3.686 \(\int \frac{x^7}{2+3 x^4} \, dx\)

Optimal. Leaf size=20 \[ \frac{x^4}{12}-\frac{1}{18} \log \left (3 x^4+2\right ) \]

[Out]

x^4/12 - Log[2 + 3*x^4]/18

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Rubi [A]  time = 0.0325867, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{x^4}{12}-\frac{1}{18} \log \left (3 x^4+2\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^7/(2 + 3*x^4),x]

[Out]

x^4/12 - Log[2 + 3*x^4]/18

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{\log{\left (3 x^{4} + 2 \right )}}{18} + \frac{\int ^{x^{4}} \frac{1}{3}\, dx}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**7/(3*x**4+2),x)

[Out]

-log(3*x**4 + 2)/18 + Integral(1/3, (x, x**4))/4

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Mathematica [A]  time = 0.00897264, size = 21, normalized size = 1.05 \[ \frac{1}{36} \left (3 x^4-2 \log \left (3 x^4+2\right )+2\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^7/(2 + 3*x^4),x]

[Out]

(2 + 3*x^4 - 2*Log[2 + 3*x^4])/36

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Maple [A]  time = 0.004, size = 17, normalized size = 0.9 \[{\frac{{x}^{4}}{12}}-{\frac{\ln \left ( 3\,{x}^{4}+2 \right ) }{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^7/(3*x^4+2),x)

[Out]

1/12*x^4-1/18*ln(3*x^4+2)

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Maxima [A]  time = 1.44082, size = 22, normalized size = 1.1 \[ \frac{1}{12} \, x^{4} - \frac{1}{18} \, \log \left (3 \, x^{4} + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^7/(3*x^4 + 2),x, algorithm="maxima")

[Out]

1/12*x^4 - 1/18*log(3*x^4 + 2)

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Fricas [A]  time = 0.223798, size = 22, normalized size = 1.1 \[ \frac{1}{12} \, x^{4} - \frac{1}{18} \, \log \left (3 \, x^{4} + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^7/(3*x^4 + 2),x, algorithm="fricas")

[Out]

1/12*x^4 - 1/18*log(3*x^4 + 2)

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Sympy [A]  time = 0.154494, size = 14, normalized size = 0.7 \[ \frac{x^{4}}{12} - \frac{\log{\left (3 x^{4} + 2 \right )}}{18} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**7/(3*x**4+2),x)

[Out]

x**4/12 - log(3*x**4 + 2)/18

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GIAC/XCAS [A]  time = 0.220127, size = 22, normalized size = 1.1 \[ \frac{1}{12} \, x^{4} - \frac{1}{18} \,{\rm ln}\left (3 \, x^{4} + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^7/(3*x^4 + 2),x, algorithm="giac")

[Out]

1/12*x^4 - 1/18*ln(3*x^4 + 2)