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

Optimal. Leaf size=11 \[ b \sqrt{b x^2} \]

[Out]

b*Sqrt[b*x^2]

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Rubi [A]  time = 0.00624031, antiderivative size = 11, 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 \[ b \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(3/2)/x^3,x]

[Out]

b*Sqrt[b*x^2]

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Rubi in Sympy [A]  time = 2.4231, size = 8, normalized size = 0.73 \[ b \sqrt{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*sqrt(b*x**2)

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Mathematica [A]  time = 0.00184982, size = 13, normalized size = 1.18 \[ \frac{\left (b x^2\right )^{3/2}}{x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(3/2)/x^3,x]

[Out]

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

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Maple [A]  time = 0.002, size = 12, normalized size = 1.1 \[{\frac{1}{{x}^{2}} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(3/2)/x^3,x)

[Out]

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

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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^3,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.243445, size = 12, normalized size = 1.09 \[ \sqrt{b x^{2}} b \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(b*x^2)*b

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Sympy [A]  time = 2.07942, size = 14, normalized size = 1.27 \[ \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.212526, size = 9, normalized size = 0.82 \[ b^{\frac{3}{2}} x{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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