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

Optimal. Leaf size=16 \[ \frac{x^2}{b^2 \sqrt{b x^2}} \]

[Out]

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

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Rubi [A]  time = 0.0075292, antiderivative size = 16, 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 \[ \frac{x^2}{b^2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x^5/(b*x^2)^(5/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 2.6918, size = 10, normalized size = 0.62 \[ \frac{\sqrt{b x^{2}}}{b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00207733, size = 13, normalized size = 0.81 \[ \frac{x^6}{\left (b x^2\right )^{5/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/(b*x^2)^(5/2),x]

[Out]

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

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Maple [A]  time = 0.003, size = 12, normalized size = 0.8 \[{{x}^{6} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(b*x^2)^(5/2),x)

[Out]

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

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Maxima [A]  time = 1.44348, size = 19, normalized size = 1.19 \[ \frac{x^{4}}{\left (b x^{2}\right )^{\frac{3}{2}} b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.212822, size = 15, normalized size = 0.94 \[ \frac{\sqrt{b x^{2}}}{b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 3.08571, size = 14, normalized size = 0.88 \[ \frac{x^{6}}{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.211248, size = 15, normalized size = 0.94 \[ \frac{\sqrt{b x^{2}}}{b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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