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

Optimal. Leaf size=13 \[ b^2 \sqrt{b x^2} \]

[Out]

b^2*Sqrt[b*x^2]

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Rubi [A]  time = 0.00704443, antiderivative size = 13, 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 \[ b^2 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2)/x^5,x]

[Out]

b^2*Sqrt[b*x^2]

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Rubi in Sympy [A]  time = 2.62398, size = 10, normalized size = 0.77 \[ b^{2} \sqrt{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b**2*sqrt(b*x**2)

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Mathematica [A]  time = 0.00256498, size = 13, normalized size = 1. \[ \frac{\left (b x^2\right )^{5/2}}{x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2)/x^5,x]

[Out]

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

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Maple [A]  time = 0.003, size = 12, normalized size = 0.9 \[{\frac{1}{{x}^{4}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2)/x^5,x)

[Out]

(b*x^2)^(5/2)/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)^(5/2)/x^5,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.216556, size = 15, normalized size = 1.15 \[ \sqrt{b x^{2}} b^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 4.72937, size = 14, normalized size = 1.08 \[ \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.218944, size = 9, normalized size = 0.69 \[ b^{\frac{5}{2}} x{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b^(5/2)*x*sign(x)