 + (C/(2*b**3) - 3*sqrt(-a*b**7)*(-B*b + 5*D*a)/(16*a*b**7))*log(x + (8*C*a - 16*a*b**3*(C/(2*b**3) - 3*sqrt(-a*b**7)*(-B*b + 5*D*a)/(16*a*b**7)))/(-3*B*b + 15*D*a)) + (C/(2*b**3) + 3*sqrt(-a*b**7)*(-B*b + 5*D*a)/(16*a*b**7))*log(x + (8*C*a - 16*a*b**3*(C/(2*b**3) + 3*sqrt(-a*b**7)*(-B*b + 5*D*a)/(16*a*b**7)))/(-3*B*b + 15*D*a)) + (-2*A*a*b + 6*C*a**2 + x**3*(-5*B*b**2 + 9*D*a*b) + x**2*(-4*A*b**2 + 8*C*a*b) + x*(-3*B*a*b + 7*D*a**2))/(8*a**2*b**3 + 16*a*b**4*x**2 + 8*b**5*x**4)","B",0
104,1,304,0,20.010067," ","integrate(x**2*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**3,x)","\left(\frac{D}{2 b^{3}} - \frac{\sqrt{- a^{3} b^{7}} \left(A b + 3 C a\right)}{16 a^{3} b^{6}}\right) \log{\left(x + \frac{- 8 D a^{2} + 16 a^{2} b^{3} \left(\frac{D}{2 b^{3}} - \frac{\sqrt{- a^{3} b^{7}} \left(A b + 3 C a\right)}{16 a^{3} b^{6}}\right)}{A b^{2} + 3 C a b} \right)} + \left(\frac{D}{2 b^{3}} + \frac{\sqrt{- a^{3} b^{7}} \left(A b + 3 C a\right)}{16 a^{3} b^{6}}\right) \log{\left(x + \frac{- 8 D a^{2} + 16 a^{2} b^{3} \left(\frac{D}{2 b^{3}} + \frac{\sqrt{- a^{3} b^{7}} \left(A b + 3 C a\right)}{16 a^{3} b^{6}}\right)}{A b^{2} + 3 C a b} \right)} + \frac{- 2 B a^{2} b + 6 D a^{3} + x^{3} \left(A b^{3} - 5 C a b^{2}\right) + x^{2} \left(- 4 B a b^{2} + 8 D a^{2} b\right) + x \left(- A a b^{2} - 3 C a^{2} b\right)}{8 a^{3} b^{3} + 16 a^{2} b^{4} x^{2} + 8 a b^{5} x^{4}}"," ",0,"(D/(2*b**3) - sqrt(-a**3*b**7)*(A*b + 3*C*a)/(16*a**3*b**6))*log(x + (-8*D*a**2 + 16*a**2*b**3*(D/(2*b**3) - sqrt(-a**3*b**7)*(A*b + 3*C*a)/(16*a**3*b**6)))/(A*b**2 + 3*C*a*b)) + (D/(2*b**3) + sqrt(-a**3*b**7)*(A*b + 3*C*a)/(16*a**3*b**6))*log(x + (-8*D*a**2 + 16*a**2*b**3*(D/(2*b**3) + sqrt(-a**3*b**7)*(A*b + 3*C*a)/(16*a**3*b**6)))/(A*b**2 + 3*C*a*b)) + (-2*B*a**2*b + 6*D*a**3 + x**3*(A*b**3 - 5*C*a*b**2) + x**2*(-4*B*a*b**2 + 8*D*a**2*b) + x*(-A*a*b**2 - 3*C*a**2*b))/(8*a**3*b**3 + 16*a**2*b**4*x**2 + 8*a*b**5*x**4)","B",0
105,1,178,0,16.371900," ","integrate(x*(D*x**3+C*x**2+B*x+A)/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(B b + 3 D 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(B b + 3 D a\right) \log{\left(a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} + x \right)}}{16} + \frac{- 2 A a b - 2 C a^{2} - 4 C a b x^{2} + x^{3} \left(B b^{2} - 5 D a b\right) + x \left(- B a b - 3 D 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))*(B*b + 3*D*a)*log(-a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/16 + sqrt(-1/(a**3*b**5))*(B*b + 3*D*a)*log(a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/16 + (-2*A*a*b - 2*C*a**2 - 4*C*a*b*x**2 + x**3*(B*b**2 - 5*D*a*b) + x*(-B*a*b - 3*D*a**2))/(8*a**3*b**2 + 16*a**2*b**3*x**2 + 8*a*b**4*x**4)","A",0
106,1,184,0,11.271675," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(3 A b + C 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 + C a\right) \log{\left(a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{16} + \frac{- 2 B a^{2} b - 2 D a^{3} - 4 D a^{2} b x^{2} + x^{3} \left(3 A b^{3} + C a b^{2}\right) + x \left(5 A a b^{2} - C a^{2} b\right)}{8 a^{4} b^{2} + 16 a^{3} b^{3} x^{2} + 8 a^{2} b^{4} x^{4}}"," ",0,"-sqrt(-1/(a**5*b**3))*(3*A*b + C*a)*log(-a**3*b*sqrt(-1/(a**5*b**3)) + x)/16 + sqrt(-1/(a**5*b**3))*(3*A*b + C*a)*log(a**3*b*sqrt(-1/(a**5*b**3)) + x)/16 + (-2*B*a**2*b - 2*D*a**3 - 4*D*a**2*b*x**2 + x**3*(3*A*b**3 + C*a*b**2) + x*(5*A*a*b**2 - C*a**2*b))/(8*a**4*b**2 + 16*a**3*b**3*x**2 + 8*a**2*b**4*x**4)","A",0
107,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x**2/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/x**3/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,1,15,0,0.174181," ","integrate((4*x**3-x)/(x**2+5)**2,x)","2 \log{\left(x^{2} + 5 \right)} + \frac{21}{2 x^{2} + 10}"," ",0,"2*log(x**2 + 5) + 21/(2*x**2 + 10)","A",0
111,1,22,0,0.693588," ","integrate((x**3-x)/(x**2-2)**(1/2),x)","\frac{x^{2} \sqrt{x^{2} - 2}}{3} + \frac{\sqrt{x^{2} - 2}}{3}"," ",0,"x**2*sqrt(x**2 - 2)/3 + sqrt(x**2 - 2)/3","A",0
112,1,20,0,0.141088," ","integrate((2*x**4-x**2)/(2*x**2+1),x)","\frac{x^{3}}{3} - x + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x \right)}}{2}"," ",0,"x**3/3 - x + sqrt(2)*atan(sqrt(2)*x)/2","A",0
113,1,22,0,0.111243," ","integrate((x**4+x**3)/(x**2+1),x)","\frac{x^{3}}{3} + \frac{x^{2}}{2} - x - \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)}"," ",0,"x**3/3 + x**2/2 - x - log(x**2 + 1)/2 + atan(x)","A",0
114,1,384,0,1.652033," ","integrate(x**6*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a),x)","x^{9} \left(- \frac{a f}{9 b^{2}} + \frac{e}{9 b}\right) + x^{7} \left(\frac{a^{2} f}{7 b^{3}} - \frac{a e}{7 b^{2}} + \frac{d}{7 b}\right) + x^{5} \left(- \frac{a^{3} f}{5 b^{4}} + \frac{a^{2} e}{5 b^{3}} - \frac{a d}{5 b^{2}} + \frac{c}{5 b}\right) + x^{3} \left(\frac{a^{4} f}{3 b^{5}} - \frac{a^{3} e}{3 b^{4}} + \frac{a^{2} d}{3 b^{3}} - \frac{a c}{3 b^{2}}\right) + x \left(- \frac{a^{5} f}{b^{6}} + \frac{a^{4} e}{b^{5}} - \frac{a^{3} d}{b^{4}} + \frac{a^{2} c}{b^{3}}\right) - \frac{\sqrt{- \frac{a^{5}}{b^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- \frac{b^{6} \sqrt{- \frac{a^{5}}{b^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{5} f - a^{4} b e + a^{3} b^{2} d - a^{2} b^{3} c} + x \right)}}{2} + \frac{\sqrt{- \frac{a^{5}}{b^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{b^{6} \sqrt{- \frac{a^{5}}{b^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{5} f - a^{4} b e + a^{3} b^{2} d - a^{2} b^{3} c} + x \right)}}{2} + \frac{f x^{11}}{11 b}"," ",0,"x**9*(-a*f/(9*b**2) + e/(9*b)) + x**7*(a**2*f/(7*b**3) - a*e/(7*b**2) + d/(7*b)) + x**5*(-a**3*f/(5*b**4) + a**2*e/(5*b**3) - a*d/(5*b**2) + c/(5*b)) + x**3*(a**4*f/(3*b**5) - a**3*e/(3*b**4) + a**2*d/(3*b**3) - a*c/(3*b**2)) + x*(-a**5*f/b**6 + a**4*e/b**5 - a**3*d/b**4 + a**2*c/b**3) - sqrt(-a**5/b**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-b**6*sqrt(-a**5/b**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**5*f - a**4*b*e + a**3*b**2*d - a**2*b**3*c) + x)/2 + sqrt(-a**5/b**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(b**6*sqrt(-a**5/b**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**5*f - a**4*b*e + a**3*b**2*d - a**2*b**3*c) + x)/2 + f*x**11/(11*b)","A",0
115,1,337,0,1.321108," ","integrate(x**4*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a),x)","x^{7} \left(- \frac{a f}{7 b^{2}} + \frac{e}{7 b}\right) + x^{5} \left(\frac{a^{2} f}{5 b^{3}} - \frac{a e}{5 b^{2}} + \frac{d}{5 b}\right) + x^{3} \left(- \frac{a^{3} f}{3 b^{4}} + \frac{a^{2} e}{3 b^{3}} - \frac{a d}{3 b^{2}} + \frac{c}{3 b}\right) + x \left(\frac{a^{4} f}{b^{5}} - \frac{a^{3} e}{b^{4}} + \frac{a^{2} d}{b^{3}} - \frac{a c}{b^{2}}\right) + \frac{\sqrt{- \frac{a^{3}}{b^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- \frac{b^{5} \sqrt{- \frac{a^{3}}{b^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{4} f - a^{3} b e + a^{2} b^{2} d - a b^{3} c} + x \right)}}{2} - \frac{\sqrt{- \frac{a^{3}}{b^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{b^{5} \sqrt{- \frac{a^{3}}{b^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{4} f - a^{3} b e + a^{2} b^{2} d - a b^{3} c} + x \right)}}{2} + \frac{f x^{9}}{9 b}"," ",0,"x**7*(-a*f/(7*b**2) + e/(7*b)) + x**5*(a**2*f/(5*b**3) - a*e/(5*b**2) + d/(5*b)) + x**3*(-a**3*f/(3*b**4) + a**2*e/(3*b**3) - a*d/(3*b**2) + c/(3*b)) + x*(a**4*f/b**5 - a**3*e/b**4 + a**2*d/b**3 - a*c/b**2) + sqrt(-a**3/b**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-b**5*sqrt(-a**3/b**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**4*f - a**3*b*e + a**2*b**2*d - a*b**3*c) + x)/2 - sqrt(-a**3/b**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(b**5*sqrt(-a**3/b**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**4*f - a**3*b*e + a**2*b**2*d - a*b**3*c) + x)/2 + f*x**9/(9*b)","B",0
116,1,185,0,1.128331," ","integrate(x**2*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a),x)","x^{5} \left(- \frac{a f}{5 b^{2}} + \frac{e}{5 b}\right) + x^{3} \left(\frac{a^{2} f}{3 b^{3}} - \frac{a e}{3 b^{2}} + \frac{d}{3 b}\right) + x \left(- \frac{a^{3} f}{b^{4}} + \frac{a^{2} e}{b^{3}} - \frac{a d}{b^{2}} + \frac{c}{b}\right) - \frac{\sqrt{- \frac{a}{b^{9}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- b^{4} \sqrt{- \frac{a}{b^{9}}} + x \right)}}{2} + \frac{\sqrt{- \frac{a}{b^{9}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(b^{4} \sqrt{- \frac{a}{b^{9}}} + x \right)}}{2} + \frac{f x^{7}}{7 b}"," ",0,"x**5*(-a*f/(5*b**2) + e/(5*b)) + x**3*(a**2*f/(3*b**3) - a*e/(3*b**2) + d/(3*b)) + x*(-a**3*f/b**4 + a**2*e/b**3 - a*d/b**2 + c/b) - sqrt(-a/b**9)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-b**4*sqrt(-a/b**9) + x)/2 + sqrt(-a/b**9)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(b**4*sqrt(-a/b**9) + x)/2 + f*x**7/(7*b)","A",0
117,1,160,0,1.149491," ","integrate((f*x**6+e*x**4+d*x**2+c)/(b*x**2+a),x)","x^{3} \left(- \frac{a f}{3 b^{2}} + \frac{e}{3 b}\right) + x \left(\frac{a^{2} f}{b^{3}} - \frac{a e}{b^{2}} + \frac{d}{b}\right) + \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- a b^{3} \sqrt{- \frac{1}{a b^{7}}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a b^{3} \sqrt{- \frac{1}{a b^{7}}} + x \right)}}{2} + \frac{f x^{5}}{5 b}"," ",0,"x**3*(-a*f/(3*b**2) + e/(3*b)) + x*(a**2*f/b**3 - a*e/b**2 + d/b) + sqrt(-1/(a*b**7))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-a*b**3*sqrt(-1/(a*b**7)) + x)/2 - sqrt(-1/(a*b**7))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a*b**3*sqrt(-1/(a*b**7)) + x)/2 + f*x**5/(5*b)","A",0
118,1,150,0,1.637672," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**2/(b*x**2+a),x)","x \left(- \frac{a f}{b^{2}} + \frac{e}{b}\right) - \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} + x \right)}}{2} + \frac{f x^{3}}{3 b} - \frac{c}{a x}"," ",0,"x*(-a*f/b**2 + e/b) - sqrt(-1/(a**3*b**5))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/2 + sqrt(-1/(a**3*b**5))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a**2*b**2*sqrt(-1/(a**3*b**5)) + x)/2 + f*x**3/(3*b) - c/(a*x)","B",0
119,1,151,0,2.265947," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**4/(b*x**2+a),x)","\frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{2} + \frac{f x}{b} + \frac{- a c + x^{2} \left(- 3 a d + 3 b c\right)}{3 a^{2} x^{3}}"," ",0,"sqrt(-1/(a**5*b**3))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-a**3*b*sqrt(-1/(a**5*b**3)) + x)/2 - sqrt(-1/(a**5*b**3))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a**3*b*sqrt(-1/(a**5*b**3)) + x)/2 + f*x/b + (-a*c + x**2*(-3*a*d + 3*b*c))/(3*a**2*x**3)","B",0
120,1,167,0,6.727704," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**6/(b*x**2+a),x)","- \frac{\sqrt{- \frac{1}{a^{7} b}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- a^{4} \sqrt{- \frac{1}{a^{7} b}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a^{7} b}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(a^{4} \sqrt{- \frac{1}{a^{7} b}} + x \right)}}{2} + \frac{- 3 a^{2} c + x^{4} \left(- 15 a^{2} e + 15 a b d - 15 b^{2} c\right) + x^{2} \left(- 5 a^{2} d + 5 a b c\right)}{15 a^{3} x^{5}}"," ",0,"-sqrt(-1/(a**7*b))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-a**4*sqrt(-1/(a**7*b)) + x)/2 + sqrt(-1/(a**7*b))*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a**4*sqrt(-1/(a**7*b)) + x)/2 + (-3*a**2*c + x**4*(-15*a**2*e + 15*a*b*d - 15*b**2*c) + x**2*(-5*a**2*d + 5*a*b*c))/(15*a**3*x**5)","A",0
121,1,301,0,21.646290," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**8/(b*x**2+a),x)","\frac{\sqrt{- \frac{b}{a^{9}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- \frac{a^{5} \sqrt{- \frac{b}{a^{9}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{3} b f - a^{2} b^{2} e + a b^{3} d - b^{4} c} + x \right)}}{2} - \frac{\sqrt{- \frac{b}{a^{9}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{a^{5} \sqrt{- \frac{b}{a^{9}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{3} b f - a^{2} b^{2} e + a b^{3} d - b^{4} c} + x \right)}}{2} + \frac{- 15 a^{3} c + x^{6} \left(- 105 a^{3} f + 105 a^{2} b e - 105 a b^{2} d + 105 b^{3} c\right) + x^{4} \left(- 35 a^{3} e + 35 a^{2} b d - 35 a b^{2} c\right) + x^{2} \left(- 21 a^{3} d + 21 a^{2} b c\right)}{105 a^{4} x^{7}}"," ",0,"sqrt(-b/a**9)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-a**5*sqrt(-b/a**9)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**3*b*f - a**2*b**2*e + a*b**3*d - b**4*c) + x)/2 - sqrt(-b/a**9)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a**5*sqrt(-b/a**9)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**3*b*f - a**2*b**2*e + a*b**3*d - b**4*c) + x)/2 + (-15*a**3*c + x**6*(-105*a**3*f + 105*a**2*b*e - 105*a*b**2*d + 105*b**3*c) + x**4*(-35*a**3*e + 35*a**2*b*d - 35*a*b**2*c) + x**2*(-21*a**3*d + 21*a**2*b*c))/(105*a**4*x**7)","B",0
122,1,354,0,32.721434," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**10/(b*x**2+a),x)","- \frac{\sqrt{- \frac{b^{3}}{a^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- \frac{a^{6} \sqrt{- \frac{b^{3}}{a^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{3} b^{2} f - a^{2} b^{3} e + a b^{4} d - b^{5} c} + x \right)}}{2} + \frac{\sqrt{- \frac{b^{3}}{a^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{a^{6} \sqrt{- \frac{b^{3}}{a^{11}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{3} b^{2} f - a^{2} b^{3} e + a b^{4} d - b^{5} c} + x \right)}}{2} + \frac{- 35 a^{4} c + x^{8} \left(315 a^{3} b f - 315 a^{2} b^{2} e + 315 a b^{3} d - 315 b^{4} c\right) + x^{6} \left(- 105 a^{4} f + 105 a^{3} b e - 105 a^{2} b^{2} d + 105 a b^{3} c\right) + x^{4} \left(- 63 a^{4} e + 63 a^{3} b d - 63 a^{2} b^{2} c\right) + x^{2} \left(- 45 a^{4} d + 45 a^{3} b c\right)}{315 a^{5} x^{9}}"," ",0,"-sqrt(-b**3/a**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-a**6*sqrt(-b**3/a**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**3*b**2*f - a**2*b**3*e + a*b**4*d - b**5*c) + x)/2 + sqrt(-b**3/a**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a**6*sqrt(-b**3/a**11)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**3*b**2*f - a**2*b**3*e + a*b**4*d - b**5*c) + x)/2 + (-35*a**4*c + x**8*(315*a**3*b*f - 315*a**2*b**2*e + 315*a*b**3*d - 315*b**4*c) + x**6*(-105*a**4*f + 105*a**3*b*e - 105*a**2*b**2*d + 105*a*b**3*c) + x**4*(-63*a**4*e + 63*a**3*b*d - 63*a**2*b**2*c) + x**2*(-45*a**4*d + 45*a**3*b*c))/(315*a**5*x**9)","B",0
123,1,398,0,84.141993," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**12/(b*x**2+a),x)","\frac{\sqrt{- \frac{b^{5}}{a^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(- \frac{a^{7} \sqrt{- \frac{b^{5}}{a^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{3} b^{3} f - a^{2} b^{4} e + a b^{5} d - b^{6} c} + x \right)}}{2} - \frac{\sqrt{- \frac{b^{5}}{a^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right) \log{\left(\frac{a^{7} \sqrt{- \frac{b^{5}}{a^{13}}} \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{a^{3} b^{3} f - a^{2} b^{4} e + a b^{5} d - b^{6} c} + x \right)}}{2} + \frac{- 315 a^{5} c + x^{10} \left(- 3465 a^{3} b^{2} f + 3465 a^{2} b^{3} e - 3465 a b^{4} d + 3465 b^{5} c\right) + x^{8} \left(1155 a^{4} b f - 1155 a^{3} b^{2} e + 1155 a^{2} b^{3} d - 1155 a b^{4} c\right) + x^{6} \left(- 693 a^{5} f + 693 a^{4} b e - 693 a^{3} b^{2} d + 693 a^{2} b^{3} c\right) + x^{4} \left(- 495 a^{5} e + 495 a^{4} b d - 495 a^{3} b^{2} c\right) + x^{2} \left(- 385 a^{5} d + 385 a^{4} b c\right)}{3465 a^{6} x^{11}}"," ",0,"sqrt(-b**5/a**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(-a**7*sqrt(-b**5/a**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**3*b**3*f - a**2*b**4*e + a*b**5*d - b**6*c) + x)/2 - sqrt(-b**5/a**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)*log(a**7*sqrt(-b**5/a**13)*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(a**3*b**3*f - a**2*b**4*e + a*b**5*d - b**6*c) + x)/2 + (-315*a**5*c + x**10*(-3465*a**3*b**2*f + 3465*a**2*b**3*e - 3465*a*b**4*d + 3465*b**5*c) + x**8*(1155*a**4*b*f - 1155*a**3*b**2*e + 1155*a**2*b**3*d - 1155*a*b**4*c) + x**6*(-693*a**5*f + 693*a**4*b*e - 693*a**3*b**2*d + 693*a**2*b**3*c) + x**4*(-495*a**5*e + 495*a**4*b*d - 495*a**3*b**2*c) + x**2*(-385*a**5*d + 385*a**4*b*c))/(3465*a**6*x**11)","A",0
124,1,444,0,3.069502," ","integrate(x**6*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**2,x)","x^{7} \left(- \frac{2 a f}{7 b^{3}} + \frac{e}{7 b^{2}}\right) + x^{5} \left(\frac{3 a^{2} f}{5 b^{4}} - \frac{2 a e}{5 b^{3}} + \frac{d}{5 b^{2}}\right) + x^{3} \left(- \frac{4 a^{3} f}{3 b^{5}} + \frac{a^{2} e}{b^{4}} - \frac{2 a d}{3 b^{3}} + \frac{c}{3 b^{2}}\right) + x \left(\frac{5 a^{4} f}{b^{6}} - \frac{4 a^{3} e}{b^{5}} + \frac{3 a^{2} d}{b^{4}} - \frac{2 a c}{b^{3}}\right) + \frac{x \left(a^{5} f - a^{4} b e + a^{3} b^{2} d - a^{2} b^{3} c\right)}{2 a b^{6} + 2 b^{7} x^{2}} + \frac{\sqrt{- \frac{a^{3}}{b^{13}}} \left(11 a^{3} f - 9 a^{2} b e + 7 a b^{2} d - 5 b^{3} c\right) \log{\left(- \frac{b^{6} \sqrt{- \frac{a^{3}}{b^{13}}} \left(11 a^{3} f - 9 a^{2} b e + 7 a b^{2} d - 5 b^{3} c\right)}{11 a^{4} f - 9 a^{3} b e + 7 a^{2} b^{2} d - 5 a b^{3} c} + x \right)}}{4} - \frac{\sqrt{- \frac{a^{3}}{b^{13}}} \left(11 a^{3} f - 9 a^{2} b e + 7 a b^{2} d - 5 b^{3} c\right) \log{\left(\frac{b^{6} \sqrt{- \frac{a^{3}}{b^{13}}} \left(11 a^{3} f - 9 a^{2} b e + 7 a b^{2} d - 5 b^{3} c\right)}{11 a^{4} f - 9 a^{3} b e + 7 a^{2} b^{2} d - 5 a b^{3} c} + x \right)}}{4} + \frac{f x^{9}}{9 b^{2}}"," ",0,"x**7*(-2*a*f/(7*b**3) + e/(7*b**2)) + x**5*(3*a**2*f/(5*b**4) - 2*a*e/(5*b**3) + d/(5*b**2)) + x**3*(-4*a**3*f/(3*b**5) + a**2*e/b**4 - 2*a*d/(3*b**3) + c/(3*b**2)) + x*(5*a**4*f/b**6 - 4*a**3*e/b**5 + 3*a**2*d/b**4 - 2*a*c/b**3) + x*(a**5*f - a**4*b*e + a**3*b**2*d - a**2*b**3*c)/(2*a*b**6 + 2*b**7*x**2) + sqrt(-a**3/b**13)*(11*a**3*f - 9*a**2*b*e + 7*a*b**2*d - 5*b**3*c)*log(-b**6*sqrt(-a**3/b**13)*(11*a**3*f - 9*a**2*b*e + 7*a*b**2*d - 5*b**3*c)/(11*a**4*f - 9*a**3*b*e + 7*a**2*b**2*d - 5*a*b**3*c) + x)/4 - sqrt(-a**3/b**13)*(11*a**3*f - 9*a**2*b*e + 7*a*b**2*d - 5*b**3*c)*log(b**6*sqrt(-a**3/b**13)*(11*a**3*f - 9*a**2*b*e + 7*a*b**2*d - 5*b**3*c)/(11*a**4*f - 9*a**3*b*e + 7*a**2*b**2*d - 5*a*b**3*c) + x)/4 + f*x**9/(9*b**2)","A",0
125,1,257,0,4.761945," ","integrate(x**4*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**2,x)","x^{5} \left(- \frac{2 a f}{5 b^{3}} + \frac{e}{5 b^{2}}\right) + x^{3} \left(\frac{a^{2} f}{b^{4}} - \frac{2 a e}{3 b^{3}} + \frac{d}{3 b^{2}}\right) + x \left(- \frac{4 a^{3} f}{b^{5}} + \frac{3 a^{2} e}{b^{4}} - \frac{2 a d}{b^{3}} + \frac{c}{b^{2}}\right) + \frac{x \left(- a^{4} f + a^{3} b e - a^{2} b^{2} d + a b^{3} c\right)}{2 a b^{5} + 2 b^{6} x^{2}} - \frac{\sqrt{- \frac{a}{b^{11}}} \left(9 a^{3} f - 7 a^{2} b e + 5 a b^{2} d - 3 b^{3} c\right) \log{\left(- b^{5} \sqrt{- \frac{a}{b^{11}}} + x \right)}}{4} + \frac{\sqrt{- \frac{a}{b^{11}}} \left(9 a^{3} f - 7 a^{2} b e + 5 a b^{2} d - 3 b^{3} c\right) \log{\left(b^{5} \sqrt{- \frac{a}{b^{11}}} + x \right)}}{4} + \frac{f x^{7}}{7 b^{2}}"," ",0,"x**5*(-2*a*f/(5*b**3) + e/(5*b**2)) + x**3*(a**2*f/b**4 - 2*a*e/(3*b**3) + d/(3*b**2)) + x*(-4*a**3*f/b**5 + 3*a**2*e/b**4 - 2*a*d/b**3 + c/b**2) + x*(-a**4*f + a**3*b*e - a**2*b**2*d + a*b**3*c)/(2*a*b**5 + 2*b**6*x**2) - sqrt(-a/b**11)*(9*a**3*f - 7*a**2*b*e + 5*a*b**2*d - 3*b**3*c)*log(-b**5*sqrt(-a/b**11) + x)/4 + sqrt(-a/b**11)*(9*a**3*f - 7*a**2*b*e + 5*a*b**2*d - 3*b**3*c)*log(b**5*sqrt(-a/b**11) + x)/4 + f*x**7/(7*b**2)","A",0
126,1,221,0,3.036193," ","integrate(x**2*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**2,x)","x^{3} \left(- \frac{2 a f}{3 b^{3}} + \frac{e}{3 b^{2}}\right) + x \left(\frac{3 a^{2} f}{b^{4}} - \frac{2 a e}{b^{3}} + \frac{d}{b^{2}}\right) + \frac{x \left(a^{3} f - a^{2} b e + a b^{2} d - b^{3} c\right)}{2 a b^{4} + 2 b^{5} x^{2}} + \frac{\sqrt{- \frac{1}{a b^{9}}} \left(7 a^{3} f - 5 a^{2} b e + 3 a b^{2} d - b^{3} c\right) \log{\left(- a b^{4} \sqrt{- \frac{1}{a b^{9}}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a b^{9}}} \left(7 a^{3} f - 5 a^{2} b e + 3 a b^{2} d - b^{3} c\right) \log{\left(a b^{4} \sqrt{- \frac{1}{a b^{9}}} + x \right)}}{4} + \frac{f x^{5}}{5 b^{2}}"," ",0,"x**3*(-2*a*f/(3*b**3) + e/(3*b**2)) + x*(3*a**2*f/b**4 - 2*a*e/b**3 + d/b**2) + x*(a**3*f - a**2*b*e + a*b**2*d - b**3*c)/(2*a*b**4 + 2*b**5*x**2) + sqrt(-1/(a*b**9))*(7*a**3*f - 5*a**2*b*e + 3*a*b**2*d - b**3*c)*log(-a*b**4*sqrt(-1/(a*b**9)) + x)/4 - sqrt(-1/(a*b**9))*(7*a**3*f - 5*a**2*b*e + 3*a*b**2*d - b**3*c)*log(a*b**4*sqrt(-1/(a*b**9)) + x)/4 + f*x**5/(5*b**2)","A",0
127,1,201,0,2.876981," ","integrate((f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**2,x)","x \left(- \frac{2 a f}{b^{3}} + \frac{e}{b^{2}}\right) + \frac{x \left(- a^{3} f + a^{2} b e - a b^{2} d + b^{3} c\right)}{2 a^{2} b^{3} + 2 a b^{4} x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b^{7}}} \left(5 a^{3} f - 3 a^{2} b e + a b^{2} d + b^{3} c\right) \log{\left(- a^{2} b^{3} \sqrt{- \frac{1}{a^{3} b^{7}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b^{7}}} \left(5 a^{3} f - 3 a^{2} b e + a b^{2} d + b^{3} c\right) \log{\left(a^{2} b^{3} \sqrt{- \frac{1}{a^{3} b^{7}}} + x \right)}}{4} + \frac{f x^{3}}{3 b^{2}}"," ",0,"x*(-2*a*f/b**3 + e/b**2) + x*(-a**3*f + a**2*b*e - a*b**2*d + b**3*c)/(2*a**2*b**3 + 2*a*b**4*x**2) - sqrt(-1/(a**3*b**7))*(5*a**3*f - 3*a**2*b*e + a*b**2*d + b**3*c)*log(-a**2*b**3*sqrt(-1/(a**3*b**7)) + x)/4 + sqrt(-1/(a**3*b**7))*(5*a**3*f - 3*a**2*b*e + a*b**2*d + b**3*c)*log(a**2*b**3*sqrt(-1/(a**3*b**7)) + x)/4 + f*x**3/(3*b**2)","A",0
128,1,197,0,9.464848," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**2/(b*x**2+a)**2,x)","\frac{\sqrt{- \frac{1}{a^{5} b^{5}}} \left(3 a^{3} f - a^{2} b e - a b^{2} d + 3 b^{3} c\right) \log{\left(- a^{3} b^{2} \sqrt{- \frac{1}{a^{5} b^{5}}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a^{5} b^{5}}} \left(3 a^{3} f - a^{2} b e - a b^{2} d + 3 b^{3} c\right) \log{\left(a^{3} b^{2} \sqrt{- \frac{1}{a^{5} b^{5}}} + x \right)}}{4} + \frac{- 2 a b^{2} c + x^{2} \left(a^{3} f - a^{2} b e + a b^{2} d - 3 b^{3} c\right)}{2 a^{3} b^{2} x + 2 a^{2} b^{3} x^{3}} + \frac{f x}{b^{2}}"," ",0,"sqrt(-1/(a**5*b**5))*(3*a**3*f - a**2*b*e - a*b**2*d + 3*b**3*c)*log(-a**3*b**2*sqrt(-1/(a**5*b**5)) + x)/4 - sqrt(-1/(a**5*b**5))*(3*a**3*f - a**2*b*e - a*b**2*d + 3*b**3*c)*log(a**3*b**2*sqrt(-1/(a**5*b**5)) + x)/4 + (-2*a*b**2*c + x**2*(a**3*f - a**2*b*e + a*b**2*d - 3*b**3*c))/(2*a**3*b**2*x + 2*a**2*b**3*x**3) + f*x/b**2","A",0
129,1,212,0,25.991965," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**4/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{7} b^{3}}} \left(a^{3} f + a^{2} b e - 3 a b^{2} d + 5 b^{3} c\right) \log{\left(- a^{4} b \sqrt{- \frac{1}{a^{7} b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{7} b^{3}}} \left(a^{3} f + a^{2} b e - 3 a b^{2} d + 5 b^{3} c\right) \log{\left(a^{4} b \sqrt{- \frac{1}{a^{7} b^{3}}} + x \right)}}{4} + \frac{- 2 a^{2} b c + x^{4} \left(- 3 a^{3} f + 3 a^{2} b e - 9 a b^{2} d + 15 b^{3} c\right) + x^{2} \left(- 6 a^{2} b d + 10 a b^{2} c\right)}{6 a^{4} b x^{3} + 6 a^{3} b^{2} x^{5}}"," ",0,"-sqrt(-1/(a**7*b**3))*(a**3*f + a**2*b*e - 3*a*b**2*d + 5*b**3*c)*log(-a**4*b*sqrt(-1/(a**7*b**3)) + x)/4 + sqrt(-1/(a**7*b**3))*(a**3*f + a**2*b*e - 3*a*b**2*d + 5*b**3*c)*log(a**4*b*sqrt(-1/(a**7*b**3)) + x)/4 + (-2*a**2*b*c + x**4*(-3*a**3*f + 3*a**2*b*e - 9*a*b**2*d + 15*b**3*c) + x**2*(-6*a**2*b*d + 10*a*b**2*c))/(6*a**4*b*x**3 + 6*a**3*b**2*x**5)","A",0
130,1,226,0,32.023659," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**6/(b*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{9} b}} \left(a^{3} f - 3 a^{2} b e + 5 a b^{2} d - 7 b^{3} c\right) \log{\left(- a^{5} \sqrt{- \frac{1}{a^{9} b}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{9} b}} \left(a^{3} f - 3 a^{2} b e + 5 a b^{2} d - 7 b^{3} c\right) \log{\left(a^{5} \sqrt{- \frac{1}{a^{9} b}} + x \right)}}{4} + \frac{- 6 a^{3} c + x^{6} \left(15 a^{3} f - 45 a^{2} b e + 75 a b^{2} d - 105 b^{3} c\right) + x^{4} \left(- 30 a^{3} e + 50 a^{2} b d - 70 a b^{2} c\right) + x^{2} \left(- 10 a^{3} d + 14 a^{2} b c\right)}{30 a^{5} x^{5} + 30 a^{4} b x^{7}}"," ",0,"-sqrt(-1/(a**9*b))*(a**3*f - 3*a**2*b*e + 5*a*b**2*d - 7*b**3*c)*log(-a**5*sqrt(-1/(a**9*b)) + x)/4 + sqrt(-1/(a**9*b))*(a**3*f - 3*a**2*b*e + 5*a*b**2*d - 7*b**3*c)*log(a**5*sqrt(-1/(a**9*b)) + x)/4 + (-6*a**3*c + x**6*(15*a**3*f - 45*a**2*b*e + 75*a*b**2*d - 105*b**3*c) + x**4*(-30*a**3*e + 50*a**2*b*d - 70*a*b**2*c) + x**2*(-10*a**3*d + 14*a**2*b*c))/(30*a**5*x**5 + 30*a**4*b*x**7)","A",0
131,1,394,0,99.021956," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**8/(b*x**2+a)**2,x)","\frac{\sqrt{- \frac{b}{a^{11}}} \left(3 a^{3} f - 5 a^{2} b e + 7 a b^{2} d - 9 b^{3} c\right) \log{\left(- \frac{a^{6} \sqrt{- \frac{b}{a^{11}}} \left(3 a^{3} f - 5 a^{2} b e + 7 a b^{2} d - 9 b^{3} c\right)}{3 a^{3} b f - 5 a^{2} b^{2} e + 7 a b^{3} d - 9 b^{4} c} + x \right)}}{4} - \frac{\sqrt{- \frac{b}{a^{11}}} \left(3 a^{3} f - 5 a^{2} b e + 7 a b^{2} d - 9 b^{3} c\right) \log{\left(\frac{a^{6} \sqrt{- \frac{b}{a^{11}}} \left(3 a^{3} f - 5 a^{2} b e + 7 a b^{2} d - 9 b^{3} c\right)}{3 a^{3} b f - 5 a^{2} b^{2} e + 7 a b^{3} d - 9 b^{4} c} + x \right)}}{4} + \frac{- 30 a^{4} c + x^{8} \left(- 315 a^{3} b f + 525 a^{2} b^{2} e - 735 a b^{3} d + 945 b^{4} c\right) + x^{6} \left(- 210 a^{4} f + 350 a^{3} b e - 490 a^{2} b^{2} d + 630 a b^{3} c\right) + x^{4} \left(- 70 a^{4} e + 98 a^{3} b d - 126 a^{2} b^{2} c\right) + x^{2} \left(- 42 a^{4} d + 54 a^{3} b c\right)}{210 a^{6} x^{7} + 210 a^{5} b x^{9}}"," ",0,"sqrt(-b/a**11)*(3*a**3*f - 5*a**2*b*e + 7*a*b**2*d - 9*b**3*c)*log(-a**6*sqrt(-b/a**11)*(3*a**3*f - 5*a**2*b*e + 7*a*b**2*d - 9*b**3*c)/(3*a**3*b*f - 5*a**2*b**2*e + 7*a*b**3*d - 9*b**4*c) + x)/4 - sqrt(-b/a**11)*(3*a**3*f - 5*a**2*b*e + 7*a*b**2*d - 9*b**3*c)*log(a**6*sqrt(-b/a**11)*(3*a**3*f - 5*a**2*b*e + 7*a*b**2*d - 9*b**3*c)/(3*a**3*b*f - 5*a**2*b**2*e + 7*a*b**3*d - 9*b**4*c) + x)/4 + (-30*a**4*c + x**8*(-315*a**3*b*f + 525*a**2*b**2*e - 735*a*b**3*d + 945*b**4*c) + x**6*(-210*a**4*f + 350*a**3*b*e - 490*a**2*b**2*d + 630*a*b**3*c) + x**4*(-70*a**4*e + 98*a**3*b*d - 126*a**2*b**2*c) + x**2*(-42*a**4*d + 54*a**3*b*c))/(210*a**6*x**7 + 210*a**5*b*x**9)","B",0
132,-1,0,0,0.000000," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**10/(b*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,1,503,0,16.433466," ","integrate(x**8*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**3,x)","x^{7} \left(- \frac{3 a f}{7 b^{4}} + \frac{e}{7 b^{3}}\right) + x^{5} \left(\frac{6 a^{2} f}{5 b^{5}} - \frac{3 a e}{5 b^{4}} + \frac{d}{5 b^{3}}\right) + x^{3} \left(- \frac{10 a^{3} f}{3 b^{6}} + \frac{2 a^{2} e}{b^{5}} - \frac{a d}{b^{4}} + \frac{c}{3 b^{3}}\right) + x \left(\frac{15 a^{4} f}{b^{7}} - \frac{10 a^{3} e}{b^{6}} + \frac{6 a^{2} d}{b^{5}} - \frac{3 a c}{b^{4}}\right) + \frac{\sqrt{- \frac{a^{3}}{b^{15}}} \left(143 a^{3} f - 99 a^{2} b e + 63 a b^{2} d - 35 b^{3} c\right) \log{\left(- \frac{b^{7} \sqrt{- \frac{a^{3}}{b^{15}}} \left(143 a^{3} f - 99 a^{2} b e + 63 a b^{2} d - 35 b^{3} c\right)}{143 a^{4} f - 99 a^{3} b e + 63 a^{2} b^{2} d - 35 a b^{3} c} + x \right)}}{16} - \frac{\sqrt{- \frac{a^{3}}{b^{15}}} \left(143 a^{3} f - 99 a^{2} b e + 63 a b^{2} d - 35 b^{3} c\right) \log{\left(\frac{b^{7} \sqrt{- \frac{a^{3}}{b^{15}}} \left(143 a^{3} f - 99 a^{2} b e + 63 a b^{2} d - 35 b^{3} c\right)}{143 a^{4} f - 99 a^{3} b e + 63 a^{2} b^{2} d - 35 a b^{3} c} + x \right)}}{16} + \frac{x^{3} \left(25 a^{5} b f - 21 a^{4} b^{2} e + 17 a^{3} b^{3} d - 13 a^{2} b^{4} c\right) + x \left(23 a^{6} f - 19 a^{5} b e + 15 a^{4} b^{2} d - 11 a^{3} b^{3} c\right)}{8 a^{2} b^{7} + 16 a b^{8} x^{2} + 8 b^{9} x^{4}} + \frac{f x^{9}}{9 b^{3}}"," ",0,"x**7*(-3*a*f/(7*b**4) + e/(7*b**3)) + x**5*(6*a**2*f/(5*b**5) - 3*a*e/(5*b**4) + d/(5*b**3)) + x**3*(-10*a**3*f/(3*b**6) + 2*a**2*e/b**5 - a*d/b**4 + c/(3*b**3)) + x*(15*a**4*f/b**7 - 10*a**3*e/b**6 + 6*a**2*d/b**5 - 3*a*c/b**4) + sqrt(-a**3/b**15)*(143*a**3*f - 99*a**2*b*e + 63*a*b**2*d - 35*b**3*c)*log(-b**7*sqrt(-a**3/b**15)*(143*a**3*f - 99*a**2*b*e + 63*a*b**2*d - 35*b**3*c)/(143*a**4*f - 99*a**3*b*e + 63*a**2*b**2*d - 35*a*b**3*c) + x)/16 - sqrt(-a**3/b**15)*(143*a**3*f - 99*a**2*b*e + 63*a*b**2*d - 35*b**3*c)*log(b**7*sqrt(-a**3/b**15)*(143*a**3*f - 99*a**2*b*e + 63*a*b**2*d - 35*b**3*c)/(143*a**4*f - 99*a**3*b*e + 63*a**2*b**2*d - 35*a*b**3*c) + x)/16 + (x**3*(25*a**5*b*f - 21*a**4*b**2*e + 17*a**3*b**3*d - 13*a**2*b**4*c) + x*(23*a**6*f - 19*a**5*b*e + 15*a**4*b**2*d - 11*a**3*b**3*c))/(8*a**2*b**7 + 16*a*b**8*x**2 + 8*b**9*x**4) + f*x**9/(9*b**3)","A",0
134,1,316,0,18.216001," ","integrate(x**6*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**3,x)","x^{5} \left(- \frac{3 a f}{5 b^{4}} + \frac{e}{5 b^{3}}\right) + x^{3} \left(\frac{2 a^{2} f}{b^{5}} - \frac{a e}{b^{4}} + \frac{d}{3 b^{3}}\right) + x \left(- \frac{10 a^{3} f}{b^{6}} + \frac{6 a^{2} e}{b^{5}} - \frac{3 a d}{b^{4}} + \frac{c}{b^{3}}\right) - \frac{\sqrt{- \frac{a}{b^{13}}} \left(99 a^{3} f - 63 a^{2} b e + 35 a b^{2} d - 15 b^{3} c\right) \log{\left(- b^{6} \sqrt{- \frac{a}{b^{13}}} + x \right)}}{16} + \frac{\sqrt{- \frac{a}{b^{13}}} \left(99 a^{3} f - 63 a^{2} b e + 35 a b^{2} d - 15 b^{3} c\right) \log{\left(b^{6} \sqrt{- \frac{a}{b^{13}}} + x \right)}}{16} + \frac{x^{3} \left(- 21 a^{4} b f + 17 a^{3} b^{2} e - 13 a^{2} b^{3} d + 9 a b^{4} c\right) + x \left(- 19 a^{5} f + 15 a^{4} b e - 11 a^{3} b^{2} d + 7 a^{2} b^{3} c\right)}{8 a^{2} b^{6} + 16 a b^{7} x^{2} + 8 b^{8} x^{4}} + \frac{f x^{7}}{7 b^{3}}"," ",0,"x**5*(-3*a*f/(5*b**4) + e/(5*b**3)) + x**3*(2*a**2*f/b**5 - a*e/b**4 + d/(3*b**3)) + x*(-10*a**3*f/b**6 + 6*a**2*e/b**5 - 3*a*d/b**4 + c/b**3) - sqrt(-a/b**13)*(99*a**3*f - 63*a**2*b*e + 35*a*b**2*d - 15*b**3*c)*log(-b**6*sqrt(-a/b**13) + x)/16 + sqrt(-a/b**13)*(99*a**3*f - 63*a**2*b*e + 35*a*b**2*d - 15*b**3*c)*log(b**6*sqrt(-a/b**13) + x)/16 + (x**3*(-21*a**4*b*f + 17*a**3*b**2*e - 13*a**2*b**3*d + 9*a*b**4*c) + x*(-19*a**5*f + 15*a**4*b*e - 11*a**3*b**2*d + 7*a**2*b**3*c))/(8*a**2*b**6 + 16*a*b**7*x**2 + 8*b**8*x**4) + f*x**7/(7*b**3)","A",0
135,1,280,0,17.839999," ","integrate(x**4*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**3,x)","x^{3} \left(- \frac{a f}{b^{4}} + \frac{e}{3 b^{3}}\right) + x \left(\frac{6 a^{2} f}{b^{5}} - \frac{3 a e}{b^{4}} + \frac{d}{b^{3}}\right) + \frac{\sqrt{- \frac{1}{a b^{11}}} \left(63 a^{3} f - 35 a^{2} b e + 15 a b^{2} d - 3 b^{3} c\right) \log{\left(- a b^{5} \sqrt{- \frac{1}{a b^{11}}} + x \right)}}{16} - \frac{\sqrt{- \frac{1}{a b^{11}}} \left(63 a^{3} f - 35 a^{2} b e + 15 a b^{2} d - 3 b^{3} c\right) \log{\left(a b^{5} \sqrt{- \frac{1}{a b^{11}}} + x \right)}}{16} + \frac{x^{3} \left(17 a^{3} b f - 13 a^{2} b^{2} e + 9 a b^{3} d - 5 b^{4} c\right) + x \left(15 a^{4} f - 11 a^{3} b e + 7 a^{2} b^{2} d - 3 a b^{3} c\right)}{8 a^{2} b^{5} + 16 a b^{6} x^{2} + 8 b^{7} x^{4}} + \frac{f x^{5}}{5 b^{3}}"," ",0,"x**3*(-a*f/b**4 + e/(3*b**3)) + x*(6*a**2*f/b**5 - 3*a*e/b**4 + d/b**3) + sqrt(-1/(a*b**11))*(63*a**3*f - 35*a**2*b*e + 15*a*b**2*d - 3*b**3*c)*log(-a*b**5*sqrt(-1/(a*b**11)) + x)/16 - sqrt(-1/(a*b**11))*(63*a**3*f - 35*a**2*b*e + 15*a*b**2*d - 3*b**3*c)*log(a*b**5*sqrt(-1/(a*b**11)) + x)/16 + (x**3*(17*a**3*b*f - 13*a**2*b**2*e + 9*a*b**3*d - 5*b**4*c) + x*(15*a**4*f - 11*a**3*b*e + 7*a**2*b**2*d - 3*a*b**3*c))/(8*a**2*b**5 + 16*a*b**6*x**2 + 8*b**7*x**4) + f*x**5/(5*b**3)","A",0
136,1,260,0,13.069134," ","integrate(x**2*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**3,x)","x \left(- \frac{3 a f}{b^{4}} + \frac{e}{b^{3}}\right) - \frac{\sqrt{- \frac{1}{a^{3} b^{9}}} \left(35 a^{3} f - 15 a^{2} b e + 3 a b^{2} d + b^{3} c\right) \log{\left(- a^{2} b^{4} \sqrt{- \frac{1}{a^{3} b^{9}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{3} b^{9}}} \left(35 a^{3} f - 15 a^{2} b e + 3 a b^{2} d + b^{3} c\right) \log{\left(a^{2} b^{4} \sqrt{- \frac{1}{a^{3} b^{9}}} + x \right)}}{16} + \frac{x^{3} \left(- 13 a^{3} b f + 9 a^{2} b^{2} e - 5 a b^{3} d + b^{4} c\right) + x \left(- 11 a^{4} f + 7 a^{3} b e - 3 a^{2} b^{2} d - a b^{3} c\right)}{8 a^{3} b^{4} + 16 a^{2} b^{5} x^{2} + 8 a b^{6} x^{4}} + \frac{f x^{3}}{3 b^{3}}"," ",0,"x*(-3*a*f/b**4 + e/b**3) - sqrt(-1/(a**3*b**9))*(35*a**3*f - 15*a**2*b*e + 3*a*b**2*d + b**3*c)*log(-a**2*b**4*sqrt(-1/(a**3*b**9)) + x)/16 + sqrt(-1/(a**3*b**9))*(35*a**3*f - 15*a**2*b*e + 3*a*b**2*d + b**3*c)*log(a**2*b**4*sqrt(-1/(a**3*b**9)) + x)/16 + (x**3*(-13*a**3*b*f + 9*a**2*b**2*e - 5*a*b**3*d + b**4*c) + x*(-11*a**4*f + 7*a**3*b*e - 3*a**2*b**2*d - a*b**3*c))/(8*a**3*b**4 + 16*a**2*b**5*x**2 + 8*a*b**6*x**4) + f*x**3/(3*b**3)","A",0
137,1,243,0,10.094935," ","integrate((f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**3,x)","\frac{\sqrt{- \frac{1}{a^{5} b^{7}}} \left(15 a^{3} f - 3 a^{2} b e - a b^{2} d - 3 b^{3} c\right) \log{\left(- a^{3} b^{3} \sqrt{- \frac{1}{a^{5} b^{7}}} + x \right)}}{16} - \frac{\sqrt{- \frac{1}{a^{5} b^{7}}} \left(15 a^{3} f - 3 a^{2} b e - a b^{2} d - 3 b^{3} c\right) \log{\left(a^{3} b^{3} \sqrt{- \frac{1}{a^{5} b^{7}}} + x \right)}}{16} + \frac{x^{3} \left(9 a^{3} b f - 5 a^{2} b^{2} e + a b^{3} d + 3 b^{4} c\right) + x \left(7 a^{4} f - 3 a^{3} b e - a^{2} b^{2} d + 5 a b^{3} c\right)}{8 a^{4} b^{3} + 16 a^{3} b^{4} x^{2} + 8 a^{2} b^{5} x^{4}} + \frac{f x}{b^{3}}"," ",0,"sqrt(-1/(a**5*b**7))*(15*a**3*f - 3*a**2*b*e - a*b**2*d - 3*b**3*c)*log(-a**3*b**3*sqrt(-1/(a**5*b**7)) + x)/16 - sqrt(-1/(a**5*b**7))*(15*a**3*f - 3*a**2*b*e - a*b**2*d - 3*b**3*c)*log(a**3*b**3*sqrt(-1/(a**5*b**7)) + x)/16 + (x**3*(9*a**3*b*f - 5*a**2*b**2*e + a*b**3*d + 3*b**4*c) + x*(7*a**4*f - 3*a**3*b*e - a**2*b**2*d + 5*a*b**3*c))/(8*a**4*b**3 + 16*a**3*b**4*x**2 + 8*a**2*b**5*x**4) + f*x/b**3","A",0
138,1,250,0,26.562882," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**2/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{7} b^{5}}} \left(3 a^{3} f + a^{2} b e + 3 a b^{2} d - 15 b^{3} c\right) \log{\left(- a^{4} b^{2} \sqrt{- \frac{1}{a^{7} b^{5}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{7} b^{5}}} \left(3 a^{3} f + a^{2} b e + 3 a b^{2} d - 15 b^{3} c\right) \log{\left(a^{4} b^{2} \sqrt{- \frac{1}{a^{7} b^{5}}} + x \right)}}{16} + \frac{- 8 a^{2} b^{2} c + x^{4} \left(- 5 a^{3} b f + a^{2} b^{2} e + 3 a b^{3} d - 15 b^{4} c\right) + x^{2} \left(- 3 a^{4} f - a^{3} b e + 5 a^{2} b^{2} d - 25 a b^{3} c\right)}{8 a^{5} b^{2} x + 16 a^{4} b^{3} x^{3} + 8 a^{3} b^{4} x^{5}}"," ",0,"-sqrt(-1/(a**7*b**5))*(3*a**3*f + a**2*b*e + 3*a*b**2*d - 15*b**3*c)*log(-a**4*b**2*sqrt(-1/(a**7*b**5)) + x)/16 + sqrt(-1/(a**7*b**5))*(3*a**3*f + a**2*b*e + 3*a*b**2*d - 15*b**3*c)*log(a**4*b**2*sqrt(-1/(a**7*b**5)) + x)/16 + (-8*a**2*b**2*c + x**4*(-5*a**3*b*f + a**2*b**2*e + 3*a*b**3*d - 15*b**4*c) + x**2*(-3*a**4*f - a**3*b*e + 5*a**2*b**2*d - 25*a*b**3*c))/(8*a**5*b**2*x + 16*a**4*b**3*x**3 + 8*a**3*b**4*x**5)","A",0
139,1,270,0,70.489549," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**4/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{9} b^{3}}} \left(a^{3} f + 3 a^{2} b e - 15 a b^{2} d + 35 b^{3} c\right) \log{\left(- a^{5} b \sqrt{- \frac{1}{a^{9} b^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{9} b^{3}}} \left(a^{3} f + 3 a^{2} b e - 15 a b^{2} d + 35 b^{3} c\right) \log{\left(a^{5} b \sqrt{- \frac{1}{a^{9} b^{3}}} + x \right)}}{16} + \frac{- 8 a^{3} b c + x^{6} \left(3 a^{3} b f + 9 a^{2} b^{2} e - 45 a b^{3} d + 105 b^{4} c\right) + x^{4} \left(- 3 a^{4} f + 15 a^{3} b e - 75 a^{2} b^{2} d + 175 a b^{3} c\right) + x^{2} \left(- 24 a^{3} b d + 56 a^{2} b^{2} c\right)}{24 a^{6} b x^{3} + 48 a^{5} b^{2} x^{5} + 24 a^{4} b^{3} x^{7}}"," ",0,"-sqrt(-1/(a**9*b**3))*(a**3*f + 3*a**2*b*e - 15*a*b**2*d + 35*b**3*c)*log(-a**5*b*sqrt(-1/(a**9*b**3)) + x)/16 + sqrt(-1/(a**9*b**3))*(a**3*f + 3*a**2*b*e - 15*a*b**2*d + 35*b**3*c)*log(a**5*b*sqrt(-1/(a**9*b**3)) + x)/16 + (-8*a**3*b*c + x**6*(3*a**3*b*f + 9*a**2*b**2*e - 45*a*b**3*d + 105*b**4*c) + x**4*(-3*a**4*f + 15*a**3*b*e - 75*a**2*b**2*d + 175*a*b**3*c) + x**2*(-24*a**3*b*d + 56*a**2*b**2*c))/(24*a**6*b*x**3 + 48*a**5*b**2*x**5 + 24*a**4*b**3*x**7)","A",0
140,1,284,0,150.750782," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**6/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{11} b}} \left(3 a^{3} f - 15 a^{2} b e + 35 a b^{2} d - 63 b^{3} c\right) \log{\left(- a^{6} \sqrt{- \frac{1}{a^{11} b}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{11} b}} \left(3 a^{3} f - 15 a^{2} b e + 35 a b^{2} d - 63 b^{3} c\right) \log{\left(a^{6} \sqrt{- \frac{1}{a^{11} b}} + x \right)}}{16} + \frac{- 24 a^{4} c + x^{8} \left(45 a^{3} b f - 225 a^{2} b^{2} e + 525 a b^{3} d - 945 b^{4} c\right) + x^{6} \left(75 a^{4} f - 375 a^{3} b e + 875 a^{2} b^{2} d - 1575 a b^{3} c\right) + x^{4} \left(- 120 a^{4} e + 280 a^{3} b d - 504 a^{2} b^{2} c\right) + x^{2} \left(- 40 a^{4} d + 72 a^{3} b c\right)}{120 a^{7} x^{5} + 240 a^{6} b x^{7} + 120 a^{5} b^{2} x^{9}}"," ",0,"-sqrt(-1/(a**11*b))*(3*a**3*f - 15*a**2*b*e + 35*a*b**2*d - 63*b**3*c)*log(-a**6*sqrt(-1/(a**11*b)) + x)/16 + sqrt(-1/(a**11*b))*(3*a**3*f - 15*a**2*b*e + 35*a*b**2*d - 63*b**3*c)*log(a**6*sqrt(-1/(a**11*b)) + x)/16 + (-24*a**4*c + x**8*(45*a**3*b*f - 225*a**2*b**2*e + 525*a*b**3*d - 945*b**4*c) + x**6*(75*a**4*f - 375*a**3*b*e + 875*a**2*b**2*d - 1575*a*b**3*c) + x**4*(-120*a**4*e + 280*a**3*b*d - 504*a**2*b**2*c) + x**2*(-40*a**4*d + 72*a**3*b*c))/(120*a**7*x**5 + 240*a**6*b*x**7 + 120*a**5*b**2*x**9)","A",0
141,-1,0,0,0.000000," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**8/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**10/(b*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,1,442,0,4.676018," ","integrate(x**5*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{256 a^{5} f \sqrt{a + b x^{2}}}{693 b^{6}} + \frac{128 a^{4} e \sqrt{a + b x^{2}}}{315 b^{5}} + \frac{128 a^{4} f x^{2} \sqrt{a + b x^{2}}}{693 b^{5}} - \frac{16 a^{3} d \sqrt{a + b x^{2}}}{35 b^{4}} - \frac{64 a^{3} e x^{2} \sqrt{a + b x^{2}}}{315 b^{4}} - \frac{32 a^{3} f x^{4} \sqrt{a + b x^{2}}}{231 b^{4}} + \frac{8 a^{2} c \sqrt{a + b x^{2}}}{15 b^{3}} + \frac{8 a^{2} d x^{2} \sqrt{a + b x^{2}}}{35 b^{3}} + \frac{16 a^{2} e x^{4} \sqrt{a + b x^{2}}}{105 b^{3}} + \frac{80 a^{2} f x^{6} \sqrt{a + b x^{2}}}{693 b^{3}} - \frac{4 a c x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} - \frac{6 a d x^{4} \sqrt{a + b x^{2}}}{35 b^{2}} - \frac{8 a e x^{6} \sqrt{a + b x^{2}}}{63 b^{2}} - \frac{10 a f x^{8} \sqrt{a + b x^{2}}}{99 b^{2}} + \frac{c x^{4} \sqrt{a + b x^{2}}}{5 b} + \frac{d x^{6} \sqrt{a + b x^{2}}}{7 b} + \frac{e x^{8} \sqrt{a + b x^{2}}}{9 b} + \frac{f x^{10} \sqrt{a + b x^{2}}}{11 b} & \text{for}\: b \neq 0 \\\frac{\frac{c x^{6}}{6} + \frac{d x^{8}}{8} + \frac{e x^{10}}{10} + \frac{f x^{12}}{12}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-256*a**5*f*sqrt(a + b*x**2)/(693*b**6) + 128*a**4*e*sqrt(a + b*x**2)/(315*b**5) + 128*a**4*f*x**2*sqrt(a + b*x**2)/(693*b**5) - 16*a**3*d*sqrt(a + b*x**2)/(35*b**4) - 64*a**3*e*x**2*sqrt(a + b*x**2)/(315*b**4) - 32*a**3*f*x**4*sqrt(a + b*x**2)/(231*b**4) + 8*a**2*c*sqrt(a + b*x**2)/(15*b**3) + 8*a**2*d*x**2*sqrt(a + b*x**2)/(35*b**3) + 16*a**2*e*x**4*sqrt(a + b*x**2)/(105*b**3) + 80*a**2*f*x**6*sqrt(a + b*x**2)/(693*b**3) - 4*a*c*x**2*sqrt(a + b*x**2)/(15*b**2) - 6*a*d*x**4*sqrt(a + b*x**2)/(35*b**2) - 8*a*e*x**6*sqrt(a + b*x**2)/(63*b**2) - 10*a*f*x**8*sqrt(a + b*x**2)/(99*b**2) + c*x**4*sqrt(a + b*x**2)/(5*b) + d*x**6*sqrt(a + b*x**2)/(7*b) + e*x**8*sqrt(a + b*x**2)/(9*b) + f*x**10*sqrt(a + b*x**2)/(11*b), Ne(b, 0)), ((c*x**6/6 + d*x**8/8 + e*x**10/10 + f*x**12/12)/sqrt(a), True))","A",0
144,1,340,0,2.904626," ","integrate(x**3*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**(1/2),x)","\begin{cases} \frac{128 a^{4} f \sqrt{a + b x^{2}}}{315 b^{5}} - \frac{16 a^{3} e \sqrt{a + b x^{2}}}{35 b^{4}} - \frac{64 a^{3} f x^{2} \sqrt{a + b x^{2}}}{315 b^{4}} + \frac{8 a^{2} d \sqrt{a + b x^{2}}}{15 b^{3}} + \frac{8 a^{2} e x^{2} \sqrt{a + b x^{2}}}{35 b^{3}} + \frac{16 a^{2} f x^{4} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{2 a c \sqrt{a + b x^{2}}}{3 b^{2}} - \frac{4 a d x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} - \frac{6 a e x^{4} \sqrt{a + b x^{2}}}{35 b^{2}} - \frac{8 a f x^{6} \sqrt{a + b x^{2}}}{63 b^{2}} + \frac{c x^{2} \sqrt{a + b x^{2}}}{3 b} + \frac{d x^{4} \sqrt{a + b x^{2}}}{5 b} + \frac{e x^{6} \sqrt{a + b x^{2}}}{7 b} + \frac{f x^{8} \sqrt{a + b x^{2}}}{9 b} & \text{for}\: b \neq 0 \\\frac{\frac{c x^{4}}{4} + \frac{d x^{6}}{6} + \frac{e x^{8}}{8} + \frac{f x^{10}}{10}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*a**4*f*sqrt(a + b*x**2)/(315*b**5) - 16*a**3*e*sqrt(a + b*x**2)/(35*b**4) - 64*a**3*f*x**2*sqrt(a + b*x**2)/(315*b**4) + 8*a**2*d*sqrt(a + b*x**2)/(15*b**3) + 8*a**2*e*x**2*sqrt(a + b*x**2)/(35*b**3) + 16*a**2*f*x**4*sqrt(a + b*x**2)/(105*b**3) - 2*a*c*sqrt(a + b*x**2)/(3*b**2) - 4*a*d*x**2*sqrt(a + b*x**2)/(15*b**2) - 6*a*e*x**4*sqrt(a + b*x**2)/(35*b**2) - 8*a*f*x**6*sqrt(a + b*x**2)/(63*b**2) + c*x**2*sqrt(a + b*x**2)/(3*b) + d*x**4*sqrt(a + b*x**2)/(5*b) + e*x**6*sqrt(a + b*x**2)/(7*b) + f*x**8*sqrt(a + b*x**2)/(9*b), Ne(b, 0)), ((c*x**4/4 + d*x**6/6 + e*x**8/8 + f*x**10/10)/sqrt(a), True))","A",0
145,1,238,0,2.189162," ","integrate(x*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{16 a^{3} f \sqrt{a + b x^{2}}}{35 b^{4}} + \frac{8 a^{2} e \sqrt{a + b x^{2}}}{15 b^{3}} + \frac{8 a^{2} f x^{2} \sqrt{a + b x^{2}}}{35 b^{3}} - \frac{2 a d \sqrt{a + b x^{2}}}{3 b^{2}} - \frac{4 a e x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} - \frac{6 a f x^{4} \sqrt{a + b x^{2}}}{35 b^{2}} + \frac{c \sqrt{a + b x^{2}}}{b} + \frac{d x^{2} \sqrt{a + b x^{2}}}{3 b} + \frac{e x^{4} \sqrt{a + b x^{2}}}{5 b} + \frac{f x^{6} \sqrt{a + b x^{2}}}{7 b} & \text{for}\: b \neq 0 \\\frac{\frac{c x^{2}}{2} + \frac{d x^{4}}{4} + \frac{e x^{6}}{6} + \frac{f x^{8}}{8}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**3*f*sqrt(a + b*x**2)/(35*b**4) + 8*a**2*e*sqrt(a + b*x**2)/(15*b**3) + 8*a**2*f*x**2*sqrt(a + b*x**2)/(35*b**3) - 2*a*d*sqrt(a + b*x**2)/(3*b**2) - 4*a*e*x**2*sqrt(a + b*x**2)/(15*b**2) - 6*a*f*x**4*sqrt(a + b*x**2)/(35*b**2) + c*sqrt(a + b*x**2)/b + d*x**2*sqrt(a + b*x**2)/(3*b) + e*x**4*sqrt(a + b*x**2)/(5*b) + f*x**6*sqrt(a + b*x**2)/(7*b), Ne(b, 0)), ((c*x**2/2 + d*x**4/4 + e*x**6/6 + f*x**8/8)/sqrt(a), True))","A",0
146,1,102,0,37.870249," ","integrate((f*x**6+e*x**4+d*x**2+c)/x/(b*x**2+a)**(1/2),x)","\frac{f \left(a + b x^{2}\right)^{\frac{5}{2}}}{5 b^{3}} - \frac{\left(a + b x^{2}\right)^{\frac{3}{2}} \left(2 a f - b e\right)}{3 b^{3}} + \frac{\sqrt{a + b x^{2}} \left(a^{2} f - a b e + b^{2} d\right)}{b^{3}} + \frac{c \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{a}} \sqrt{a + b x^{2}}} \right)}}{a \sqrt{- \frac{1}{a}}}"," ",0,"f*(a + b*x**2)**(5/2)/(5*b**3) - (a + b*x**2)**(3/2)*(2*a*f - b*e)/(3*b**3) + sqrt(a + b*x**2)*(a**2*f - a*b*e + b**2*d)/b**3 + c*atan(1/(sqrt(-1/a)*sqrt(a + b*x**2)))/(a*sqrt(-1/a))","A",0
147,1,138,0,127.425786," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**3/(b*x**2+a)**(1/2),x)","e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: b = 0 \\\frac{\sqrt{a + b x^{2}}}{b} & \text{otherwise} \end{cases}\right) + f \left(\begin{cases} - \frac{2 a \sqrt{a + b x^{2}}}{3 b^{2}} + \frac{x^{2} \sqrt{a + b x^{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) - \frac{\sqrt{b} c \sqrt{\frac{a}{b x^{2}} + 1}}{2 a x} - \frac{d \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{\sqrt{a}} + \frac{b c \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} x} \right)}}{2 a^{\frac{3}{2}}}"," ",0,"e*Piecewise((x**2/(2*sqrt(a)), Eq(b, 0)), (sqrt(a + b*x**2)/b, True)) + f*Piecewise((-2*a*sqrt(a + b*x**2)/(3*b**2) + x**2*sqrt(a + b*x**2)/(3*b), Ne(b, 0)), (x**4/(4*sqrt(a)), True)) - sqrt(b)*c*sqrt(a/(b*x**2) + 1)/(2*a*x) - d*asinh(sqrt(a)/(sqrt(b)*x))/sqrt(a) + b*c*asinh(sqrt(a)/(sqrt(b)*x))/(2*a**(3/2))","A",0
148,-1,0,0,0.000000," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**5/(b*x**2+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**7/(b*x**2+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**9/(b*x**2+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,1,586,0,42.122076," ","integrate(x**4*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**(1/2),x)","\frac{63 a^{\frac{9}{2}} f x}{256 b^{5} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{35 a^{\frac{7}{2}} e x}{128 b^{4} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{21 a^{\frac{7}{2}} f x^{3}}{256 b^{4} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{5}{2}} d x}{16 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{35 a^{\frac{5}{2}} e x^{3}}{384 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{21 a^{\frac{5}{2}} f x^{5}}{640 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{3}{2}} c x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{3}{2}} d x^{3}}{48 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{7 a^{\frac{3}{2}} e x^{5}}{192 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{\frac{3}{2}} f x^{7}}{160 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} c x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} d x^{5}}{24 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} e x^{7}}{48 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} f x^{9}}{80 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{63 a^{5} f \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{11}{2}}} + \frac{35 a^{4} e \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{9}{2}}} - \frac{5 a^{3} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{7}{2}}} + \frac{3 a^{2} c \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} + \frac{c x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{d x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{e x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{f x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"63*a**(9/2)*f*x/(256*b**5*sqrt(1 + b*x**2/a)) - 35*a**(7/2)*e*x/(128*b**4*sqrt(1 + b*x**2/a)) + 21*a**(7/2)*f*x**3/(256*b**4*sqrt(1 + b*x**2/a)) + 5*a**(5/2)*d*x/(16*b**3*sqrt(1 + b*x**2/a)) - 35*a**(5/2)*e*x**3/(384*b**3*sqrt(1 + b*x**2/a)) - 21*a**(5/2)*f*x**5/(640*b**3*sqrt(1 + b*x**2/a)) - 3*a**(3/2)*c*x/(8*b**2*sqrt(1 + b*x**2/a)) + 5*a**(3/2)*d*x**3/(48*b**2*sqrt(1 + b*x**2/a)) + 7*a**(3/2)*e*x**5/(192*b**2*sqrt(1 + b*x**2/a)) + 3*a**(3/2)*f*x**7/(160*b**2*sqrt(1 + b*x**2/a)) - sqrt(a)*c*x**3/(8*b*sqrt(1 + b*x**2/a)) - sqrt(a)*d*x**5/(24*b*sqrt(1 + b*x**2/a)) - sqrt(a)*e*x**7/(48*b*sqrt(1 + b*x**2/a)) - sqrt(a)*f*x**9/(80*b*sqrt(1 + b*x**2/a)) - 63*a**5*f*asinh(sqrt(b)*x/sqrt(a))/(256*b**(11/2)) + 35*a**4*e*asinh(sqrt(b)*x/sqrt(a))/(128*b**(9/2)) - 5*a**3*d*asinh(sqrt(b)*x/sqrt(a))/(16*b**(7/2)) + 3*a**2*c*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) + c*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + d*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) + e*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a)) + f*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
152,1,444,0,32.561938," ","integrate(x**2*(f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**(1/2),x)","- \frac{35 a^{\frac{7}{2}} f x}{128 b^{4} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{5}{2}} e x}{16 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{35 a^{\frac{5}{2}} f x^{3}}{384 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{3}{2}} d x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{3}{2}} e x^{3}}{48 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{7 a^{\frac{3}{2}} f x^{5}}{192 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{\sqrt{a} c x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{\sqrt{a} d x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} e x^{5}}{24 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} f x^{7}}{48 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 a^{4} f \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{9}{2}}} - \frac{5 a^{3} e \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{7}{2}}} + \frac{3 a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} - \frac{a c \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} + \frac{d x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{e x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{f x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-35*a**(7/2)*f*x/(128*b**4*sqrt(1 + b*x**2/a)) + 5*a**(5/2)*e*x/(16*b**3*sqrt(1 + b*x**2/a)) - 35*a**(5/2)*f*x**3/(384*b**3*sqrt(1 + b*x**2/a)) - 3*a**(3/2)*d*x/(8*b**2*sqrt(1 + b*x**2/a)) + 5*a**(3/2)*e*x**3/(48*b**2*sqrt(1 + b*x**2/a)) + 7*a**(3/2)*f*x**5/(192*b**2*sqrt(1 + b*x**2/a)) + sqrt(a)*c*x*sqrt(1 + b*x**2/a)/(2*b) - sqrt(a)*d*x**3/(8*b*sqrt(1 + b*x**2/a)) - sqrt(a)*e*x**5/(24*b*sqrt(1 + b*x**2/a)) - sqrt(a)*f*x**7/(48*b*sqrt(1 + b*x**2/a)) + 35*a**4*f*asinh(sqrt(b)*x/sqrt(a))/(128*b**(9/2)) - 5*a**3*e*asinh(sqrt(b)*x/sqrt(a))/(16*b**(7/2)) + 3*a**2*d*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) - a*c*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2)) + d*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + e*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) + f*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
153,1,362,0,13.710757," ","integrate((f*x**6+e*x**4+d*x**2+c)/(b*x**2+a)**(1/2),x)","\frac{5 a^{\frac{5}{2}} f x}{16 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{3}{2}} e x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{3}{2}} f x^{3}}{48 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{\sqrt{a} d x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{\sqrt{a} e x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} f x^{5}}{24 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 a^{3} f \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{7}{2}}} + \frac{3 a^{2} e \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} - \frac{a d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} + c \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{e x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{f x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"5*a**(5/2)*f*x/(16*b**3*sqrt(1 + b*x**2/a)) - 3*a**(3/2)*e*x/(8*b**2*sqrt(1 + b*x**2/a)) + 5*a**(3/2)*f*x**3/(48*b**2*sqrt(1 + b*x**2/a)) + sqrt(a)*d*x*sqrt(1 + b*x**2/a)/(2*b) - sqrt(a)*e*x**3/(8*b*sqrt(1 + b*x**2/a)) - sqrt(a)*f*x**5/(24*b*sqrt(1 + b*x**2/a)) - 5*a**3*f*asinh(sqrt(b)*x/sqrt(a))/(16*b**(7/2)) + 3*a**2*e*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) - a*d*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2)) + c*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))) + e*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + f*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
154,1,250,0,9.051680," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**2/(b*x**2+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} f x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{\sqrt{a} e x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{\sqrt{a} f x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{2} f \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} - \frac{a e \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} + d \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{\sqrt{b} c \sqrt{\frac{a}{b x^{2}} + 1}}{a} + \frac{f x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(3/2)*f*x/(8*b**2*sqrt(1 + b*x**2/a)) + sqrt(a)*e*x*sqrt(1 + b*x**2/a)/(2*b) - sqrt(a)*f*x**3/(8*b*sqrt(1 + b*x**2/a)) + 3*a**2*f*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) - a*e*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2)) + d*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))) - sqrt(b)*c*sqrt(a/(b*x**2) + 1)/a + f*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
155,1,197,0,4.728963," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**4/(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} f x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{a f \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} + e \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{\sqrt{b} c \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} - \frac{\sqrt{b} d \sqrt{\frac{a}{b x^{2}} + 1}}{a} + \frac{2 b^{\frac{3}{2}} c \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}}"," ",0,"sqrt(a)*f*x*sqrt(1 + b*x**2/a)/(2*b) - a*f*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2)) + e*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))) - sqrt(b)*c*sqrt(a/(b*x**2) + 1)/(3*a*x**2) - sqrt(b)*d*sqrt(a/(b*x**2) + 1)/a + 2*b**(3/2)*c*sqrt(a/(b*x**2) + 1)/(3*a**2)","A",0
156,1,456,0,6.206819," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**6/(b*x**2+a)**(1/2),x)","- \frac{3 a^{4} b^{\frac{9}{2}} c \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^{3} b^{\frac{11}{2}} c 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^{2} b^{\frac{13}{2}} c 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 b^{\frac{15}{2}} c 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^{\frac{17}{2}} c 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}} + f \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{\sqrt{b} d \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} - \frac{\sqrt{b} e \sqrt{\frac{a}{b x^{2}} + 1}}{a} + \frac{2 b^{\frac{3}{2}} d \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}}"," ",0,"-3*a**4*b**(9/2)*c*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**3*b**(11/2)*c*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**2*b**(13/2)*c*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*b**(15/2)*c*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**(17/2)*c*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) + f*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))) - sqrt(b)*d*sqrt(a/(b*x**2) + 1)/(3*a*x**2) - sqrt(b)*e*sqrt(a/(b*x**2) + 1)/a + 2*b**(3/2)*d*sqrt(a/(b*x**2) + 1)/(3*a**2)","A",0
157,1,891,0,6.711556," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**8/(b*x**2+a)**(1/2),x)","- \frac{5 a^{6} b^{\frac{19}{2}} c \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^{5} b^{\frac{21}{2}} c 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^{4} b^{\frac{23}{2}} c 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{3 a^{4} b^{\frac{9}{2}} d \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{5 a^{3} b^{\frac{25}{2}} c 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{2 a^{3} b^{\frac{11}{2}} d 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{30 a^{2} b^{\frac{27}{2}} c 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{3 a^{2} b^{\frac{13}{2}} d 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{40 a b^{\frac{29}{2}} c 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{12 a b^{\frac{15}{2}} d 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{16 b^{\frac{31}{2}} c 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{8 b^{\frac{17}{2}} d 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{\sqrt{b} e \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} - \frac{\sqrt{b} f \sqrt{\frac{a}{b x^{2}} + 1}}{a} + \frac{2 b^{\frac{3}{2}} e \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}}"," ",0,"-5*a**6*b**(19/2)*c*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**5*b**(21/2)*c*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**4*b**(23/2)*c*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) - 3*a**4*b**(9/2)*d*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) + 5*a**3*b**(25/2)*c*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) - 2*a**3*b**(11/2)*d*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) + 30*a**2*b**(27/2)*c*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) - 3*a**2*b**(13/2)*d*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) + 40*a*b**(29/2)*c*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) - 12*a*b**(15/2)*d*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) + 16*b**(31/2)*c*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) - 8*b**(17/2)*d*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) - sqrt(b)*e*sqrt(a/(b*x**2) + 1)/(3*a*x**2) - sqrt(b)*f*sqrt(a/(b*x**2) + 1)/a + 2*b**(3/2)*e*sqrt(a/(b*x**2) + 1)/(3*a**2)","B",0
158,1,1642,0,7.689095," ","integrate((f*x**6+e*x**4+d*x**2+c)/x**10/(b*x**2+a)**(1/2),x)","- \frac{35 a^{8} b^{\frac{33}{2}} c \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} - \frac{100 a^{7} b^{\frac{35}{2}} c x^{2} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} - \frac{98 a^{6} b^{\frac{37}{2}} c x^{4} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} - \frac{5 a^{6} b^{\frac{19}{2}} d \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{28 a^{5} b^{\frac{39}{2}} c x^{6} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} - \frac{9 a^{5} b^{\frac{21}{2}} d 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{35 a^{4} b^{\frac{41}{2}} c x^{8} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} - \frac{5 a^{4} b^{\frac{23}{2}} d 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{3 a^{4} b^{\frac{9}{2}} e \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{280 a^{3} b^{\frac{43}{2}} c x^{10} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} + \frac{5 a^{3} b^{\frac{25}{2}} d 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{2 a^{3} b^{\frac{11}{2}} e 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{560 a^{2} b^{\frac{45}{2}} c x^{12} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} + \frac{30 a^{2} b^{\frac{27}{2}} d 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{3 a^{2} b^{\frac{13}{2}} e 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{448 a b^{\frac{47}{2}} c x^{14} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} + \frac{40 a b^{\frac{29}{2}} d 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{12 a b^{\frac{15}{2}} e 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{128 b^{\frac{49}{2}} c x^{16} \sqrt{\frac{a}{b x^{2}} + 1}}{315 a^{9} b^{16} x^{8} + 1260 a^{8} b^{17} x^{10} + 1890 a^{7} b^{18} x^{12} + 1260 a^{6} b^{19} x^{14} + 315 a^{5} b^{20} x^{16}} + \frac{16 b^{\frac{31}{2}} d 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{8 b^{\frac{17}{2}} e 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{\sqrt{b} f \sqrt{\frac{a}{b x^{2}} + 1}}{3 a x^{2}} + \frac{2 b^{\frac{3}{2}} f \sqrt{\frac{a}{b x^{2}} + 1}}{3 a^{2}}"," ",0,"-35*a**8*b**(33/2)*c*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) - 100*a**7*b**(35/2)*c*x**2*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) - 98*a**6*b**(37/2)*c*x**4*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) - 5*a**6*b**(19/2)*d*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) - 28*a**5*b**(39/2)*c*x**6*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) - 9*a**5*b**(21/2)*d*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) - 35*a**4*b**(41/2)*c*x**8*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) - 5*a**4*b**(23/2)*d*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) - 3*a**4*b**(9/2)*e*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) - 280*a**3*b**(43/2)*c*x**10*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) + 5*a**3*b**(25/2)*d*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) - 2*a**3*b**(11/2)*e*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) - 560*a**2*b**(45/2)*c*x**12*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) + 30*a**2*b**(27/2)*d*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) - 3*a**2*b**(13/2)*e*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) - 448*a*b**(47/2)*c*x**14*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) + 40*a*b**(29/2)*d*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) - 12*a*b**(15/2)*e*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) - 128*b**(49/2)*c*x**16*sqrt(a/(b*x**2) + 1)/(315*a**9*b**16*x**8 + 1260*a**8*b**17*x**10 + 1890*a**7*b**18*x**12 + 1260*a**6*b**19*x**14 + 315*a**5*b**20*x**16) + 16*b**(31/2)*d*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) - 8*b**(17/2)*e*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) - sqrt(b)*f*sqrt(a/(b*x**2) + 1)/(3*a*x**2) + 2*b**(3/2)*f*sqrt(a/(b*x**2) + 1)/(3*a**2)","B",0
159,-1,0,0,0.000000," ","integrate(x**8*(D*x**6+C*x**4+B*x**2+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate(x**6*(D*x**6+C*x**4+B*x**2+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate(x**4*(D*x**6+C*x**4+B*x**2+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate(x**2*(D*x**6+C*x**4+B*x**2+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((D*x**6+C*x**4+B*x**2+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate((D*x**6+C*x**4+B*x**2+A)/x**2/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((D*x**6+C*x**4+B*x**2+A)/x**4/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((D*x**6+C*x**4+B*x**2+A)/x**6/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((D*x**6+C*x**4+B*x**2+A)/x**8/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((D*x**6+C*x**4+B*x**2+A)/x**10/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,1,442,0,9.372427," ","integrate((f*x**11+e*x**9+d*x**7+c*x**5)/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{256 a^{5} f \sqrt{a + b x^{2}}}{693 b^{6}} + \frac{128 a^{4} e \sqrt{a + b x^{2}}}{315 b^{5}} + \frac{128 a^{4} f x^{2} \sqrt{a + b x^{2}}}{693 b^{5}} - \frac{16 a^{3} d \sqrt{a + b x^{2}}}{35 b^{4}} - \frac{64 a^{3} e x^{2} \sqrt{a + b x^{2}}}{315 b^{4}} - \frac{32 a^{3} f x^{4} \sqrt{a + b x^{2}}}{231 b^{4}} + \frac{8 a^{2} c \sqrt{a + b x^{2}}}{15 b^{3}} + \frac{8 a^{2} d x^{2} \sqrt{a + b x^{2}}}{35 b^{3}} + \frac{16 a^{2} e x^{4} \sqrt{a + b x^{2}}}{105 b^{3}} + \frac{80 a^{2} f x^{6} \sqrt{a + b x^{2}}}{693 b^{3}} - \frac{4 a c x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} - \frac{6 a d x^{4} \sqrt{a + b x^{2}}}{35 b^{2}} - \frac{8 a e x^{6} \sqrt{a + b x^{2}}}{63 b^{2}} - \frac{10 a f x^{8} \sqrt{a + b x^{2}}}{99 b^{2}} + \frac{c x^{4} \sqrt{a + b x^{2}}}{5 b} + \frac{d x^{6} \sqrt{a + b x^{2}}}{7 b} + \frac{e x^{8} \sqrt{a + b x^{2}}}{9 b} + \frac{f x^{10} \sqrt{a + b x^{2}}}{11 b} & \text{for}\: b \neq 0 \\\frac{\frac{c x^{6}}{6} + \frac{d x^{8}}{8} + \frac{e x^{10}}{10} + \frac{f x^{12}}{12}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-256*a**5*f*sqrt(a + b*x**2)/(693*b**6) + 128*a**4*e*sqrt(a + b*x**2)/(315*b**5) + 128*a**4*f*x**2*sqrt(a + b*x**2)/(693*b**5) - 16*a**3*d*sqrt(a + b*x**2)/(35*b**4) - 64*a**3*e*x**2*sqrt(a + b*x**2)/(315*b**4) - 32*a**3*f*x**4*sqrt(a + b*x**2)/(231*b**4) + 8*a**2*c*sqrt(a + b*x**2)/(15*b**3) + 8*a**2*d*x**2*sqrt(a + b*x**2)/(35*b**3) + 16*a**2*e*x**4*sqrt(a + b*x**2)/(105*b**3) + 80*a**2*f*x**6*sqrt(a + b*x**2)/(693*b**3) - 4*a*c*x**2*sqrt(a + b*x**2)/(15*b**2) - 6*a*d*x**4*sqrt(a + b*x**2)/(35*b**2) - 8*a*e*x**6*sqrt(a + b*x**2)/(63*b**2) - 10*a*f*x**8*sqrt(a + b*x**2)/(99*b**2) + c*x**4*sqrt(a + b*x**2)/(5*b) + d*x**6*sqrt(a + b*x**2)/(7*b) + e*x**8*sqrt(a + b*x**2)/(9*b) + f*x**10*sqrt(a + b*x**2)/(11*b), Ne(b, 0)), ((c*x**6/6 + d*x**8/8 + e*x**10/10 + f*x**12/12)/sqrt(a), True))","A",0
170,1,340,0,5.408942," ","integrate((f*x**9+e*x**7+d*x**5+c*x**3)/(b*x**2+a)**(1/2),x)","\begin{cases} \frac{128 a^{4} f \sqrt{a + b x^{2}}}{315 b^{5}} - \frac{16 a^{3} e \sqrt{a + b x^{2}}}{35 b^{4}} - \frac{64 a^{3} f x^{2} \sqrt{a + b x^{2}}}{315 b^{4}} + \frac{8 a^{2} d \sqrt{a + b x^{2}}}{15 b^{3}} + \frac{8 a^{2} e x^{2} \sqrt{a + b x^{2}}}{35 b^{3}} + \frac{16 a^{2} f x^{4} \sqrt{a + b x^{2}}}{105 b^{3}} - \frac{2 a c \sqrt{a + b x^{2}}}{3 b^{2}} - \frac{4 a d x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} - \frac{6 a e x^{4} \sqrt{a + b x^{2}}}{35 b^{2}} - \frac{8 a f x^{6} \sqrt{a + b x^{2}}}{63 b^{2}} + \frac{c x^{2} \sqrt{a + b x^{2}}}{3 b} + \frac{d x^{4} \sqrt{a + b x^{2}}}{5 b} + \frac{e x^{6} \sqrt{a + b x^{2}}}{7 b} + \frac{f x^{8} \sqrt{a + b x^{2}}}{9 b} & \text{for}\: b \neq 0 \\\frac{\frac{c x^{4}}{4} + \frac{d x^{6}}{6} + \frac{e x^{8}}{8} + \frac{f x^{10}}{10}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*a**4*f*sqrt(a + b*x**2)/(315*b**5) - 16*a**3*e*sqrt(a + b*x**2)/(35*b**4) - 64*a**3*f*x**2*sqrt(a + b*x**2)/(315*b**4) + 8*a**2*d*sqrt(a + b*x**2)/(15*b**3) + 8*a**2*e*x**2*sqrt(a + b*x**2)/(35*b**3) + 16*a**2*f*x**4*sqrt(a + b*x**2)/(105*b**3) - 2*a*c*sqrt(a + b*x**2)/(3*b**2) - 4*a*d*x**2*sqrt(a + b*x**2)/(15*b**2) - 6*a*e*x**4*sqrt(a + b*x**2)/(35*b**2) - 8*a*f*x**6*sqrt(a + b*x**2)/(63*b**2) + c*x**2*sqrt(a + b*x**2)/(3*b) + d*x**4*sqrt(a + b*x**2)/(5*b) + e*x**6*sqrt(a + b*x**2)/(7*b) + f*x**8*sqrt(a + b*x**2)/(9*b), Ne(b, 0)), ((c*x**4/4 + d*x**6/6 + e*x**8/8 + f*x**10/10)/sqrt(a), True))","A",0
171,1,238,0,3.405558," ","integrate((f*x**7+e*x**5+d*x**3+c*x)/(b*x**2+a)**(1/2),x)","\begin{cases} - \frac{16 a^{3} f \sqrt{a + b x^{2}}}{35 b^{4}} + \frac{8 a^{2} e \sqrt{a + b x^{2}}}{15 b^{3}} + \frac{8 a^{2} f x^{2} \sqrt{a + b x^{2}}}{35 b^{3}} - \frac{2 a d \sqrt{a + b x^{2}}}{3 b^{2}} - \frac{4 a e x^{2} \sqrt{a + b x^{2}}}{15 b^{2}} - \frac{6 a f x^{4} \sqrt{a + b x^{2}}}{35 b^{2}} + \frac{c \sqrt{a + b x^{2}}}{b} + \frac{d x^{2} \sqrt{a + b x^{2}}}{3 b} + \frac{e x^{4} \sqrt{a + b x^{2}}}{5 b} + \frac{f x^{6} \sqrt{a + b x^{2}}}{7 b} & \text{for}\: b \neq 0 \\\frac{\frac{c x^{2}}{2} + \frac{d x^{4}}{4} + \frac{e x^{6}}{6} + \frac{f x^{8}}{8}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*a**3*f*sqrt(a + b*x**2)/(35*b**4) + 8*a**2*e*sqrt(a + b*x**2)/(15*b**3) + 8*a**2*f*x**2*sqrt(a + b*x**2)/(35*b**3) - 2*a*d*sqrt(a + b*x**2)/(3*b**2) - 4*a*e*x**2*sqrt(a + b*x**2)/(15*b**2) - 6*a*f*x**4*sqrt(a + b*x**2)/(35*b**2) + c*sqrt(a + b*x**2)/b + d*x**2*sqrt(a + b*x**2)/(3*b) + e*x**4*sqrt(a + b*x**2)/(5*b) + f*x**6*sqrt(a + b*x**2)/(7*b), Ne(b, 0)), ((c*x**2/2 + d*x**4/4 + e*x**6/6 + f*x**8/8)/sqrt(a), True))","A",0
172,-1,0,0,0.000000," ","integrate(x**2*(F*x**8+D*x**6+C*x**4+B*x**2+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((F*x**8+D*x**6+C*x**4+B*x**2+A)/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((F*x**8+D*x**6+C*x**4+B*x**2+A)/x**2/(b*x**2+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
