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

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

[Out]

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

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Rubi [A]  time = 0.00884721, antiderivative size = 19, 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 \[ -\frac{1}{2 b^2 x \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x^2/(b*x^2)^(5/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 2.37507, size = 17, normalized size = 0.89 \[ - \frac{\sqrt{b x^{2}}}{2 b^{3} x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00283697, size = 16, normalized size = 0.84 \[ -\frac{x^3}{2 \left (b x^2\right )^{5/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2/(b*x^2)^(5/2),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2/(b*x^2)^(5/2),x)

[Out]

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

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Maxima [A]  time = 1.43291, size = 11, normalized size = 0.58 \[ -\frac{1}{2 \, b^{\frac{5}{2}} x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.216139, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{2 \, b^{3} x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 3.0454, size = 17, normalized size = 0.89 \[ - \frac{x^{3}}{2 b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.527038, size = 4, normalized size = 0.21 \[ \mathit{sage}_{0} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sage0*x