3.157 \(\int \frac{x^2}{9-10 x^3+x^6} \, dx\)

Optimal. Leaf size=25 \[ \frac{1}{24} \log \left (9-x^3\right )-\frac{1}{24} \log \left (1-x^3\right ) \]

[Out]

-Log[1 - x^3]/24 + Log[9 - x^3]/24

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Rubi [A]  time = 0.0356861, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \frac{1}{24} \log \left (9-x^3\right )-\frac{1}{24} \log \left (1-x^3\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^2/(9 - 10*x^3 + x^6),x]

[Out]

-Log[1 - x^3]/24 + Log[9 - x^3]/24

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Rubi in Sympy [A]  time = 2.66058, size = 15, normalized size = 0.6 \[ - \frac{\log{\left (- x^{3} + 1 \right )}}{24} + \frac{\log{\left (- x^{3} + 9 \right )}}{24} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2/(x**6-10*x**3+9),x)

[Out]

-log(-x**3 + 1)/24 + log(-x**3 + 9)/24

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Mathematica [A]  time = 0.00649757, size = 25, normalized size = 1. \[ \frac{1}{24} \log \left (9-x^3\right )-\frac{1}{24} \log \left (1-x^3\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^2/(9 - 10*x^3 + x^6),x]

[Out]

-Log[1 - x^3]/24 + Log[9 - x^3]/24

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Maple [A]  time = 0.008, size = 18, normalized size = 0.7 \[{\frac{\ln \left ({x}^{3}-9 \right ) }{24}}-{\frac{\ln \left ({x}^{3}-1 \right ) }{24}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2/(x^6-10*x^3+9),x)

[Out]

1/24*ln(x^3-9)-1/24*ln(x^3-1)

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Maxima [A]  time = 1.35314, size = 23, normalized size = 0.92 \[ -\frac{1}{24} \, \log \left (x^{3} - 1\right ) + \frac{1}{24} \, \log \left (x^{3} - 9\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/(x^6 - 10*x^3 + 9),x, algorithm="maxima")

[Out]

-1/24*log(x^3 - 1) + 1/24*log(x^3 - 9)

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Fricas [A]  time = 0.194433, size = 23, normalized size = 0.92 \[ -\frac{1}{24} \, \log \left (x^{3} - 1\right ) + \frac{1}{24} \, \log \left (x^{3} - 9\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/(x^6 - 10*x^3 + 9),x, algorithm="fricas")

[Out]

-1/24*log(x^3 - 1) + 1/24*log(x^3 - 9)

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Sympy [A]  time = 0.11688, size = 15, normalized size = 0.6 \[ \frac{\log{\left (x^{3} - 9 \right )}}{24} - \frac{\log{\left (x^{3} - 1 \right )}}{24} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2/(x**6-10*x**3+9),x)

[Out]

log(x**3 - 9)/24 - log(x**3 - 1)/24

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GIAC/XCAS [A]  time = 0.201907, size = 26, normalized size = 1.04 \[ -\frac{1}{24} \,{\rm ln}\left ({\left | x^{3} - 1 \right |}\right ) + \frac{1}{24} \,{\rm ln}\left ({\left | x^{3} - 9 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/(x^6 - 10*x^3 + 9),x, algorithm="giac")

[Out]

-1/24*ln(abs(x^3 - 1)) + 1/24*ln(abs(x^3 - 9))