3.1710 \(\int \frac {(a+\frac {b}{x})^{3/2}}{x^6} \, dx\)
Optimal. Leaf size=101 \[ -\frac {2 a^4 \left (a+\frac {b}{x}\right )^{5/2}}{5 b^5}+\frac {8 a^3 \left (a+\frac {b}{x}\right )^{7/2}}{7 b^5}-\frac {4 a^2 \left (a+\frac {b}{x}\right )^{9/2}}{3 b^5}-\frac {2 \left (a+\frac {b}{x}\right )^{13/2}}{13 b^5}+\frac {8 a \left (a+\frac {b}{x}\right )^{11/2}}{11 b^5} \]
[Out]
-2/5*a^4*(a+b/x)^(5/2)/b^5+8/7*a^3*(a+b/x)^(7/2)/b^5-4/3*a^2*(a+b/x)^(9/2)/b^5+8/11*a*(a+b/x)^(11/2)/b^5-2/13*
(a+b/x)^(13/2)/b^5
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Rubi [A] time = 0.04, antiderivative size = 101, 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} \[ -\frac {4 a^2 \left (a+\frac {b}{x}\right )^{9/2}}{3 b^5}+\frac {8 a^3 \left (a+\frac {b}{x}\right )^{7/2}}{7 b^5}-\frac {2 a^4 \left (a+\frac {b}{x}\right )^{5/2}}{5 b^5}-\frac {2 \left (a+\frac {b}{x}\right )^{13/2}}{13 b^5}+\frac {8 a \left (a+\frac {b}{x}\right )^{11/2}}{11 b^5} \]
Antiderivative was successfully verified.
[In]
Int[(a + b/x)^(3/2)/x^6,x]
[Out]
(-2*a^4*(a + b/x)^(5/2))/(5*b^5) + (8*a^3*(a + b/x)^(7/2))/(7*b^5) - (4*a^2*(a + b/x)^(9/2))/(3*b^5) + (8*a*(a
+ b/x)^(11/2))/(11*b^5) - (2*(a + b/x)^(13/2))/(13*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 {\left (a+\frac {b}{x}\right )^{3/2}}{x^6} \, dx &=-\operatorname {Subst}\left (\int x^4 (a+b x)^{3/2} \, dx,x,\frac {1}{x}\right )\\ &=-\operatorname {Subst}\left (\int \left (\frac {a^4 (a+b x)^{3/2}}{b^4}-\frac {4 a^3 (a+b x)^{5/2}}{b^4}+\frac {6 a^2 (a+b x)^{7/2}}{b^4}-\frac {4 a (a+b x)^{9/2}}{b^4}+\frac {(a+b x)^{11/2}}{b^4}\right ) \, dx,x,\frac {1}{x}\right )\\ &=-\frac {2 a^4 \left (a+\frac {b}{x}\right )^{5/2}}{5 b^5}+\frac {8 a^3 \left (a+\frac {b}{x}\right )^{7/2}}{7 b^5}-\frac {4 a^2 \left (a+\frac {b}{x}\right )^{9/2}}{3 b^5}+\frac {8 a \left (a+\frac {b}{x}\right )^{11/2}}{11 b^5}-\frac {2 \left (a+\frac {b}{x}\right )^{13/2}}{13 b^5}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 69, normalized size = 0.68 \[ -\frac {2 \sqrt {a+\frac {b}{x}} (a x+b)^2 \left (128 a^4 x^4-320 a^3 b x^3+560 a^2 b^2 x^2-840 a b^3 x+1155 b^4\right )}{15015 b^5 x^6} \]
Antiderivative was successfully verified.
[In]
Integrate[(a + b/x)^(3/2)/x^6,x]
[Out]
(-2*Sqrt[a + b/x]*(b + a*x)^2*(1155*b^4 - 840*a*b^3*x + 560*a^2*b^2*x^2 - 320*a^3*b*x^3 + 128*a^4*x^4))/(15015
*b^5*x^6)
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fricas [A] time = 1.09, size = 82, normalized size = 0.81 \[ -\frac {2 \, {\left (128 \, a^{6} x^{6} - 64 \, a^{5} b x^{5} + 48 \, a^{4} b^{2} x^{4} - 40 \, a^{3} b^{3} x^{3} + 35 \, a^{2} b^{4} x^{2} + 1470 \, a b^{5} x + 1155 \, b^{6}\right )} \sqrt {\frac {a x + b}{x}}}{15015 \, b^{5} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((a+b/x)^(3/2)/x^6,x, algorithm="fricas")
[Out]
-2/15015*(128*a^6*x^6 - 64*a^5*b*x^5 + 48*a^4*b^2*x^4 - 40*a^3*b^3*x^3 + 35*a^2*b^4*x^2 + 1470*a*b^5*x + 1155*
b^6)*sqrt((a*x + b)/x)/(b^5*x^6)
________________________________________________________________________________________
giac [B] time = 0.33, size = 270, normalized size = 2.67 \[ \frac {2 \, {\left (48048 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{8} a^{4} \mathrm {sgn}\relax (x) + 240240 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{7} a^{\frac {7}{2}} b \mathrm {sgn}\relax (x) + 531960 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{6} a^{3} b^{2} \mathrm {sgn}\relax (x) + 675675 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{5} a^{\frac {5}{2}} b^{3} \mathrm {sgn}\relax (x) + 535535 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{4} a^{2} b^{4} \mathrm {sgn}\relax (x) + 270270 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{3} a^{\frac {3}{2}} b^{5} \mathrm {sgn}\relax (x) + 84630 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{2} a b^{6} \mathrm {sgn}\relax (x) + 15015 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )} \sqrt {a} b^{7} \mathrm {sgn}\relax (x) + 1155 \, b^{8} \mathrm {sgn}\relax (x)\right )}}{15015 \, {\left (\sqrt {a} x - \sqrt {a x^{2} + b x}\right )}^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((a+b/x)^(3/2)/x^6,x, algorithm="giac")
[Out]
2/15015*(48048*(sqrt(a)*x - sqrt(a*x^2 + b*x))^8*a^4*sgn(x) + 240240*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)
*b*sgn(x) + 531960*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b^2*sgn(x) + 675675*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5
*a^(5/2)*b^3*sgn(x) + 535535*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^4*sgn(x) + 270270*(sqrt(a)*x - sqrt(a*x^2
+ b*x))^3*a^(3/2)*b^5*sgn(x) + 84630*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^6*sgn(x) + 15015*(sqrt(a)*x - sqrt
(a*x^2 + b*x))*sqrt(a)*b^7*sgn(x) + 1155*b^8*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^13
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maple [A] time = 0.01, size = 66, normalized size = 0.65 \[ -\frac {2 \left (a x +b \right ) \left (128 a^{4} x^{4}-320 a^{3} x^{3} b +560 a^{2} x^{2} b^{2}-840 a x \,b^{3}+1155 b^{4}\right ) \left (\frac {a x +b}{x}\right )^{\frac {3}{2}}}{15015 b^{5} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((a+b/x)^(3/2)/x^6,x)
[Out]
-2/15015*(a*x+b)*(128*a^4*x^4-320*a^3*b*x^3+560*a^2*b^2*x^2-840*a*b^3*x+1155*b^4)*((a*x+b)/x)^(3/2)/x^5/b^5
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maxima [A] time = 1.06, size = 81, normalized size = 0.80 \[ -\frac {2 \, {\left (a + \frac {b}{x}\right )}^{\frac {13}{2}}}{13 \, b^{5}} + \frac {8 \, {\left (a + \frac {b}{x}\right )}^{\frac {11}{2}} a}{11 \, b^{5}} - \frac {4 \, {\left (a + \frac {b}{x}\right )}^{\frac {9}{2}} a^{2}}{3 \, b^{5}} + \frac {8 \, {\left (a + \frac {b}{x}\right )}^{\frac {7}{2}} a^{3}}{7 \, b^{5}} - \frac {2 \, {\left (a + \frac {b}{x}\right )}^{\frac {5}{2}} a^{4}}{5 \, b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((a+b/x)^(3/2)/x^6,x, algorithm="maxima")
[Out]
-2/13*(a + b/x)^(13/2)/b^5 + 8/11*(a + b/x)^(11/2)*a/b^5 - 4/3*(a + b/x)^(9/2)*a^2/b^5 + 8/7*(a + b/x)^(7/2)*a
^3/b^5 - 2/5*(a + b/x)^(5/2)*a^4/b^5
________________________________________________________________________________________
mupad [B] time = 2.31, size = 128, normalized size = 1.27 \[ \frac {16\,a^3\,\sqrt {a+\frac {b}{x}}}{3003\,b^2\,x^3}-\frac {2\,b\,\sqrt {a+\frac {b}{x}}}{13\,x^6}-\frac {256\,a^6\,\sqrt {a+\frac {b}{x}}}{15015\,b^5}-\frac {2\,a^2\,\sqrt {a+\frac {b}{x}}}{429\,b\,x^4}-\frac {28\,a\,\sqrt {a+\frac {b}{x}}}{143\,x^5}-\frac {32\,a^4\,\sqrt {a+\frac {b}{x}}}{5005\,b^3\,x^2}+\frac {128\,a^5\,\sqrt {a+\frac {b}{x}}}{15015\,b^4\,x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((a + b/x)^(3/2)/x^6,x)
[Out]
(16*a^3*(a + b/x)^(1/2))/(3003*b^2*x^3) - (2*b*(a + b/x)^(1/2))/(13*x^6) - (256*a^6*(a + b/x)^(1/2))/(15015*b^
5) - (2*a^2*(a + b/x)^(1/2))/(429*b*x^4) - (28*a*(a + b/x)^(1/2))/(143*x^5) - (32*a^4*(a + b/x)^(1/2))/(5005*b
^3*x^2) + (128*a^5*(a + b/x)^(1/2))/(15015*b^4*x)
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sympy [B] time = 6.15, size = 5289, normalized size = 52.37 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((a+b/x)**(3/2)/x**6,x)
[Out]
-256*a**(45/2)*b**(49/2)*x**16*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(3
1/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2
) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2)
+ 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 243
2*a**(43/2)*b**(51/2)*x**15*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2
) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) +
3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 6
75675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 10336*
a**(41/2)*b**(53/2)*x**14*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2)
+ 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3
783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675
675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 25840*a*
*(39/2)*b**(55/2)*x**13*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) +
675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 378
3780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 67567
5*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 41990*a**(
37/2)*b**(57/2)*x**12*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 67
5675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 37837
80*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*
a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 49192*a**(35
/2)*b**(59/2)*x**11*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 6756
75*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780
*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a*
*(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 66924*a**(33/2
)*b**(61/2)*x**10*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675
*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a
**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(
17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 175032*a**(31/2)
*b**(63/2)*x**9*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a
**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**
(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17
/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 467610*a**(29/2)*b
**(65/2)*x**8*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**
(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(2
3/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2
)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 903760*a**(27/2)*b**
(67/2)*x**7*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(2
9/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/
2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*
b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 1234376*a**(25/2)*b**(
69/2)*x**6*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29
/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2
)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b
**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 1205152*a**(23/2)*b**(7
1/2)*x**5*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/
2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)
*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b*
*37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 840346*a**(21/2)*b**(73/
2)*x**4*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)
*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b
**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**3
7*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 410120*a**(19/2)*b**(75/2)
*x**3*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b
**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**
34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*
x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 133420*a**(17/2)*b**(77/2)*x
**2*sqrt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**
31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34
*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x*
*(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 26040*a**(15/2)*b**(79/2)*x*sq
rt(a*x/b + 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**
(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(2
3/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2
) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) - 2310*a**(13/2)*b**(81/2)*sqrt(a*x/b
+ 1)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) +
1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 31
53150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 15015
0*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 256*a**23*b**24*x**(33/2)/(15015*a**(33/2)*b*
*29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*
x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x*
*(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15
/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 2560*a**22*b**25*x**(31/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*
a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**
(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(1
9/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b
**39*x**(13/2)) + 11520*a**21*b**26*x**(29/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31
/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2)
+ 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) +
675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 3072
0*a**20*b**27*x**(27/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)
*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b
**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**3
7*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 53760*a**19*b**28*x**(25/2
)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 180
1800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 31531
50*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a
**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 64512*a**18*b**29*x**(23/2)/(15015*a**(33/2)*b**
29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x
**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**
(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/
2) + 15015*a**(13/2)*b**39*x**(13/2)) + 53760*a**17*b**30*x**(21/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*
a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**
(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(1
9/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b
**39*x**(13/2)) + 30720*a**16*b**31*x**(19/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31
/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2)
+ 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) +
675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 1152
0*a**15*b**32*x**(17/2)/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)
*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b
**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**3
7*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 2560*a**14*b**33*x**(15/2)
/(15015*a**(33/2)*b**29*x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801
800*a**(27/2)*b**32*x**(27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 315315
0*a**(21/2)*b**35*x**(21/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a*
*(15/2)*b**38*x**(15/2) + 15015*a**(13/2)*b**39*x**(13/2)) + 256*a**13*b**34*x**(13/2)/(15015*a**(33/2)*b**29*
x**(33/2) + 150150*a**(31/2)*b**30*x**(31/2) + 675675*a**(29/2)*b**31*x**(29/2) + 1801800*a**(27/2)*b**32*x**(
27/2) + 3153150*a**(25/2)*b**33*x**(25/2) + 3783780*a**(23/2)*b**34*x**(23/2) + 3153150*a**(21/2)*b**35*x**(21
/2) + 1801800*a**(19/2)*b**36*x**(19/2) + 675675*a**(17/2)*b**37*x**(17/2) + 150150*a**(15/2)*b**38*x**(15/2)
+ 15015*a**(13/2)*b**39*x**(13/2))
________________________________________________________________________________________