3.28 \(\int \frac{\left (b x^2\right )^{5/2}}{x^4} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00791702, 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 \[ \frac{1}{2} b^2 x \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2)/x^4,x]

[Out]

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

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{b^{2} \sqrt{b x^{2}} \int x\, dx}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(5/2)/x**4,x)

[Out]

b**2*sqrt(b*x**2)*Integral(x, x)/x

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Mathematica [A]  time = 0.00193942, size = 17, normalized size = 1. \[ \frac{1}{2} b^2 x \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2)/x^4,x]

[Out]

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

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Maple [A]  time = 0.001, size = 13, normalized size = 0.8 \[{\frac{1}{2\,{x}^{3}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2)/x^4,x)

[Out]

1/2*(b*x^2)^(5/2)/x^3

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^4,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.247291, size = 18, normalized size = 1.06 \[ \frac{1}{2} \, \sqrt{b x^{2}} b^{2} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^4,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 4.66929, size = 15, normalized size = 0.88 \[ \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{2 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(5/2)/x**4,x)

[Out]

b**(5/2)*(x**2)**(5/2)/(2*x**3)

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GIAC/XCAS [A]  time = 0.212449, size = 14, normalized size = 0.82 \[ \frac{1}{2} \, b^{\frac{5}{2}} x^{2}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^4,x, algorithm="giac")

[Out]

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