3.450 \(\int \frac{-2+3 x^6}{x \left (5+2 x^6\right )} \, dx\)

Optimal. Leaf size=19 \[ \frac{19}{60} \log \left (2 x^6+5\right )-\frac{2 \log (x)}{5} \]

[Out]

(-2*Log[x])/5 + (19*Log[5 + 2*x^6])/60

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Rubi [A]  time = 0.0529364, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{19}{60} \log \left (2 x^6+5\right )-\frac{2 \log (x)}{5} \]

Antiderivative was successfully verified.

[In]  Int[(-2 + 3*x^6)/(x*(5 + 2*x^6)),x]

[Out]

(-2*Log[x])/5 + (19*Log[5 + 2*x^6])/60

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Rubi in Sympy [A]  time = 8.06544, size = 17, normalized size = 0.89 \[ - \frac{\log{\left (x^{6} \right )}}{15} + \frac{19 \log{\left (2 x^{6} + 5 \right )}}{60} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3*x**6-2)/x/(2*x**6+5),x)

[Out]

-log(x**6)/15 + 19*log(2*x**6 + 5)/60

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Mathematica [A]  time = 0.0083234, size = 19, normalized size = 1. \[ \frac{19}{60} \log \left (2 x^6+5\right )-\frac{2 \log (x)}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[(-2 + 3*x^6)/(x*(5 + 2*x^6)),x]

[Out]

(-2*Log[x])/5 + (19*Log[5 + 2*x^6])/60

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Maple [A]  time = 0.008, size = 16, normalized size = 0.8 \[ -{\frac{2\,\ln \left ( x \right ) }{5}}+{\frac{19\,\ln \left ( 2\,{x}^{6}+5 \right ) }{60}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3*x^6-2)/x/(2*x^6+5),x)

[Out]

-2/5*ln(x)+19/60*ln(2*x^6+5)

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Maxima [A]  time = 0.78885, size = 23, normalized size = 1.21 \[ \frac{19}{60} \, \log \left (2 \, x^{6} + 5\right ) - \frac{1}{15} \, \log \left (x^{6}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^6 - 2)/((2*x^6 + 5)*x),x, algorithm="maxima")

[Out]

19/60*log(2*x^6 + 5) - 1/15*log(x^6)

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Fricas [A]  time = 0.254399, size = 20, normalized size = 1.05 \[ \frac{19}{60} \, \log \left (2 \, x^{6} + 5\right ) - \frac{2}{5} \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^6 - 2)/((2*x^6 + 5)*x),x, algorithm="fricas")

[Out]

19/60*log(2*x^6 + 5) - 2/5*log(x)

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Sympy [A]  time = 0.257758, size = 17, normalized size = 0.89 \[ - \frac{2 \log{\left (x \right )}}{5} + \frac{19 \log{\left (2 x^{6} + 5 \right )}}{60} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x**6-2)/x/(2*x**6+5),x)

[Out]

-2*log(x)/5 + 19*log(2*x**6 + 5)/60

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GIAC/XCAS [A]  time = 0.266006, size = 23, normalized size = 1.21 \[ \frac{19}{60} \,{\rm ln}\left (2 \, x^{6} + 5\right ) - \frac{1}{15} \,{\rm ln}\left (x^{6}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^6 - 2)/((2*x^6 + 5)*x),x, algorithm="giac")

[Out]

19/60*ln(2*x^6 + 5) - 1/15*ln(x^6)