3.31 \(\int \frac{\left (b x^2\right )^{5/2}}{x^7} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00841907, 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 \[ -\frac{b^2 \sqrt{b x^2}}{x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2)/x^7,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.51637, size = 12, normalized size = 0.71 \[ - \frac{b^{3}}{\sqrt{b x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(5/2)/x**7,x)

[Out]

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

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Mathematica [A]  time = 0.00360493, size = 14, normalized size = 0.82 \[ -\frac{\left (b x^2\right )^{5/2}}{x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2)/x^7,x]

[Out]

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

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Maple [A]  time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{1}{{x}^{6}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2)/x^7,x)

[Out]

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

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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^7,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.239668, size = 20, normalized size = 1.18 \[ -\frac{\sqrt{b x^{2}} b^{2}}{x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^7,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 7.02758, size = 15, normalized size = 0.88 \[ - \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(5/2)/x**7,x)

[Out]

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

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GIAC/XCAS [A]  time = 0.215353, size = 14, normalized size = 0.82 \[ -\frac{b^{\frac{5}{2}}{\rm sign}\left (x\right )}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^7,x, algorithm="giac")

[Out]

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