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

Optimal. Leaf size=17 \[ \frac{1}{4} b x^3 \sqrt{b x^2} \]

[Out]

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

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Rubi [A]  time = 0.00743225, antiderivative size = 17, 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 \[ \frac{1}{4} b x^3 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(3/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.21657, size = 14, normalized size = 0.82 \[ \frac{b x^{3} \sqrt{b x^{2}}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00134681, size = 14, normalized size = 0.82 \[ \frac{1}{4} x \left (b x^2\right )^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(3/2),x]

[Out]

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

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Maple [A]  time = 0.002, size = 11, normalized size = 0.7 \[{\frac{x}{4} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(3/2),x)

[Out]

1/4*x*(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, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.240521, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, \sqrt{b x^{2}} b x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.16193, size = 14, normalized size = 0.82 \[ \frac{b^{\frac{3}{2}} x \left (x^{2}\right )^{\frac{3}{2}}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(3/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.210435, size = 14, normalized size = 0.82 \[ \frac{1}{4} \, b^{\frac{3}{2}} x^{4}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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