3.1444 \(\int \frac{x^6}{a-b x^7} \, dx\)

Optimal. Leaf size=16 \[ -\frac{\log \left (a-b x^7\right )}{7 b} \]

[Out]

-Log[a - b*x^7]/(7*b)

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Rubi [A]  time = 0.00865842, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ -\frac{\log \left (a-b x^7\right )}{7 b} \]

Antiderivative was successfully verified.

[In]  Int[x^6/(a - b*x^7),x]

[Out]

-Log[a - b*x^7]/(7*b)

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Rubi in Sympy [A]  time = 2.4637, size = 12, normalized size = 0.75 \[ - \frac{\log{\left (a - b x^{7} \right )}}{7 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**6/(-b*x**7+a),x)

[Out]

-log(a - b*x**7)/(7*b)

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Mathematica [A]  time = 0.00484294, size = 16, normalized size = 1. \[ -\frac{\log \left (a-b x^7\right )}{7 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^6/(a - b*x^7),x]

[Out]

-Log[a - b*x^7]/(7*b)

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Maple [A]  time = 0., size = 16, normalized size = 1. \[ -{\frac{\ln \left ( b{x}^{7}-a \right ) }{7\,b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^6/(-b*x^7+a),x)

[Out]

-1/7/b*ln(b*x^7-a)

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Maxima [A]  time = 1.44596, size = 20, normalized size = 1.25 \[ -\frac{\log \left (b x^{7} - a\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^6/(b*x^7 - a),x, algorithm="maxima")

[Out]

-1/7*log(b*x^7 - a)/b

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Fricas [A]  time = 0.21131, size = 20, normalized size = 1.25 \[ -\frac{\log \left (b x^{7} - a\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^6/(b*x^7 - a),x, algorithm="fricas")

[Out]

-1/7*log(b*x^7 - a)/b

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Sympy [A]  time = 0.549263, size = 12, normalized size = 0.75 \[ - \frac{\log{\left (- a + b x^{7} \right )}}{7 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**6/(-b*x**7+a),x)

[Out]

-log(-a + b*x**7)/(7*b)

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GIAC/XCAS [A]  time = 0.222828, size = 22, normalized size = 1.38 \[ -\frac{{\rm ln}\left ({\left | b x^{7} - a \right |}\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^6/(b*x^7 - a),x, algorithm="giac")

[Out]

-1/7*ln(abs(b*x^7 - a))/b