3.55 \(\int \frac{x}{\left (b x^2\right )^{5/2}} \, dx\)

Optimal. Leaf size=19 \[ -\frac{1}{3 b^2 x^2 \sqrt{b x^2}} \]

[Out]

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

_______________________________________________________________________________________

Rubi [A]  time = 0.00903984, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{1}{3 b^2 x^2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x/(b*x^2)^(5/2),x]

[Out]

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

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.17288, size = 14, normalized size = 0.74 \[ - \frac{1}{3 b \left (b x^{2}\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/(b*x**2)**(5/2),x)

[Out]

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

_______________________________________________________________________________________

Mathematica [A]  time = 0.00137081, size = 16, normalized size = 0.84 \[ -\frac{x^2}{3 \left (b x^2\right )^{5/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x/(b*x^2)^(5/2),x]

[Out]

-x^2/(3*(b*x^2)^(5/2))

_______________________________________________________________________________________

Maple [A]  time = 0.004, size = 13, normalized size = 0.7 \[ -{\frac{{x}^{2}}{3} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(b*x^2)^(5/2),x)

[Out]

-1/3*x^2/(b*x^2)^(5/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.41008, size = 16, normalized size = 0.84 \[ -\frac{1}{3 \, \left (b x^{2}\right )^{\frac{3}{2}} b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(b*x^2)^(5/2),x, algorithm="maxima")

[Out]

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

_______________________________________________________________________________________

Fricas [A]  time = 0.238555, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{3 \, b^{3} x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(b*x^2)^(5/2),x, algorithm="fricas")

[Out]

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

_______________________________________________________________________________________

Sympy [A]  time = 3.09319, size = 17, normalized size = 0.89 \[ - \frac{x^{2}}{3 b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(b*x**2)**(5/2),x)

[Out]

-x**2/(3*b**(5/2)*(x**2)**(5/2))

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.221392, size = 20, normalized size = 1.05 \[ -\frac{1}{3 \, \sqrt{b x^{2}} b^{2} x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(b*x^2)^(5/2),x, algorithm="giac")

[Out]

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