3.77 \(\int \sqrt{b x^3} \, dx\)

Optimal. Leaf size=14 \[ \frac{2}{5} x \sqrt{b x^3} \]

[Out]

(2*x*Sqrt[b*x^3])/5

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Rubi [A]  time = 0.00659037, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{2}{5} x \sqrt{b x^3} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b*x^3],x]

[Out]

(2*x*Sqrt[b*x^3])/5

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Rubi in Sympy [A]  time = 1.16916, size = 12, normalized size = 0.86 \[ \frac{2 x \sqrt{b x^{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*x*sqrt(b*x**3)/5

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Mathematica [A]  time = 0.00226548, size = 14, normalized size = 1. \[ \frac{2}{5} x \sqrt{b x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b*x^3],x]

[Out]

(2*x*Sqrt[b*x^3])/5

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Maple [A]  time = 0.003, size = 11, normalized size = 0.8 \[{\frac{2\,x}{5}\sqrt{b{x}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3)^(1/2),x)

[Out]

2/5*x*(b*x^3)^(1/2)

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Maxima [A]  time = 1.43633, size = 14, normalized size = 1. \[ \frac{2}{5} \, \sqrt{b x^{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*sqrt(b*x^3)*x

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Fricas [A]  time = 0.256495, size = 14, normalized size = 1. \[ \frac{2}{5} \, \sqrt{b x^{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*sqrt(b*x^3)*x

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Sympy [A]  time = 0.378517, size = 15, normalized size = 1.07 \[ \frac{2 \sqrt{b} x \sqrt{x^{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3)**(1/2),x)

[Out]

2*sqrt(b)*x*sqrt(x**3)/5

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GIAC/XCAS [A]  time = 0.227197, size = 16, normalized size = 1.14 \[ \frac{2}{5} \, \sqrt{b x} x^{2}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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