3.1541 \(\int \frac{x^5}{9+x^{12}} \, dx\)

Optimal. Leaf size=12 \[ \frac{1}{18} \tan ^{-1}\left (\frac{x^6}{3}\right ) \]

[Out]

ArcTan[x^6/3]/18

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Rubi [A]  time = 0.0169258, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{1}{18} \tan ^{-1}\left (\frac{x^6}{3}\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^5/(9 + x^12),x]

[Out]

ArcTan[x^6/3]/18

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Rubi in Sympy [A]  time = 2.70656, size = 7, normalized size = 0.58 \[ \frac{\operatorname{atan}{\left (\frac{x^{6}}{3} \right )}}{18} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**5/(x**12+9),x)

[Out]

atan(x**6/3)/18

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Mathematica [A]  time = 0.00731801, size = 12, normalized size = 1. \[ \frac{1}{18} \tan ^{-1}\left (\frac{x^6}{3}\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/(9 + x^12),x]

[Out]

ArcTan[x^6/3]/18

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Maple [A]  time = 0.004, size = 9, normalized size = 0.8 \[{\frac{1}{18}\arctan \left ({\frac{{x}^{6}}{3}} \right ) } \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(x^12+9),x)

[Out]

1/18*arctan(1/3*x^6)

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Maxima [A]  time = 1.58771, size = 11, normalized size = 0.92 \[ \frac{1}{18} \, \arctan \left (\frac{1}{3} \, x^{6}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(x^12 + 9),x, algorithm="maxima")

[Out]

1/18*arctan(1/3*x^6)

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Fricas [A]  time = 0.222916, size = 11, normalized size = 0.92 \[ \frac{1}{18} \, \arctan \left (\frac{1}{3} \, x^{6}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(x^12 + 9),x, algorithm="fricas")

[Out]

1/18*arctan(1/3*x^6)

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Sympy [A]  time = 0.320024, size = 7, normalized size = 0.58 \[ \frac{\operatorname{atan}{\left (\frac{x^{6}}{3} \right )}}{18} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5/(x**12+9),x)

[Out]

atan(x**6/3)/18

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GIAC/XCAS [A]  time = 0.233799, size = 11, normalized size = 0.92 \[ \frac{1}{18} \, \arctan \left (\frac{1}{3} \, x^{6}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(x^12 + 9),x, algorithm="giac")

[Out]

1/18*arctan(1/3*x^6)