3.1442 \(\int \frac{1}{x \left (a+b x^7\right )} \, dx\)

Optimal. Leaf size=22 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^7\right )}{7 a} \]

[Out]

Log[x]/a - Log[a + b*x^7]/(7*a)

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Rubi [A]  time = 0.0309884, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^7\right )}{7 a} \]

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 = 5.51768, size = 19, normalized size = 0.86 \[ \frac{\log{\left (x^{7} \right )}}{7 a} - \frac{\log{\left (a + b x^{7} \right )}}{7 a} \]

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 = 0.00981516, size = 22, 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 = 0.006, size = 21, 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*ln(b*x^7+a)/a

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Maxima [A]  time = 1.44201, size = 31, normalized size = 1.41 \[ -\frac{\log \left (b x^{7} + a\right )}{7 \, a} + \frac{\log \left (x^{7}\right )}{7 \, a} \]

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 = 0.222208, size = 24, normalized size = 1.09 \[ -\frac{\log \left (b x^{7} + a\right ) - 7 \, \log \left (x\right )}{7 \, a} \]

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 = 0.909634, size = 15, normalized size = 0.68 \[ \frac{\log{\left (x \right )}}{a} - \frac{\log{\left (\frac{a}{b} + x^{7} \right )}}{7 a} \]

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 = 0.223043, size = 30, normalized size = 1.36 \[ -\frac{{\rm ln}\left ({\left | b x^{7} + a \right |}\right )}{7 \, a} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a} \]

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