3.35 \(\int \frac{x^3}{\sqrt{b x^2}} \, dx\)

Optimal. Leaf size=16 \[ \frac{x^4}{3 \sqrt{b x^2}} \]

[Out]

x^4/(3*Sqrt[b*x^2])

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Rubi [A]  time = 0.00708122, 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 \[ \frac{x^4}{3 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x^3/Sqrt[b*x^2],x]

[Out]

x^4/(3*Sqrt[b*x^2])

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Rubi in Sympy [A]  time = 2.55473, size = 12, normalized size = 0.75 \[ \frac{\left (b x^{2}\right )^{\frac{3}{2}}}{3 b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3/(b*x**2)**(1/2),x)

[Out]

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

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Mathematica [A]  time = 0.0034347, size = 16, normalized size = 1. \[ \frac{x^4}{3 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3/Sqrt[b*x^2],x]

[Out]

x^4/(3*Sqrt[b*x^2])

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Maple [A]  time = 0.002, size = 13, normalized size = 0.8 \[{\frac{{x}^{4}}{3}{\frac{1}{\sqrt{b{x}^{2}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3/(b*x^2)^(1/2),x)

[Out]

1/3*x^4/(b*x^2)^(1/2)

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Maxima [A]  time = 1.43558, size = 20, normalized size = 1.25 \[ \frac{\sqrt{b x^{2}} x^{2}}{3 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*sqrt(b*x^2)*x^2/b

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Fricas [A]  time = 0.234714, size = 20, normalized size = 1.25 \[ \frac{\sqrt{b x^{2}} x^{2}}{3 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*sqrt(b*x^2)*x^2/b

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Sympy [A]  time = 1.91037, size = 15, normalized size = 0.94 \[ \frac{x^{4}}{3 \sqrt{b} \sqrt{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3/(b*x**2)**(1/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.212475, size = 20, normalized size = 1.25 \[ \frac{\sqrt{b x^{2}} x^{2}}{3 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*sqrt(b*x^2)*x^2/b