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

Optimal. Leaf size=19 \[ \frac{1}{4} b^2 x^3 \sqrt{b x^2} \]

[Out]

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

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Rubi [A]  time = 0.00771991, antiderivative size = 19, 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 \[ \frac{1}{4} b^2 x^3 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2)/x^2,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.29541, size = 15, normalized size = 0.79 \[ \frac{b^{2} x^{3} \sqrt{b x^{2}}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00173271, size = 15, normalized size = 0.79 \[ \frac{1}{4} b x \left (b x^2\right )^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2)/x^2,x]

[Out]

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

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Maple [A]  time = 0.003, size = 13, normalized size = 0.7 \[{\frac{1}{4\,x} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2)/x^2,x)

[Out]

1/4*(b*x^2)^(5/2)/x

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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^2,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.253092, size = 20, normalized size = 1.05 \[ \frac{1}{4} \, \sqrt{b x^{2}} b^{2} x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 3.66137, size = 14, normalized size = 0.74 \[ \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{4 x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b**(5/2)*(x**2)**(5/2)/(4*x)

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GIAC/XCAS [A]  time = 0.212302, size = 14, normalized size = 0.74 \[ \frac{1}{4} \, b^{\frac{5}{2}} x^{4}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b^(5/2)*x^4*sign(x)