∖int 1_______________ ∖left(a+ b x∖right)3∕2x6 ∖,dx

3.1738 \(\int \frac{1}{\left (a+\frac{b}{x}\right )^{3/2} x^6} \, dx\)

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]

(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)

_______________________________________________________________________________________

Rubi [A] time = 0.115017, antiderivative size = 95, 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 \[ \frac{2 a^4}{b^5 \sqrt{a+\frac{b}{x}}}+\frac{8 a^3 \sqrt{a+\frac{b}{x}}}{b^5}-\frac{4 a^2 \left (a+\frac{b}{x}\right )^{3/2}}{b^5}+\frac{8 a \left (a+\frac{b}{x}\right )^{5/2}}{5 b^5}-\frac{2 \left (a+\frac{b}{x}\right )^{7/2}}{7 b^5} \]

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)

_______________________________________________________________________________________

Rubi in Sympy [A] time = 16.0452, size = 82, normalized size = 0.86 \[ \frac{2 a^{4}}{b^{5} \sqrt{a + \frac{b}{x}}} + \frac{8 a^{3} \sqrt{a + \frac{b}{x}}}{b^{5}} - \frac{4 a^{2} \left (a + \frac{b}{x}\right )^{\frac{3}{2}}}{b^{5}} + \frac{8 a \left (a + \frac{b}{x}\right )^{\frac{5}{2}}}{5 b^{5}} - \frac{2 \left (a + \frac{b}{x}\right )^{\frac{7}{2}}}{7 b^{5}} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In] rubi_integrate(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)

_______________________________________________________________________________________

Mathematica [A] time = 0.0484931, size = 69, normalized size = 0.73 \[ \frac{2 \sqrt{a+\frac{b}{x}} \left (128 a^4 x^4+64 a^3 b x^3-16 a^2 b^2 x^2+8 a b^3 x-5 b^4\right )}{35 b^5 x^3 (a x+b)} \]

Antiderivative was successfully veriﬁed.

[In] Integrate[1/((a + b/x)^(3/2)*x^6),x]

[Out]

(2*Sqrt[a + b/x]*(-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*x^3*(b + a*x))

_______________________________________________________________________________________

Maple [A] time = 0.008, size = 66, normalized size = 0.7 \[{\frac{ \left ( 2\,ax+2\,b \right ) \left ( 128\,{a}^{4}{x}^{4}+64\,{a}^{3}{x}^{3}b-16\,{a}^{2}{x}^{2}{b}^{2}+8\,ax{b}^{3}-5\,{b}^{4} \right ) }{35\,{x}^{5}{b}^{5}} \left ({\frac{ax+b}{x}} \right ) ^{-{\frac{3}{2}}}} \]

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 = 1.44271, size = 109, normalized size = 1.15 \[ -\frac{2 \,{\left (a + \frac{b}{x}\right )}^{\frac{7}{2}}}{7 \, b^{5}} + \frac{8 \,{\left (a + \frac{b}{x}\right )}^{\frac{5}{2}} a}{5 \, b^{5}} - \frac{4 \,{\left (a + \frac{b}{x}\right )}^{\frac{3}{2}} a^{2}}{b^{5}} + \frac{8 \, \sqrt{a + \frac{b}{x}} a^{3}}{b^{5}} + \frac{2 \, a^{4}}{\sqrt{a + \frac{b}{x}} b^{5}} \]

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)

_______________________________________________________________________________________

Fricas [A] time = 0.233181, size = 81, normalized size = 0.85 \[ \frac{2 \,{\left (128 \, a^{4} x^{4} + 64 \, a^{3} b x^{3} - 16 \, a^{2} b^{2} x^{2} + 8 \, a b^{3} x - 5 \, b^{4}\right )}}{35 \, b^{5} x^{4} \sqrt{\frac{a x + b}{x}}} \]

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)/(b^5*x^4*

sqrt((a*x + b)/x))

_______________________________________________________________________________________

Sympy [A] time = 19.5361, 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) + 35

0*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**(1

1/2)*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**(1

7/2) + 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)) + 25840*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) + 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)) + 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) + 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)) + 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**3

4*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) + 420

0*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**2

9*x**(27/2) + 350*a**(25/2)*b**30*x**(25/2) + 1575*a**(23/2)*b**31*x**(23/2) + 4

200*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) + 350*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**3

4*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)) - 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**(1

7/2) + 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) + 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**(1

1/2) + 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) + 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)) - 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**3

1*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) + 420

0*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) + 7

350*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)) - 64

512*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) + 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**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) + 42

00*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**3

6*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) + 35*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) + 8820*a**(17/2)*b**34*x**(17/2) + 7350*a**(1

5/2)*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) + 157

5*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))

_______________________________________________________________________________________

GIAC/XCAS [A] time = 0.266196, size = 171, normalized size = 1.8 \[ \frac{2}{35} \, b{\left (\frac{35 \, a^{4}}{b^{6} \sqrt{\frac{a x + b}{x}}} + \frac{140 \, a^{3} b^{36} \sqrt{\frac{a x + b}{x}} - \frac{70 \,{\left (a x + b\right )} a^{2} b^{36} \sqrt{\frac{a x + b}{x}}}{x} + \frac{28 \,{\left (a x + b\right )}^{2} a b^{36} \sqrt{\frac{a x + b}{x}}}{x^{2}} - \frac{5 \,{\left (a x + b\right )}^{3} b^{36} \sqrt{\frac{a x + b}{x}}}{x^{3}}}{b^{42}}\right )} \]

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*b*(35*a^4/(b^6*sqrt((a*x + b)/x)) + (140*a^3*b^36*sqrt((a*x + b)/x) - 70*(a

*x + b)*a^2*b^36*sqrt((a*x + b)/x)/x + 28*(a*x + b)^2*a*b^36*sqrt((a*x + b)/x)/x

^2 - 5*(a*x + b)^3*b^36*sqrt((a*x + b)/x)/x^3)/b^42)

[next] [prev] [prev-tail] [front] [up]