3.1294 \(\int \frac{x^9}{1+x^5} \, dx\)

Optimal. Leaf size=18 \[ \frac{x^5}{5}-\frac{1}{5} \log \left (x^5+1\right ) \]

[Out]

x^5/5 - Log[1 + x^5]/5

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Rubi [A]  time = 0.0229031, antiderivative size = 18, 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 \[ \frac{x^5}{5}-\frac{1}{5} \log \left (x^5+1\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^9/(1 + x^5),x]

[Out]

x^5/5 - Log[1 + x^5]/5

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Rubi in Sympy [A]  time = 3.61391, size = 12, normalized size = 0.67 \[ \frac{x^{5}}{5} - \frac{\log{\left (x^{5} + 1 \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**9/(x**5+1),x)

[Out]

x**5/5 - log(x**5 + 1)/5

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Mathematica [A]  time = 0.00397867, size = 18, normalized size = 1. \[ \frac{x^5}{5}-\frac{1}{5} \log \left (x^5+1\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^9/(1 + x^5),x]

[Out]

x^5/5 - Log[1 + x^5]/5

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Maple [A]  time = 0.003, size = 15, normalized size = 0.8 \[{\frac{{x}^{5}}{5}}-{\frac{\ln \left ({x}^{5}+1 \right ) }{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^9/(x^5+1),x)

[Out]

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

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Maxima [A]  time = 1.43322, size = 19, normalized size = 1.06 \[ \frac{1}{5} \, x^{5} - \frac{1}{5} \, \log \left (x^{5} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(x^5 + 1),x, algorithm="maxima")

[Out]

1/5*x^5 - 1/5*log(x^5 + 1)

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Fricas [A]  time = 0.218979, size = 19, normalized size = 1.06 \[ \frac{1}{5} \, x^{5} - \frac{1}{5} \, \log \left (x^{5} + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(x^5 + 1),x, algorithm="fricas")

[Out]

1/5*x^5 - 1/5*log(x^5 + 1)

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Sympy [A]  time = 0.170339, size = 12, normalized size = 0.67 \[ \frac{x^{5}}{5} - \frac{\log{\left (x^{5} + 1 \right )}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**9/(x**5+1),x)

[Out]

x**5/5 - log(x**5 + 1)/5

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GIAC/XCAS [A]  time = 0.227233, size = 20, normalized size = 1.11 \[ \frac{1}{5} \, x^{5} - \frac{1}{5} \,{\rm ln}\left ({\left | x^{5} + 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(x^5 + 1),x, algorithm="giac")

[Out]

1/5*x^5 - 1/5*ln(abs(x^5 + 1))