3.32 \(\int \frac{\left (b x^2\right )^{5/2}}{x^8} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.0083058, 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 \[ -\frac{b^2 \sqrt{b x^2}}{2 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2)/x^8,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.28584, size = 17, normalized size = 0.89 \[ - \frac{b^{2} \sqrt{b x^{2}}}{2 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(5/2)/x**8,x)

[Out]

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

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Mathematica [A]  time = 0.00287313, size = 16, normalized size = 0.84 \[ -\frac{\left (b x^2\right )^{5/2}}{2 x^7} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2)/x^8,x]

[Out]

-(b*x^2)^(5/2)/(2*x^7)

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Maple [A]  time = 0.003, size = 13, normalized size = 0.7 \[ -{\frac{1}{2\,{x}^{7}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2)/x^8,x)

[Out]

-1/2*(b*x^2)^(5/2)/x^7

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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^8,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.262848, size = 20, normalized size = 1.05 \[ -\frac{\sqrt{b x^{2}} b^{2}}{2 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^8,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 8.65853, size = 17, normalized size = 0.89 \[ - \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{2 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(5/2)/x**8,x)

[Out]

-b**(5/2)*(x**2)**(5/2)/(2*x**7)

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GIAC/XCAS [A]  time = 0.232869, size = 14, normalized size = 0.74 \[ -\frac{b^{\frac{5}{2}}{\rm sign}\left (x\right )}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^8,x, algorithm="giac")

[Out]

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