3.120 \(\int \frac{x^2}{a^3+x^3} \, dx\)

Optimal. Leaf size=12 \[ \frac{1}{3} \log \left (a^3+x^3\right ) \]

[Out]

Log[a^3 + x^3]/3

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Rubi [A]  time = 0.00599168, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{3} \log \left (a^3+x^3\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^2/(a^3 + x^3),x]

[Out]

Log[a^3 + x^3]/3

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Rubi in Sympy [A]  time = 0.898281, size = 8, normalized size = 0.67 \[ \frac{\log{\left (a^{3} + x^{3} \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2/(a**3+x**3),x)

[Out]

log(a**3 + x**3)/3

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Mathematica [A]  time = 0.0033611, size = 12, normalized size = 1. \[ \frac{1}{3} \log \left (a^3+x^3\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^2/(a^3 + x^3),x]

[Out]

Log[a^3 + x^3]/3

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Maple [A]  time = 0.002, size = 11, normalized size = 0.9 \[{\frac{\ln \left ({a}^{3}+{x}^{3} \right ) }{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2/(a^3+x^3),x)

[Out]

1/3*ln(a^3+x^3)

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Maxima [A]  time = 1.32586, size = 14, normalized size = 1.17 \[ \frac{1}{3} \, \log \left (a^{3} + x^{3}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/(a^3 + x^3),x, algorithm="maxima")

[Out]

1/3*log(a^3 + x^3)

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Fricas [A]  time = 0.227863, size = 14, normalized size = 1.17 \[ \frac{1}{3} \, \log \left (a^{3} + x^{3}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/(a^3 + x^3),x, algorithm="fricas")

[Out]

1/3*log(a^3 + x^3)

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Sympy [A]  time = 0.096228, size = 8, normalized size = 0.67 \[ \frac{\log{\left (a^{3} + x^{3} \right )}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2/(a**3+x**3),x)

[Out]

log(a**3 + x**3)/3

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GIAC/XCAS [A]  time = 0.202165, size = 15, normalized size = 1.25 \[ \frac{1}{3} \,{\rm ln}\left ({\left | a^{3} + x^{3} \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/(a^3 + x^3),x, algorithm="giac")

[Out]

1/3*ln(abs(a^3 + x^3))