3.1740 \(\int \frac {1}{(a+\frac {b}{x})^{3/2} x^6} \, dx\)
Optimal. Leaf size=95 \[ \frac {2 a^4}{b^5 \sqrt {a+\frac {b}{x}}}+\frac {8 a^3 \sqrt {a+\frac {b}{x}}}{b^5}-\frac {4 a^2 \left (a+\frac {b}{x}\right )^{3/2}}{b^5}+\frac {8 a \left (a+\frac {b}{x}\right )^{5/2}}{5 b^5}-\frac {2 \left (a+\frac {b}{x}\right )^{7/2}}{7 b^5} \]
[Out]
-4*a^2*(a+b/x)^(3/2)/b^5+8/5*a*(a+b/x)^(5/2)/b^5-2/7*(a+b/x)^(7/2)/b^5+2*a^4/b^5/(a+b/x)^(1/2)+8*a^3*(a+b/x)^(
1/2)/b^5
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 95, normalized size of antiderivative = 1.00,
number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used =
{266, 43} \[ \frac {2 a^4}{b^5 \sqrt {a+\frac {b}{x}}}+\frac {8 a^3 \sqrt {a+\frac {b}{x}}}{b^5}-\frac {4 a^2 \left (a+\frac {b}{x}\right )^{3/2}}{b^5}+\frac {8 a \left (a+\frac {b}{x}\right )^{5/2}}{5 b^5}-\frac {2 \left (a+\frac {b}{x}\right )^{7/2}}{7 b^5} \]
Antiderivative was successfully verified.
[In]
Int[1/((a + b/x)^(3/2)*x^6),x]
[Out]
(2*a^4)/(b^5*Sqrt[a + b/x]) + (8*a^3*Sqrt[a + b/x])/b^5 - (4*a^2*(a + b/x)^(3/2))/b^5 + (8*a*(a + b/x)^(5/2))/
(5*b^5) - (2*(a + b/x)^(7/2))/(7*b^5)
Rule 43
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])
Rule 266
Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Dist[1/n, Subst[Int[x^(Simplify[(m + 1)/n] - 1)*(a
+ b*x)^p, x], x, x^n], x] /; FreeQ[{a, b, m, n, p}, x] && IntegerQ[Simplify[(m + 1)/n]]
Rubi steps
\begin {align*} \int \frac {1}{\left (a+\frac {b}{x}\right )^{3/2} x^6} \, dx &=-\operatorname {Subst}\left (\int \frac {x^4}{(a+b x)^{3/2}} \, dx,x,\frac {1}{x}\right )\\ &=-\operatorname {Subst}\left (\int \left (\frac {a^4}{b^4 (a+b x)^{3/2}}-\frac {4 a^3}{b^4 \sqrt {a+b x}}+\frac {6 a^2 \sqrt {a+b x}}{b^4}-\frac {4 a (a+b x)^{3/2}}{b^4}+\frac {(a+b x)^{5/2}}{b^4}\right ) \, dx,x,\frac {1}{x}\right )\\ &=\frac {2 a^4}{b^5 \sqrt {a+\frac {b}{x}}}+\frac {8 a^3 \sqrt {a+\frac {b}{x}}}{b^5}-\frac {4 a^2 \left (a+\frac {b}{x}\right )^{3/2}}{b^5}+\frac {8 a \left (a+\frac {b}{x}\right )^{5/2}}{5 b^5}-\frac {2 \left (a+\frac {b}{x}\right )^{7/2}}{7 b^5}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 62, normalized size = 0.65 \[ \frac {2 \left (128 a^4 x^4+64 a^3 b x^3-16 a^2 b^2 x^2+8 a b^3 x-5 b^4\right )}{35 b^5 x^4 \sqrt {a+\frac {b}{x}}} \]
Antiderivative was successfully verified.
[In]
Integrate[1/((a + b/x)^(3/2)*x^6),x]
[Out]
(2*(-5*b^4 + 8*a*b^3*x - 16*a^2*b^2*x^2 + 64*a^3*b*x^3 + 128*a^4*x^4))/(35*b^5*Sqrt[a + b/x]*x^4)
________________________________________________________________________________________
fricas [A] time = 1.15, size = 72, normalized size = 0.76 \[ \frac {2 \, {\left (128 \, a^{4} x^{4} + 64 \, a^{3} b x^{3} - 16 \, a^{2} b^{2} x^{2} + 8 \, a b^{3} x - 5 \, b^{4}\right )} \sqrt {\frac {a x + b}{x}}}{35 \, {\left (a b^{5} x^{4} + b^{6} x^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b/x)^(3/2)/x^6,x, algorithm="fricas")
[Out]
2/35*(128*a^4*x^4 + 64*a^3*b*x^3 - 16*a^2*b^2*x^2 + 8*a*b^3*x - 5*b^4)*sqrt((a*x + b)/x)/(a*b^5*x^4 + b^6*x^3)
________________________________________________________________________________________
giac [A] time = 0.19, size = 109, normalized size = 1.15 \[ \frac {2 \, {\left (\frac {35 \, a^{4}}{\sqrt {\frac {a x + b}{x}}} + 140 \, a^{3} \sqrt {\frac {a x + b}{x}} - \frac {70 \, {\left (a x + b\right )} a^{2} \sqrt {\frac {a x + b}{x}}}{x} + \frac {28 \, {\left (a x + b\right )}^{2} a \sqrt {\frac {a x + b}{x}}}{x^{2}} - \frac {5 \, {\left (a x + b\right )}^{3} \sqrt {\frac {a x + b}{x}}}{x^{3}}\right )}}{35 \, b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b/x)^(3/2)/x^6,x, algorithm="giac")
[Out]
2/35*(35*a^4/sqrt((a*x + b)/x) + 140*a^3*sqrt((a*x + b)/x) - 70*(a*x + b)*a^2*sqrt((a*x + b)/x)/x + 28*(a*x +
b)^2*a*sqrt((a*x + b)/x)/x^2 - 5*(a*x + b)^3*sqrt((a*x + b)/x)/x^3)/b^5
________________________________________________________________________________________
maple [A] time = 0.01, size = 66, normalized size = 0.69 \[ \frac {2 \left (a x +b \right ) \left (128 a^{4} x^{4}+64 a^{3} x^{3} b -16 a^{2} x^{2} b^{2}+8 a x \,b^{3}-5 b^{4}\right )}{35 \left (\frac {a x +b}{x}\right )^{\frac {3}{2}} b^{5} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(a+b/x)^(3/2)/x^6,x)
[Out]
2/35*(a*x+b)*(128*a^4*x^4+64*a^3*b*x^3-16*a^2*b^2*x^2+8*a*b^3*x-5*b^4)/x^5/b^5/((a*x+b)/x)^(3/2)
________________________________________________________________________________________
maxima [A] time = 0.95, size = 81, normalized size = 0.85 \[ -\frac {2 \, {\left (a + \frac {b}{x}\right )}^{\frac {7}{2}}}{7 \, b^{5}} + \frac {8 \, {\left (a + \frac {b}{x}\right )}^{\frac {5}{2}} a}{5 \, b^{5}} - \frac {4 \, {\left (a + \frac {b}{x}\right )}^{\frac {3}{2}} a^{2}}{b^{5}} + \frac {8 \, \sqrt {a + \frac {b}{x}} a^{3}}{b^{5}} + \frac {2 \, a^{4}}{\sqrt {a + \frac {b}{x}} b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b/x)^(3/2)/x^6,x, algorithm="maxima")
[Out]
-2/7*(a + b/x)^(7/2)/b^5 + 8/5*(a + b/x)^(5/2)*a/b^5 - 4*(a + b/x)^(3/2)*a^2/b^5 + 8*sqrt(a + b/x)*a^3/b^5 + 2
*a^4/(sqrt(a + b/x)*b^5)
________________________________________________________________________________________
mupad [B] time = 1.45, size = 91, normalized size = 0.96 \[ \frac {\sqrt {a+\frac {b}{x}}\,\left (\frac {186\,a^3}{35\,b^4}+\frac {256\,a^4\,x}{35\,b^5}\right )}{b+a\,x}-\frac {2\,\sqrt {a+\frac {b}{x}}}{7\,b^2\,x^3}+\frac {26\,a\,\sqrt {a+\frac {b}{x}}}{35\,b^3\,x^2}-\frac {58\,a^2\,\sqrt {a+\frac {b}{x}}}{35\,b^4\,x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(x^6*(a + b/x)^(3/2)),x)
[Out]
((a + b/x)^(1/2)*((186*a^3)/(35*b^4) + (256*a^4*x)/(35*b^5)))/(b + a*x) - (2*(a + b/x)^(1/2))/(7*b^2*x^3) + (2
6*a*(a + b/x)^(1/2))/(35*b^3*x^2) - (58*a^2*(a + b/x)^(1/2))/(35*b^4*x)
________________________________________________________________________________________
sympy [B] time = 6.29, size = 4707, normalized size = 49.55 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b/x)**(3/2)/x**6,x)
[Out]
256*a**(33/2)*b**(49/2)*x**13*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) +
1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17
/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x
**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 2432*a**(31/2)*b**(51/2)*x**12*sqrt(a*x
/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*
a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b
**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2)
+ 35*a**(7/2)*b**39*x**(7/2)) + 10336*a**(29/2)*b**(53/2)*x**11*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2)
+ 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(
19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36
*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 2584
0*a**(27/2)*b**(55/2)*x**10*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 15
75*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2
)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**
(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 41990*a**(25/2)*b**(57/2)*x**9*sqrt(a*x/b
+ 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a*
*(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**
35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) +
35*a**(7/2)*b**39*x**(7/2)) + 46182*a**(23/2)*b**(59/2)*x**8*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) +
350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/
2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x*
*(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 34584*a
**(21/2)*b**(61/2)*x**7*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a
**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b*
*34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/
2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 17112*a**(19/2)*b**(63/2)*x**6*sqrt(a*x/b + 1
)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21
/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x
**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*
a**(7/2)*b**39*x**(7/2)) + 4980*a**(17/2)*b**(65/2)*x**5*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a
**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b*
*33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/
2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) + 340*a**(15/2
)*b**(67/2)*x**4*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2
)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**
(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 35
0*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 424*a**(13/2)*b**(69/2)*x**3*sqrt(a*x/b + 1)/(35*a**
(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32
*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2)
+ 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*
b**39*x**(7/2)) - 248*a**(11/2)*b**(71/2)*x**2*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b
**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19
/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*
a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 74*a**(9/2)*b**(73/2)*
x*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/
2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a
**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**3
8*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 10*a**(7/2)*b**(75/2)*sqrt(a*x/b + 1)/(35*a**(27/2)*b**29*x**(27/2)
+ 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(
19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36
*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 256*
a**17*b**24*x**(27/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**
(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 73
50*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*
b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 2560*a**16*b**25*x**(25/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*
a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b
**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13
/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 11520*a**15
*b**26*x**(23/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2
) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a*
*(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38
*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 30720*a**14*b**27*x**(21/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(
25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33
*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2)
+ 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 53760*a**13*b**
28*x**(19/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) +
4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15
/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**
(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 64512*a**12*b**29*x**(17/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2
)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**
(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 15
75*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 53760*a**11*b**30*x
**(15/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200
*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*
b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2
) + 35*a**(7/2)*b**39*x**(7/2)) - 30720*a**10*b**31*x**(13/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b*
*30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/
2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a
**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 11520*a**9*b**32*x**(11
/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(
21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35
*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 3
5*a**(7/2)*b**39*x**(7/2)) - 2560*a**8*b**33*x**(9/2)/(35*a**(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(
25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 882
0*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2) + 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)
*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*b**39*x**(7/2)) - 256*a**7*b**34*x**(7/2)/(35*a**
(27/2)*b**29*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4200*a**(21/2)*b**32
*x**(21/2) + 7350*a**(19/2)*b**33*x**(19/2) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(15/2)*b**35*x**(15/2)
+ 4200*a**(13/2)*b**36*x**(13/2) + 1575*a**(11/2)*b**37*x**(11/2) + 350*a**(9/2)*b**38*x**(9/2) + 35*a**(7/2)*
b**39*x**(7/2))
________________________________________________________________________________________