∖int∖left(a+ b x∖right)3∕2 ______________________________

3.1709 \(\int \frac{\left (a+\frac{b}{x}\right )^{3/2}}{x^7} \, dx\)

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

[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)

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Rubi [A] time = 0.137286, 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 \[ \frac{2 a^5 \left (a+\frac{b}{x}\right )^{5/2}}{5 b^6}-\frac{10 a^4 \left (a+\frac{b}{x}\right )^{7/2}}{7 b^6}+\frac{20 a^3 \left (a+\frac{b}{x}\right )^{9/2}}{9 b^6}-\frac{20 a^2 \left (a+\frac{b}{x}\right )^{11/2}}{11 b^6}-\frac{2 \left (a+\frac{b}{x}\right )^{15/2}}{15 b^6}+\frac{10 a \left (a+\frac{b}{x}\right )^{13/2}}{13 b^6} \]

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)

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Rubi in Sympy [A] time = 19.622, size = 105, normalized size = 0.86 \[ \frac{2 a^{5} \left (a + \frac{b}{x}\right )^{\frac{5}{2}}}{5 b^{6}} - \frac{10 a^{4} \left (a + \frac{b}{x}\right )^{\frac{7}{2}}}{7 b^{6}} + \frac{20 a^{3} \left (a + \frac{b}{x}\right )^{\frac{9}{2}}}{9 b^{6}} - \frac{20 a^{2} \left (a + \frac{b}{x}\right )^{\frac{11}{2}}}{11 b^{6}} + \frac{10 a \left (a + \frac{b}{x}\right )^{\frac{13}{2}}}{13 b^{6}} - \frac{2 \left (a + \frac{b}{x}\right )^{\frac{15}{2}}}{15 b^{6}} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In] rubi_integrate((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)

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Mathematica [A] time = 0.0561426, size = 80, normalized size = 0.66 \[ \frac{2 \sqrt{a+\frac{b}{x}} (a x+b)^2 \left (256 a^5 x^5-640 a^4 b x^4+1120 a^3 b^2 x^3-1680 a^2 b^3 x^2+2310 a b^4 x-3003 b^5\right )}{45045 b^6 x^7} \]

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)

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Maple [A] time = 0.009, size = 77, normalized size = 0.6 \[{\frac{ \left ( 2\,ax+2\,b \right ) \left ( 256\,{a}^{5}{x}^{5}-640\,{a}^{4}b{x}^{4}+1120\,{a}^{3}{b}^{2}{x}^{3}-1680\,{a}^{2}{b}^{3}{x}^{2}+2310\,a{b}^{4}x-3003\,{b}^{5} \right ) }{45045\,{x}^{6}{b}^{6}} \left ({\frac{ax+b}{x}} \right ) ^{{\frac{3}{2}}}} \]

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+231

0*a*b^4*x-3003*b^5)*((a*x+b)/x)^(3/2)/x^6/b^6

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Maxima [A] time = 1.43036, size = 132, normalized size = 1.08 \[ -\frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{15}{2}}}{15 \, b^{6}} + \frac{10 \,{\left (a + \frac{b}{x}\right )}^{\frac{13}{2}} a}{13 \, b^{6}} - \frac{20 \,{\left (a + \frac{b}{x}\right )}^{\frac{11}{2}} a^{2}}{11 \, b^{6}} + \frac{20 \,{\left (a + \frac{b}{x}\right )}^{\frac{9}{2}} a^{3}}{9 \, b^{6}} - \frac{10 \,{\left (a + \frac{b}{x}\right )}^{\frac{7}{2}} a^{4}}{7 \, b^{6}} + \frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} a^{5}}{5 \, b^{6}} \]

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

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Fricas [A] time = 0.223227, size = 126, normalized size = 1.03 \[ \frac{2 \,{\left (256 \, a^{7} x^{7} - 128 \, a^{6} b x^{6} + 96 \, a^{5} b^{2} x^{5} - 80 \, a^{4} b^{3} x^{4} + 70 \, a^{3} b^{4} x^{3} - 63 \, a^{2} b^{5} x^{2} - 3696 \, a b^{6} x - 3003 \, b^{7}\right )} \sqrt{\frac{a x + b}{x}}}{45045 \, b^{6} x^{7}} \]

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 - 3696*a*b^6*x - 3003*b^7)*sqrt((a*x + b)/x)/(b^6*x^7)

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Sympy [A] time = 34.4196, size = 10344, normalized size = 84.79 \[ \text{result too large to display} \]

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**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)) + 7424*a

**(57/2)*b**(93/2)*x**21*sqrt(a*x/b + 1)/(45045*a**(45/2)*b**51*x**(45/2) + 6756

75*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) + 6

75675*a**(17/2)*b**65*x**(17/2) + 45045*a**(15/2)*b**66*x**(15/2)) + 50112*a**(5

5/2)*b**(95/2)*x**20*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**(2

7/2) + 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) + 67567

5*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**(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) + 2

0495475*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**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) + 2049

5475*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) + 20495

475*a**(21/2)*b**63*x**(21/2) + 4729725*a**(19/2)*b**64*x**(19/2) + 675675*a**(1

7/2)*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**(3

5/2) + 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) + 1

35270135*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)) + 2305200*a**(45/2)*b**(1

05/2)*x**15*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) + 13

5270135*a**(25/2)*b**61*x**(25/2) + 61486425*a**(23/2)*b**62*x**(23/2) + 2049547

5*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**(10

7/2)*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) + 135

270135*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)) - 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) + 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) + 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) + 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)) - 12038312*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) + 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) + 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)) - 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) + 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) + 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) + 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) + 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) + 2

89864575*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) + 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) + 675675*a**(43/2)*b**5

2*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) + 28

9864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270

135*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) + 289

864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 1352701

35*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) + 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) + 2898

64575*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) + 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**(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) + 2

25450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 28986

4575*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**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**(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) + 22

5450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 289864

575*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)) - 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) + 2254

50225*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) + 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*s

qrt(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) + 61

486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 2254502

25*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**(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)) - 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) + 47

29725*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)) - 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) + 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**5

7*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**(4

5/2) + 675675*a**(43/2)*b**52*x**(43/2) + 4729725*a**(41/2)*b**53*x**(41/2) + 20

495475*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) + 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)) -

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) + 135

270135*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**(3

7/2)*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) + 4504

5*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) + 2898

64575*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) + 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**(1

5/2)) - 698880*a**26*b**49*x**(37/2)/(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**(2

7/2) + 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) + 67567

5*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) + 61

486425*a**(37/2)*b**55*x**(37/2) + 135270135*a**(35/2)*b**56*x**(35/2) + 2254502

25*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**(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) + 47297

25*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) + 204

95475*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)) - 3

294720*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**(3

5/2) + 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) + 1

35270135*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)) - 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) + 472

9725*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**(3

3/2)*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) + 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) + 225

450225*a**(27/2)*b**60*x**(27/2) + 135270135*a**(25/2)*b**61*x**(25/2) + 6148642

5*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)) - 698880*a**19*b**56*x**(23/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675

675*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**(2

3/2) + 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) + 225

450225*a**(33/2)*b**57*x**(33/2) + 289864575*a**(31/2)*b**58*x**(31/2) + 2898645

75*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**17*b**58*x**(19/2)/(4504

5*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**(2

9/2) + 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) + 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)) - 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) + 2049

5475*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)) - 51

2*a**15*b**60*x**(15/2)/(45045*a**(45/2)*b**51*x**(45/2) + 675675*a**(43/2)*b**5

2*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) + 28

9864575*a**(29/2)*b**59*x**(29/2) + 225450225*a**(27/2)*b**60*x**(27/2) + 135270

135*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/XCAS [A] time = 0.281368, size = 406, normalized size = 3.33 \[ \frac{2 \,{\left (240240 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{9} a^{\frac{9}{2}}{\rm sign}\left (x\right ) + 1338480 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{8} a^{4} b{\rm sign}\left (x\right ) + 3333330 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{7} a^{\frac{7}{2}} b^{2}{\rm sign}\left (x\right ) + 4844840 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{6} a^{3} b^{3}{\rm sign}\left (x\right ) + 4513509 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{5} a^{\frac{5}{2}} b^{4}{\rm sign}\left (x\right ) + 2788695 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{4} a^{2} b^{5}{\rm sign}\left (x\right ) + 1141140 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{3} a^{\frac{3}{2}} b^{6}{\rm sign}\left (x\right ) + 297990 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{2} a b^{7}{\rm sign}\left (x\right ) + 45045 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )} \sqrt{a} b^{8}{\rm sign}\left (x\right ) + 3003 \, b^{9}{\rm sign}\left (x\right )\right )}}{45045 \,{\left (\sqrt{a} x - \sqrt{a x^{2} + b x}\right )}^{15}} \]

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)*sign(x) + 1338480*(sqr

t(a)*x - sqrt(a*x^2 + b*x))^8*a^4*b*sign(x) + 3333330*(sqrt(a)*x - sqrt(a*x^2 +

b*x))^7*a^(7/2)*b^2*sign(x) + 4844840*(sqrt(a)*x - sqrt(a*x^2 + b*x))^6*a^3*b^3*

sign(x) + 4513509*(sqrt(a)*x - sqrt(a*x^2 + b*x))^5*a^(5/2)*b^4*sign(x) + 278869

5*(sqrt(a)*x - sqrt(a*x^2 + b*x))^4*a^2*b^5*sign(x) + 1141140*(sqrt(a)*x - sqrt(

a*x^2 + b*x))^3*a^(3/2)*b^6*sign(x) + 297990*(sqrt(a)*x - sqrt(a*x^2 + b*x))^2*a

*b^7*sign(x) + 45045*(sqrt(a)*x - sqrt(a*x^2 + b*x))*sqrt(a)*b^8*sign(x) + 3003*

b^9*sign(x))/(sqrt(a)*x - sqrt(a*x^2 + b*x))^15

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