3.248 \(\int \frac{x}{\left (a-b x^2\right )^5} \, dx\)

Optimal. Leaf size=17 \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]

[Out]

1/(8*b*(a - b*x^2)^4)

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Rubi [A]  time = 0.0112372, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]

Antiderivative was successfully verified.

[In]  Int[x/(a - b*x^2)^5,x]

[Out]

1/(8*b*(a - b*x^2)^4)

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Rubi in Sympy [A]  time = 2.68558, size = 12, normalized size = 0.71 \[ \frac{1}{8 b \left (a - b x^{2}\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/(8*b*(a - b*x**2)**4)

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Mathematica [A]  time = 0.00765399, size = 17, normalized size = 1. \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]

Antiderivative was successfully verified.

[In]  Integrate[x/(a - b*x^2)^5,x]

[Out]

1/(8*b*(a - b*x^2)^4)

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Maple [A]  time = 0.001, size = 17, normalized size = 1. \[{\frac{1}{8\,b \left ( b{x}^{2}-a \right ) ^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(-b*x^2+a)^5,x)

[Out]

1/8/b/(b*x^2-a)^4

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Maxima [A]  time = 1.34582, size = 22, normalized size = 1.29 \[ \frac{1}{8 \,{\left (b x^{2} - a\right )}^{4} b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8/((b*x^2 - a)^4*b)

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Fricas [A]  time = 0.221801, size = 65, normalized size = 3.82 \[ \frac{1}{8 \,{\left (b^{5} x^{8} - 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} - 4 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8/(b^5*x^8 - 4*a*b^4*x^6 + 6*a^2*b^3*x^4 - 4*a^3*b^2*x^2 + a^4*b)

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Sympy [A]  time = 2.69979, size = 49, normalized size = 2.88 \[ \frac{1}{8 a^{4} b - 32 a^{3} b^{2} x^{2} + 48 a^{2} b^{3} x^{4} - 32 a b^{4} x^{6} + 8 b^{5} x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-b*x**2+a)**5,x)

[Out]

1/(8*a**4*b - 32*a**3*b**2*x**2 + 48*a**2*b**3*x**4 - 32*a*b**4*x**6 + 8*b**5*x*
*8)

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GIAC/XCAS [A]  time = 0.211518, size = 22, normalized size = 1.29 \[ \frac{1}{8 \,{\left (b x^{2} - a\right )}^{4} b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8/((b*x^2 - a)^4*b)