3.38 \(\int \frac{1}{x^3 \sqrt{b x^2}} \, dx\)

Optimal. Leaf size=16 \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]

[Out]

-1/(3*x^2*Sqrt[b*x^2])

_______________________________________________________________________________________

Rubi [A]  time = 0.00631486, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[1/(x^3*Sqrt[b*x^2]),x]

[Out]

-1/(3*x^2*Sqrt[b*x^2])

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.48876, size = 12, normalized size = 0.75 \[ - \frac{b}{3 \left (b x^{2}\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**3/(b*x**2)**(1/2),x)

[Out]

-b/(3*(b*x**2)**(3/2))

_______________________________________________________________________________________

Mathematica [A]  time = 0.00404139, size = 16, normalized size = 1. \[ -\frac{1}{3 x^2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(x^3*Sqrt[b*x^2]),x]

[Out]

-1/(3*x^2*Sqrt[b*x^2])

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 13, normalized size = 0.8 \[ -{\frac{1}{3\,{x}^{2}}{\frac{1}{\sqrt{b{x}^{2}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^3/(b*x^2)^(1/2),x)

[Out]

-1/3/x^2/(b*x^2)^(1/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.43133, size = 11, normalized size = 0.69 \[ -\frac{1}{3 \, \sqrt{b} x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(b*x^2)*x^3),x, algorithm="maxima")

[Out]

-1/3/(sqrt(b)*x^3)

_______________________________________________________________________________________

Fricas [A]  time = 0.240641, size = 20, normalized size = 1.25 \[ -\frac{\sqrt{b x^{2}}}{3 \, b x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(b*x^2)*x^3),x, algorithm="fricas")

[Out]

-1/3*sqrt(b*x^2)/(b*x^4)

_______________________________________________________________________________________

Sympy [A]  time = 2.31415, size = 19, normalized size = 1.19 \[ - \frac{1}{3 \sqrt{b} x^{2} \sqrt{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**3/(b*x**2)**(1/2),x)

[Out]

-1/(3*sqrt(b)*x**2*sqrt(x**2))

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.209753, size = 16, normalized size = 1. \[ -\frac{1}{3 \, \sqrt{b x^{2}} x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(b*x^2)*x^3),x, algorithm="giac")

[Out]

-1/3/(sqrt(b*x^2)*x^2)