3.1293 \(\int \frac{x^{14}}{1+x^5} \, dx\)

Optimal. Leaf size=25 \[ \frac{x^{10}}{10}-\frac{x^5}{5}+\frac{1}{5} \log \left (x^5+1\right ) \]

[Out]

-x^5/5 + x^10/10 + Log[1 + x^5]/5

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Rubi [A]  time = 0.0313599, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{x^{10}}{10}-\frac{x^5}{5}+\frac{1}{5} \log \left (x^5+1\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^14/(1 + x^5),x]

[Out]

-x^5/5 + x^10/10 + Log[1 + x^5]/5

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{x^{5}}{5} + \frac{\log{\left (x^{5} + 1 \right )}}{5} + \frac{\int ^{x^{5}} x\, dx}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**14/(x**5+1),x)

[Out]

-x**5/5 + log(x**5 + 1)/5 + Integral(x, (x, x**5))/5

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Mathematica [A]  time = 0.00861426, size = 22, normalized size = 0.88 \[ \frac{1}{10} \left (x^{10}-2 x^5+2 \log \left (x^5+1\right )-3\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^14/(1 + x^5),x]

[Out]

(-3 - 2*x^5 + x^10 + 2*Log[1 + x^5])/10

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Maple [A]  time = 0.003, size = 20, normalized size = 0.8 \[ -{\frac{{x}^{5}}{5}}+{\frac{{x}^{10}}{10}}+{\frac{\ln \left ({x}^{5}+1 \right ) }{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^14/(x^5+1),x)

[Out]

-1/5*x^5+1/10*x^10+1/5*ln(x^5+1)

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Maxima [A]  time = 1.42698, size = 26, normalized size = 1.04 \[ \frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \, \log \left (x^{5} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(x^5 + 1),x, algorithm="maxima")

[Out]

1/10*x^10 - 1/5*x^5 + 1/5*log(x^5 + 1)

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Fricas [A]  time = 0.216397, size = 26, normalized size = 1.04 \[ \frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \, \log \left (x^{5} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(x^5 + 1),x, algorithm="fricas")

[Out]

1/10*x^10 - 1/5*x^5 + 1/5*log(x^5 + 1)

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Sympy [A]  time = 0.176321, size = 17, normalized size = 0.68 \[ \frac{x^{10}}{10} - \frac{x^{5}}{5} + \frac{\log{\left (x^{5} + 1 \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**14/(x**5+1),x)

[Out]

x**10/10 - x**5/5 + log(x**5 + 1)/5

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GIAC/XCAS [A]  time = 0.225786, size = 27, normalized size = 1.08 \[ \frac{1}{10} \, x^{10} - \frac{1}{5} \, x^{5} + \frac{1}{5} \,{\rm ln}\left ({\left | x^{5} + 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(x^5 + 1),x, algorithm="giac")

[Out]

1/10*x^10 - 1/5*x^5 + 1/5*ln(abs(x^5 + 1))