Optimal. Leaf size=23 \[ \frac{\log (x)}{2 b}-\frac{\log \left (x^5+2\right )}{10 b} \]
[Out]
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Rubi [A] time = 0.0296823, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \frac{\log (x)}{2 b}-\frac{\log \left (x^5+2\right )}{10 b} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(2*b + b*x^5)),x]
[Out]
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Rubi in Sympy [A] time = 5.87634, size = 17, normalized size = 0.74 \[ \frac{\log{\left (x^{5} \right )}}{10 b} - \frac{\log{\left (x^{5} + 2 \right )}}{10 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x**5+2*b),x)
[Out]
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Mathematica [A] time = 0.0104145, size = 23, normalized size = 1. \[ \frac{\log (x)}{2 b}-\frac{\log \left (x^5+2\right )}{10 b} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(2*b + b*x^5)),x]
[Out]
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Maple [A] time = 0.006, size = 20, normalized size = 0.9 \[{\frac{\ln \left ( x \right ) }{2\,b}}-{\frac{\ln \left ({x}^{5}+2 \right ) }{10\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x^5+2*b),x)
[Out]
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Maxima [A] time = 1.44085, size = 28, normalized size = 1.22 \[ -\frac{\log \left (x^{5} + 2\right )}{10 \, b} + \frac{\log \left (x^{5}\right )}{10 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 2*b)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220929, size = 22, normalized size = 0.96 \[ -\frac{\log \left (x^{5} + 2\right ) - 5 \, \log \left (x\right )}{10 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 2*b)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.772315, size = 15, normalized size = 0.65 \[ \frac{\log{\left (x \right )}}{2 b} - \frac{\log{\left (x^{5} + 2 \right )}}{10 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x**5+2*b),x)
[Out]
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GIAC/XCAS [A] time = 0.237359, size = 28, normalized size = 1.22 \[ -\frac{{\rm ln}\left ({\left | x^{5} + 2 \right |}\right )}{10 \, b} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 2*b)*x),x, algorithm="giac")
[Out]