3.21 \(\int \frac{\left (b x^2\right )^{3/2}}{x^7} \, dx\)

Optimal. Leaf size=17 \[ -\frac{b \sqrt{b x^2}}{3 x^4} \]

[Out]

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

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Rubi [A]  time = 0.00762647, 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 \[ -\frac{b \sqrt{b x^2}}{3 x^4} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(3/2)/x^7,x]

[Out]

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

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Rubi in Sympy [A]  time = 2.54998, size = 14, normalized size = 0.82 \[ - \frac{b^{3}}{3 \left (b x^{2}\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(3/2)/x**7,x)

[Out]

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

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Mathematica [A]  time = 0.00230196, size = 16, normalized size = 0.94 \[ -\frac{\left (b x^2\right )^{3/2}}{3 x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(3/2)/x^7,x]

[Out]

-(b*x^2)^(3/2)/(3*x^6)

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Maple [A]  time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{1}{3\,{x}^{6}} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(3/2)/x^7,x)

[Out]

-1/3*(b*x^2)^(3/2)/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)^(3/2)/x^7,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.232634, size = 18, normalized size = 1.06 \[ -\frac{\sqrt{b x^{2}} b}{3 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(3/2)/x^7,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 4.84306, size = 17, normalized size = 1. \[ - \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{3 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(3/2)/x**7,x)

[Out]

-b**(3/2)*(x**2)**(3/2)/(3*x**6)

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GIAC/XCAS [A]  time = 0.232382, size = 14, normalized size = 0.82 \[ -\frac{b^{\frac{3}{2}}{\rm sign}\left (x\right )}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(3/2)/x^7,x, algorithm="giac")

[Out]

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