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

Optimal. Leaf size=17 \[ \frac{1}{3} b x^2 \sqrt{b x^2} \]

[Out]

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

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Rubi [A]  time = 0.00756472, antiderivative size = 17, 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 \[ \frac{1}{3} b x^2 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(3/2)/x,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.29272, size = 8, normalized size = 0.47 \[ \frac{\left (b x^{2}\right )^{\frac{3}{2}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.0014124, size = 17, normalized size = 1. \[ \frac{1}{3} b x^2 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(3/2)/x,x]

[Out]

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

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Maple [A]  time = 0.003, size = 10, normalized size = 0.6 \[{\frac{1}{3} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(3/2)/x,x)

[Out]

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

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.246629, size = 18, normalized size = 1.06 \[ \frac{1}{3} \, \sqrt{b x^{2}} b x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.15799, size = 12, normalized size = 0.71 \[ \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(3/2)/x,x)

[Out]

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

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GIAC/XCAS [A]  time = 0.211269, size = 14, normalized size = 0.82 \[ \frac{1}{3} \, b^{\frac{3}{2}} x^{3}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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