3.1319 \(\int \frac{x^5}{a+b x^6} \, dx\)

Optimal. Leaf size=15 \[ \frac{\log \left (a+b x^6\right )}{6 b} \]

[Out]

Log[a + b*x^6]/(6*b)

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Rubi [A]  time = 0.0094443, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\log \left (a+b x^6\right )}{6 b} \]

Antiderivative was successfully verified.

[In]  Int[x^5/(a + b*x^6),x]

[Out]

Log[a + b*x^6]/(6*b)

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Rubi in Sympy [A]  time = 2.17189, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{6} \right )}}{6 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**5/(b*x**6+a),x)

[Out]

log(a + b*x**6)/(6*b)

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Mathematica [A]  time = 0.00649054, size = 15, normalized size = 1. \[ \frac{\log \left (a+b x^6\right )}{6 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^5/(a + b*x^6),x]

[Out]

Log[a + b*x^6]/(6*b)

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Maple [A]  time = 0.002, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( b{x}^{6}+a \right ) }{6\,b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^5/(b*x^6+a),x)

[Out]

1/6*ln(b*x^6+a)/b

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Maxima [A]  time = 1.43629, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{6} + a\right )}{6 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(b*x^6 + a),x, algorithm="maxima")

[Out]

1/6*log(b*x^6 + a)/b

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Fricas [A]  time = 0.212859, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{6} + a\right )}{6 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(b*x^6 + a),x, algorithm="fricas")

[Out]

1/6*log(b*x^6 + a)/b

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Sympy [A]  time = 0.515937, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{6} \right )}}{6 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**5/(b*x**6+a),x)

[Out]

log(a + b*x**6)/(6*b)

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GIAC/XCAS [A]  time = 0.2264, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | b x^{6} + a \right |}\right )}{6 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^5/(b*x^6 + a),x, algorithm="giac")

[Out]

1/6*ln(abs(b*x^6 + a))/b