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

Optimal. Leaf size=14 \[ \frac{1}{4} x^3 \sqrt{x^2} \]

[Out]

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

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Rubi [A]  time = 0.00505157, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{1}{4} x^3 \sqrt{x^2} \]

Antiderivative was successfully verified.

[In]  Int[(x^2)^(3/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.80833, size = 10, normalized size = 0.71 \[ \frac{x^{3} \sqrt{x^{2}}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00625599, size = 12, normalized size = 0.86 \[ \frac{1}{4} x \left (x^2\right )^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(x^2)^(3/2),x]

[Out]

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

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Maple [A]  time = 0.003, size = 11, normalized size = 0.8 \[{\frac{{x}^{3}}{4}\sqrt{{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(x^2)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.43339, size = 11, normalized size = 0.79 \[ \frac{1}{4} \,{\left (x^{2}\right )}^{\frac{3}{2}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.247358, size = 7, normalized size = 0.5 \[ \frac{1}{4} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4

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Sympy [A]  time = 0.091945, size = 3, normalized size = 0.21 \[ \frac{x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2*(x**2)**(1/2),x)

[Out]

x**4/4

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GIAC/XCAS [A]  time = 0.208861, size = 9, normalized size = 0.64 \[ \frac{1}{4} \, x^{4}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4*sign(x)