3.61 \(\int \frac{1}{x^2 \left (b x^2\right )^{5/2}} \, dx\)

Optimal. Leaf size=19 \[ -\frac{1}{6 b^2 x^5 \sqrt{b x^2}} \]

[Out]

-1/(6*b^2*x^5*Sqrt[b*x^2])

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Rubi [A]  time = 0.00847571, 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 \[ -\frac{1}{6 b^2 x^5 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[1/(x^2*(b*x^2)^(5/2)),x]

[Out]

-1/(6*b^2*x^5*Sqrt[b*x^2])

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Rubi in Sympy [A]  time = 2.29816, size = 17, normalized size = 0.89 \[ - \frac{\sqrt{b x^{2}}}{6 b^{3} x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**2/(b*x**2)**(5/2),x)

[Out]

-sqrt(b*x**2)/(6*b**3*x**7)

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Mathematica [A]  time = 0.00357741, size = 15, normalized size = 0.79 \[ -\frac{b x}{6 \left (b x^2\right )^{7/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(x^2*(b*x^2)^(5/2)),x]

[Out]

-(b*x)/(6*(b*x^2)^(7/2))

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Maple [A]  time = 0.003, size = 13, normalized size = 0.7 \[ -{\frac{1}{6\,x} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^2/(b*x^2)^(5/2),x)

[Out]

-1/6/x/(b*x^2)^(5/2)

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Maxima [A]  time = 1.4426, size = 11, normalized size = 0.58 \[ -\frac{1}{6 \, b^{\frac{5}{2}} x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((b*x^2)^(5/2)*x^2),x, algorithm="maxima")

[Out]

-1/6/(b^(5/2)*x^6)

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Fricas [A]  time = 0.216142, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}}}{6 \, b^{3} x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((b*x^2)^(5/2)*x^2),x, algorithm="fricas")

[Out]

-1/6*sqrt(b*x^2)/(b^3*x^7)

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Sympy [A]  time = 4.635, size = 17, normalized size = 0.89 \[ - \frac{1}{6 b^{\frac{5}{2}} x \left (x^{2}\right )^{\frac{5}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**2/(b*x**2)**(5/2),x)

[Out]

-1/(6*b**(5/2)*x*(x**2)**(5/2))

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GIAC/XCAS [A]  time = 0.535131, size = 4, normalized size = 0.21 \[ \mathit{sage}_{0} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((b*x^2)^(5/2)*x^2),x, algorithm="giac")

[Out]

sage0*x