3.1446 \(\int \frac{1}{x \left (a-b x^7\right )} \, dx\)

Optimal. Leaf size=23 \[ \frac{\log (x)}{a}-\frac{\log \left (a-b x^7\right )}{7 a} \]

[Out]

Log[x]/a - Log[a - b*x^7]/(7*a)

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Rubi [A]  time = 0.0396933, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{\log (x)}{a}-\frac{\log \left (a-b x^7\right )}{7 a} \]

Antiderivative was successfully verified.

[In]  Int[1/(x*(a - b*x^7)),x]

[Out]

Log[x]/a - Log[a - b*x^7]/(7*a)

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Rubi in Sympy [A]  time = 5.97916, size = 19, normalized size = 0.83 \[ \frac{\log{\left (x^{7} \right )}}{7 a} - \frac{\log{\left (a - b x^{7} \right )}}{7 a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x/(-b*x**7+a),x)

[Out]

log(x**7)/(7*a) - log(a - b*x**7)/(7*a)

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Mathematica [A]  time = 0.0117085, size = 23, normalized size = 1. \[ \frac{\log (x)}{a}-\frac{\log \left (a-b x^7\right )}{7 a} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(x*(a - b*x^7)),x]

[Out]

Log[x]/a - Log[a - b*x^7]/(7*a)

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Maple [A]  time = 0.005, size = 23, normalized size = 1. \[{\frac{\ln \left ( x \right ) }{a}}-{\frac{\ln \left ( b{x}^{7}-a \right ) }{7\,a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x/(-b*x^7+a),x)

[Out]

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

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Maxima [A]  time = 1.44683, size = 34, normalized size = 1.48 \[ -\frac{\log \left (b x^{7} - a\right )}{7 \, a} + \frac{\log \left (x^{7}\right )}{7 \, a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((b*x^7 - a)*x),x, algorithm="maxima")

[Out]

-1/7*log(b*x^7 - a)/a + 1/7*log(x^7)/a

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Fricas [A]  time = 0.224001, size = 27, normalized size = 1.17 \[ -\frac{\log \left (b x^{7} - a\right ) - 7 \, \log \left (x\right )}{7 \, a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((b*x^7 - a)*x),x, algorithm="fricas")

[Out]

-1/7*(log(b*x^7 - a) - 7*log(x))/a

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Sympy [A]  time = 0.948673, size = 15, normalized size = 0.65 \[ \frac{\log{\left (x \right )}}{a} - \frac{\log{\left (- \frac{a}{b} + x^{7} \right )}}{7 a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x/(-b*x**7+a),x)

[Out]

log(x)/a - log(-a/b + x**7)/(7*a)

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GIAC/XCAS [A]  time = 0.219977, size = 32, normalized size = 1.39 \[ -\frac{{\rm ln}\left ({\left | b x^{7} - a \right |}\right )}{7 \, a} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((b*x^7 - a)*x),x, algorithm="giac")

[Out]

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