3.1711 \(\int \frac{(a+\frac{b}{x})^{3/2}}{x^7} \, dx\)

Optimal. Leaf size=122 \[ -\frac{20 a^2 \left (a+\frac{b}{x}\right )^{11/2}}{11 b^6}+\frac{20 a^3 \left (a+\frac{b}{x}\right )^{9/2}}{9 b^6}-\frac{10 a^4 \left (a+\frac{b}{x}\right )^{7/2}}{7 b^6}+\frac{2 a^5 \left (a+\frac{b}{x}\right )^{5/2}}{5 b^6}-\frac{2 \left (a+\frac{b}{x}\right )^{15/2}}{15 b^6}+\frac{10 a \left (a+\frac{b}{x}\right )^{13/2}}{13 b^6} \]

[Out]

(2*a^5*(a + b/x)^(5/2))/(5*b^6) - (10*a^4*(a + b/x)^(7/2))/(7*b^6) + (20*a^3*(a + b/x)^(9/2))/(9*b^6) - (20*a^
2*(a + b/x)^(11/2))/(11*b^6) + (10*a*(a + b/x)^(13/2))/(13*b^6) - (2*(a + b/x)^(15/2))/(15*b^6)

________________________________________________________________________________________

Rubi [A]  time = 0.0507715, antiderivative size = 122, normalized size of antiderivative = 1., 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} \[ -\frac{20 a^2 \left (a+\frac{b}{x}\right )^{11/2}}{11 b^6}+\frac{20 a^3 \left (a+\frac{b}{x}\right )^{9/2}}{9 b^6}-\frac{10 a^4 \left (a+\frac{b}{x}\right )^{7/2}}{7 b^6}+\frac{2 a^5 \left (a+\frac{b}{x}\right )^{5/2}}{5 b^6}-\frac{2 \left (a+\frac{b}{x}\right )^{15/2}}{15 b^6}+\frac{10 a \left (a+\frac{b}{x}\right )^{13/2}}{13 b^6} \]

Antiderivative was successfully verified.

[In]

Int[(a + b/x)^(3/2)/x^7,x]

[Out]

(2*a^5*(a + b/x)^(5/2))/(5*b^6) - (10*a^4*(a + b/x)^(7/2))/(7*b^6) + (20*a^3*(a + b/x)^(9/2))/(9*b^6) - (20*a^
2*(a + b/x)^(11/2))/(11*b^6) + (10*a*(a + b/x)^(13/2))/(13*b^6) - (2*(a + b/x)^(15/2))/(15*b^6)

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]]

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])

Rubi steps

\begin{align*} \int \frac{\left (a+\frac{b}{x}\right )^{3/2}}{x^7} \, dx &=-\operatorname{Subst}\left (\int x^5 (a+b x)^{3/2} \, dx,x,\frac{1}{x}\right )\\ &=-\operatorname{Subst}\left (\int \left (-\frac{a^5 (a+b x)^{3/2}}{b^5}+\frac{5 a^4 (a+b x)^{5/2}}{b^5}-\frac{10 a^3 (a+b x)^{7/2}}{b^5}+\frac{10 a^2 (a+b x)^{9/2}}{b^5}-\frac{5 a (a+b x)^{11/2}}{b^5}+\frac{(a+b x)^{13/2}}{b^5}\right ) \, dx,x,\frac{1}{x}\right )\\ &=\frac{2 a^5 \left (a+\frac{b}{x}\right )^{5/2}}{5 b^6}-\frac{10 a^4 \left (a+\frac{b}{x}\right )^{7/2}}{7 b^6}+\frac{20 a^3 \left (a+\frac{b}{x}\right )^{9/2}}{9 b^6}-\frac{20 a^2 \left (a+\frac{b}{x}\right )^{11/2}}{11 b^6}+\frac{10 a \left (a+\frac{b}{x}\right )^{13/2}}{13 b^6}-\frac{2 \left (a+\frac{b}{x}\right )^{15/2}}{15 b^6}\\ \end{align*}

Mathematica [A]  time = 0.0390018, size = 80, normalized size = 0.66 \[ \frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^2 \left (-1680 a^2 b^3 x^2+1120 a^3 b^2 x^3-640 a^4 b x^4+256 a^5 x^5+2310 a b^4 x-3003 b^5\right )}{45045 b^6 x^7} \]

Antiderivative was successfully verified.

[In]

Integrate[(a + b/x)^(3/2)/x^7,x]

[Out]

(2*Sqrt[a + b/x]*(b + a*x)^2*(-3003*b^5 + 2310*a*b^4*x - 1680*a^2*b^3*x^2 + 1120*a^3*b^2*x^3 - 640*a^4*b*x^4 +
256*a^5*x^5))/(45045*b^6*x^7)

________________________________________________________________________________________

Maple [A]  time = 0.005, size = 77, normalized size = 0.6 \begin{align*}{\frac{ \left ( 2\,ax+2\,b \right ) \left ( 256\,{a}^{5}{x}^{5}-640\,{a}^{4}b{x}^{4}+1120\,{a}^{3}{b}^{2}{x}^{3}-1680\,{a}^{2}{b}^{3}{x}^{2}+2310\,a{b}^{4}x-3003\,{b}^{5} \right ) }{45045\,{x}^{6}{b}^{6}} \left ({\frac{ax+b}{x}} \right ) ^{{\frac{3}{2}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b/x)^(3/2)/x^7,x)

[Out]

2/45045*(a*x+b)*(256*a^5*x^5-640*a^4*b*x^4+1120*a^3*b^2*x^3-1680*a^2*b^3*x^2+2310*a*b^4*x-3003*b^5)*((a*x+b)/x
)^(3/2)/x^6/b^6

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Maxima [A]  time = 1.19813, size = 132, normalized size = 1.08 \begin{align*} -\frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{15}{2}}}{15 \, b^{6}} + \frac{10 \,{\left (a + \frac{b}{x}\right )}^{\frac{13}{2}} a}{13 \, b^{6}} - \frac{20 \,{\left (a + \frac{b}{x}\right )}^{\frac{11}{2}} a^{2}}{11 \, b^{6}} + \frac{20 \,{\left (a + \frac{b}{x}\right )}^{\frac{9}{2}} a^{3}}{9 \, b^{6}} - \frac{10 \,{\left (a + \frac{b}{x}\right )}^{\frac{7}{2}} a^{4}}{7 \, b^{6}} + \frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} a^{5}}{5 \, b^{6}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b/x)^(3/2)/x^7,x, algorithm="maxima")

[Out]

-2/15*(a + b/x)^(15/2)/b^6 + 10/13*(a + b/x)^(13/2)*a/b^6 - 20/11*(a + b/x)^(11/2)*a^2/b^6 + 20/9*(a + b/x)^(9
/2)*a^3/b^6 - 10/7*(a + b/x)^(7/2)*a^4/b^6 + 2/5*(a + b/x)^(5/2)*a^5/b^6

________________________________________________________________________________________

Fricas [A]  time = 1.64993, size = 217, normalized size = 1.78 \begin{align*} \frac{2 \,{\left (256 \, a^{7} x^{7} - 128 \, a^{6} b x^{6} + 96 \, a^{5} b^{2} x^{5} - 80 \, a^{4} b^{3} x^{4} + 70 \, a^{3} b^{4} x^{3} - 63 \, a^{2} b^{5} x^{2} - 3696 \, a b^{6} x - 3003 \, b^{7}\right )} \sqrt{\frac{a x + b}{x}}}{45045 \, b^{6} x^{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b/x)^(3/2)/x^7,x, algorithm="fricas")

[Out]

2/45045*(256*a^7*x^7 - 128*a^6*b*x^6 + 96*a^5*b^2*x^5 - 80*a^4*b^3*x^4 + 70*a^3*b^4*x^3 - 63*a^2*b^5*x^2 - 369
6*a*b^6*x - 3003*b^7)*sqrt((a*x + b)/x)/(b^6*x^7)

________________________________________________________________________________________

Sympy [B]  time = 8.98312, size = 10344, normalized size = 84.79 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b/x)**(3/2)/x**7,x)

[Out]

512*a**(59/2)*b**(91/2)*x**22*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43
/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37
/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x*
*(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**6
1*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**6
4*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 7424*a**(57/2)*b**(93/2)*x
**21*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b
**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)
*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(2
9/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a*
*(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(
17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 50112*a**(55/2)*b**(95/2)*x**20*sqrt(a*x/b + 1)/(45
045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 2049547
5*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 22545
0225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 2
25450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2)
+ 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) +
45045*a**(15/2)*b**66*x**(15/2)) + 208800*a**(53/2)*b**(97/2)*x**19*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**
(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(3
9/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x*
*(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**6
0*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b*
*63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x
**(15/2)) + 600300*a**(51/2)*b**(99/2)*x**18*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/
2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/
2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**
(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135
*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725
*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 1260630*a**
(49/2)*b**(101/2)*x**17*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) +
4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) +
135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2
) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(
25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(
19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 1988490*a**(47/2)*b**(103/2)*x**
16*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**
53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b
**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/
2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(
23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17
/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 2305200*a**(45/2)*b**(105/2)*x**15*sqrt(a*x/b + 1)/(4
5045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 204954
75*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 2254
50225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) +
225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2)
+ 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) +
45045*a**(15/2)*b**66*x**(15/2)) + 1395360*a**(43/2)*b**(107/2)*x**14*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*
x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x*
*(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57
*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b
**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)
*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**6
6*x**(15/2)) - 2395640*a**(41/2)*b**(109/2)*x**13*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a*
*(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a*
*(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 28986457
5*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 1352
70135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 47
29725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 120383
12*a**(39/2)*b**(111/2)*x**12*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43
/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37
/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x*
*(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**6
1*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**6
4*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 30264624*a**(37/2)*b**(113
/2)*x**11*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41
/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(
35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*
a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 614864
25*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675
*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 55283592*a**(35/2)*b**(115/2)*x**10*sqrt(a*x/b
+ 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2)
+ 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2
) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(
29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x
**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**
(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 78018780*a**(33/2)*b**(117/2)*x**9*sqrt(a*x/b + 1)/(45045*a**(45/2
)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*
b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/
2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**
(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a
**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15
/2)*b**66*x**(15/2)) - 86576580*a**(31/2)*b**(119/2)*x**8*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 6
75675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 614
86425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) +
289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2
) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21
/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2))
- 75888816*a**(29/2)*b**(121/2)*x**7*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52
*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55
*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b
**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/
2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/
2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 52380672*a**(27/2)*
b**(123/2)*x**6*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*
a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 13527013
5*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 2898
64575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) +
61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) +
675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 28170936*a**(25/2)*b**(125/2)*x**5*sqrt(
a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(4
1/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**
(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59
*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b*
*62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**6
5*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 11572840*a**(23/2)*b**(127/2)*x**4*sqrt(a*x/b + 1)/(45045*a**
(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(3
9/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a*
*(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 22545022
5*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495
475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a
**(15/2)*b**66*x**(15/2)) - 3510640*a**(21/2)*b**(129/2)*x**3*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2)
+ 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) +
61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2
) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(
27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x*
*(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/
2)) - 741636*a**(19/2)*b**(131/2)*x**2*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**
52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**
55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)
*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(2
5/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(1
9/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 97482*a**(17/2)*b
**(133/2)*x*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(
41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a*
*(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 28986457
5*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 6148
6425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 6756
75*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 6006*a**(15/2)*b**(135/2)*sqrt(a*x/b + 1)/(4
5045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 204954
75*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 2254
50225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) +
225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2)
+ 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) +
45045*a**(15/2)*b**66*x**(15/2)) - 512*a**30*b**45*x**(45/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43
/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37
/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a*
*(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 13527013
5*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 472972
5*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 7680*a**29
*b**46*x**(43/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53
*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**
56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)
*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23
/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2
)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 53760*a**28*b**47*x**(41/2)/(45045*a**(45/2)*b**51*x**(
45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39
/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**
(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60
*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**
63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x*
*(15/2)) - 232960*a**27*b**48*x**(39/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) +
4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) +
135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2
) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(
25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(
19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 698880*a**26*b**49*x**(37/2)/(45
045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 2049547
5*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 22545
0225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 2
25450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2)
+ 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) +
45045*a**(15/2)*b**66*x**(15/2)) - 1537536*a**25*b**50*x**(35/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**
(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**
(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575
*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 13527
0135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 472
9725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 2562560
*a**24*b**51*x**(33/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)
*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/
2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**
(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*
a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a*
*(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 3294720*a**23*b**52*x**(31/2)/(45045*a**(45/2)*b*
*51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**5
4*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b
**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/
2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(2
1/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*
b**66*x**(15/2)) - 3294720*a**22*b**53*x**(29/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**
(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**
(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58
*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b
**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b
**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 2562560*a**21*b**54*x**
(27/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2)
+ 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/
2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**
(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*
x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x*
*(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 1537536*a**20*b**55*x**(25/2)/(45045*a**(45/2)*b**51*x**(45/2) +
675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61
486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) +
289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/
2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(2
1/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2))
- 698880*a**19*b**56*x**(23/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*
a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 13527013
5*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 2898
64575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) +
61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) +
675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 232960*a**18*b**57*x**(21/2)/(45045*a**(
45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39
/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**
(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225
*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 204954
75*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a*
*(15/2)*b**66*x**(15/2)) - 53760*a**17*b**58*x**(19/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**
52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**
55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)
*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(2
5/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(1
9/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 7680*a**16*b**59*
x**(17/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41
/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 61486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(
35/2) + 225450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*
x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**
62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65
*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) - 512*a**15*b**60*x**(15/2)/(45045*a**(45/2)*b**51*x**(45/2) + 6
75675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20495475*a**(39/2)*b**54*x**(39/2) + 614
86425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 225450225*a**(33/2)*b**57*x**(33/2) +
289864575*a**(31/2)*b**58*x**(31/2) + 289864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2
) + 135270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 20495475*a**(21/2)*b**63*x**(21
/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2))

________________________________________________________________________________________

Giac [B]  time = 1.2357, size = 406, normalized size = 3.33 \begin{align*} \frac{2 \,{\left (240240 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{9} a^{\frac{9}{2}} \mathrm{sgn}\left (x\right ) + 1338480 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{8} a^{4} b \mathrm{sgn}\left (x\right ) + 3333330 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{7} a^{\frac{7}{2}} b^{2} \mathrm{sgn}\left (x\right ) + 4844840 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{6} a^{3} b^{3} \mathrm{sgn}\left (x\right ) + 4513509 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{5} a^{\frac{5}{2}} b^{4} \mathrm{sgn}\left (x\right ) + 2788695 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{4} a^{2} b^{5} \mathrm{sgn}\left (x\right ) + 1141140 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{3} a^{\frac{3}{2}} b^{6} \mathrm{sgn}\left (x\right ) + 297990 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{2} a b^{7} \mathrm{sgn}\left (x\right ) + 45045 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )} \sqrt{a} b^{8} \mathrm{sgn}\left (x\right ) + 3003 \, b^{9} \mathrm{sgn}\left (x\right )\right )}}{45045 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{15}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b/x)^(3/2)/x^7,x, algorithm="giac")

[Out]

2/45045*(240240*(sqrt(a)*x - sqrt(a*x^2 + b*x))^9*a^(9/2)*sgn(x) + 1338480*(sqrt(a)*x - sqrt(a*x^2 + b*x))^8*a
^4*b*sgn(x) + 3333330*(sqrt(a)*x - sqrt(a*x^2 + b*x))^7*a^(7/2)*b^2*sgn(x) + 4844840*(sqrt(a)*x - sqrt(a*x^2 +
b*x))^6*a^3*b^3*sgn(x) + 4513509*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^4*sgn(x) + 2788695*(sqrt(a)*x -
sqrt(a*x^2 + b*x))^4*a^2*b^5*sgn(x) + 1141140*(sqrt(a)*x - sqrt(a*x^2 + b*x))^3*a^(3/2)*b^6*sgn(x) + 297990*(s
qrt(a)*x - sqrt(a*x^2 + b*x))^2*a*b^7*sgn(x) + 45045*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^8*sgn(x) + 3003
*b^9*sgn(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^15