3.24 \(\int \left (b x^2\right )^{5/2} \, dx\)

Optimal. Leaf size=19 \[ \frac{1}{6} b^2 x^5 \sqrt{b x^2} \]

[Out]

(b^2*x^5*Sqrt[b*x^2])/6

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Rubi [A]  time = 0.00806645, antiderivative size = 19, 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 \[ \frac{1}{6} b^2 x^5 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2),x]

[Out]

(b^2*x^5*Sqrt[b*x^2])/6

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Rubi in Sympy [A]  time = 1.48504, size = 15, normalized size = 0.79 \[ \frac{b^{2} x^{5} \sqrt{b x^{2}}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(5/2),x)

[Out]

b**2*x**5*sqrt(b*x**2)/6

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Mathematica [A]  time = 0.00191318, size = 14, normalized size = 0.74 \[ \frac{1}{6} x \left (b x^2\right )^{5/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2),x]

[Out]

(x*(b*x^2)^(5/2))/6

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Maple [A]  time = 0.002, size = 11, normalized size = 0.6 \[{\frac{x}{6} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2),x)

[Out]

1/6*x*(b*x^2)^(5/2)

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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)^(5/2),x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.217386, size = 20, normalized size = 1.05 \[ \frac{1}{6} \, \sqrt{b x^{2}} b^{2} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2),x, algorithm="fricas")

[Out]

1/6*sqrt(b*x^2)*b^2*x^5

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Sympy [A]  time = 3.70095, size = 14, normalized size = 0.74 \[ \frac{b^{\frac{5}{2}} x \left (x^{2}\right )^{\frac{5}{2}}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(5/2),x)

[Out]

b**(5/2)*x*(x**2)**(5/2)/6

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GIAC/XCAS [A]  time = 0.217813, size = 14, normalized size = 0.74 \[ \frac{1}{6} \, b^{\frac{5}{2}} x^{6}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2),x, algorithm="giac")

[Out]

1/6*b^(5/2)*x^6*sign(x)