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

Optimal. Leaf size=15 \[ -\frac{b \sqrt{b x^2}}{x^2} \]

[Out]

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

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Rubi [A]  time = 0.00769047, antiderivative size = 15, 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 \[ -\frac{b \sqrt{b x^2}}{x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(3/2)/x^5,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.54001, size = 12, normalized size = 0.8 \[ - \frac{b^{2}}{\sqrt{b x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00304656, size = 14, normalized size = 0.93 \[ -\frac{\left (b x^2\right )^{3/2}}{x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(3/2)/x^5,x]

[Out]

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

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Maple [A]  time = 0.003, size = 13, normalized size = 0.9 \[ -{\frac{1}{{x}^{4}} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(3/2)/x^5,x)

[Out]

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

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.224722, size = 18, normalized size = 1.2 \[ -\frac{\sqrt{b x^{2}} b}{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 2.95135, size = 15, normalized size = 1. \[ - \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-b**(3/2)*(x**2)**(3/2)/x**4

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GIAC/XCAS [A]  time = 0.215226, size = 14, normalized size = 0.93 \[ -\frac{b^{\frac{3}{2}}{\rm sign}\left (x\right )}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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