3.688 \(\int \frac{x^3}{2+3 x^4} \, dx\)

Optimal. Leaf size=12 \[ \frac{1}{12} \log \left (3 x^4+2\right ) \]

[Out]

Log[2 + 3*x^4]/12

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Rubi [A]  time = 0.00670748, 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 \[ \frac{1}{12} \log \left (3 x^4+2\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^3/(2 + 3*x^4),x]

[Out]

Log[2 + 3*x^4]/12

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Rubi in Sympy [A]  time = 1.9416, size = 8, normalized size = 0.67 \[ \frac{\log{\left (3 x^{4} + 2 \right )}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3/(3*x**4+2),x)

[Out]

log(3*x**4 + 2)/12

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Mathematica [A]  time = 0.0045764, size = 12, normalized size = 1. \[ \frac{1}{12} \log \left (3 x^4+2\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^3/(2 + 3*x^4),x]

[Out]

Log[2 + 3*x^4]/12

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Maple [A]  time = 0.001, size = 11, normalized size = 0.9 \[{\frac{\ln \left ( 3\,{x}^{4}+2 \right ) }{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3/(3*x^4+2),x)

[Out]

1/12*ln(3*x^4+2)

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Maxima [A]  time = 1.4283, size = 14, normalized size = 1.17 \[ \frac{1}{12} \, \log \left (3 \, x^{4} + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(3*x^4 + 2),x, algorithm="maxima")

[Out]

1/12*log(3*x^4 + 2)

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Fricas [A]  time = 0.2226, size = 14, normalized size = 1.17 \[ \frac{1}{12} \, \log \left (3 \, x^{4} + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(3*x^4 + 2),x, algorithm="fricas")

[Out]

1/12*log(3*x^4 + 2)

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Sympy [A]  time = 0.144578, size = 8, normalized size = 0.67 \[ \frac{\log{\left (3 x^{4} + 2 \right )}}{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3/(3*x**4+2),x)

[Out]

log(3*x**4 + 2)/12

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GIAC/XCAS [A]  time = 0.220499, size = 14, normalized size = 1.17 \[ \frac{1}{12} \,{\rm ln}\left (3 \, x^{4} + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(3*x^4 + 2),x, algorithm="giac")

[Out]

1/12*ln(3*x^4 + 2)