3.54 \(\int \frac{x^3}{\left (b x^2\right )^{5/2}} \, dx\)

Optimal. Leaf size=14 \[ -\frac{1}{b^2 \sqrt{b x^2}} \]

[Out]

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

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Rubi [A]  time = 0.00763735, antiderivative size = 14, 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 \[ -\frac{1}{b^2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x^3/(b*x^2)^(5/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 2.70136, size = 14, normalized size = 1. \[ - \frac{1}{b^{2} \sqrt{b x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3/(b*x**2)**(5/2),x)

[Out]

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

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Mathematica [A]  time = 0.00240115, size = 14, normalized size = 1. \[ -\frac{x^4}{\left (b x^2\right )^{5/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3/(b*x^2)^(5/2),x]

[Out]

-(x^4/(b*x^2)^(5/2))

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Maple [A]  time = 0.004, size = 13, normalized size = 0.9 \[ -{{x}^{4} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3/(b*x^2)^(5/2),x)

[Out]

-x^4/(b*x^2)^(5/2)

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Maxima [A]  time = 1.43591, size = 20, normalized size = 1.43 \[ -\frac{x^{2}}{\left (b x^{2}\right )^{\frac{3}{2}} b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(b*x^2)^(5/2),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.243757, size = 20, normalized size = 1.43 \[ -\frac{\sqrt{b x^{2}}}{b^{3} x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(b*x^2)^(5/2),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 3.11036, size = 15, normalized size = 1.07 \[ - \frac{x^{4}}{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3/(b*x**2)**(5/2),x)

[Out]

-x**4/(b**(5/2)*(x**2)**(5/2))

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GIAC/XCAS [A]  time = 0.225123, size = 16, normalized size = 1.14 \[ -\frac{1}{\sqrt{b x^{2}} b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(b*x^2)^(5/2),x, algorithm="giac")

[Out]

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