Optimal. Leaf size=33 \[ -\frac{1}{10 b x^5}+\frac{\log \left (x^5+2\right )}{20 b}-\frac{\log (x)}{4 b} \]
[Out]
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Rubi [A] time = 0.0451624, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{1}{10 b x^5}+\frac{\log \left (x^5+2\right )}{20 b}-\frac{\log (x)}{4 b} \]
Antiderivative was successfully verified.
[In] Int[1/(x^6*(2*b + b*x^5)),x]
[Out]
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Rubi in Sympy [A] time = 8.06092, size = 26, normalized size = 0.79 \[ - \frac{\log{\left (x^{5} \right )}}{20 b} + \frac{\log{\left (x^{5} + 2 \right )}}{20 b} - \frac{1}{10 b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**6/(b*x**5+2*b),x)
[Out]
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Mathematica [A] time = 0.00768055, size = 33, normalized size = 1. \[ -\frac{1}{10 b x^5}+\frac{\log \left (x^5+2\right )}{20 b}-\frac{\log (x)}{4 b} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^6*(2*b + b*x^5)),x]
[Out]
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Maple [A] time = 0.01, size = 28, normalized size = 0.9 \[ -{\frac{1}{10\,b{x}^{5}}}-{\frac{\ln \left ( x \right ) }{4\,b}}+{\frac{\ln \left ({x}^{5}+2 \right ) }{20\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^6/(b*x^5+2*b),x)
[Out]
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Maxima [A] time = 1.44511, size = 39, normalized size = 1.18 \[ \frac{\log \left (x^{5} + 2\right )}{20 \, b} - \frac{\log \left (x^{5}\right )}{20 \, b} - \frac{1}{10 \, b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 2*b)*x^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220432, size = 36, normalized size = 1.09 \[ \frac{x^{5} \log \left (x^{5} + 2\right ) - 5 \, x^{5} \log \left (x\right ) - 2}{20 \, b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 2*b)*x^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.80609, size = 24, normalized size = 0.73 \[ - \frac{\log{\left (x \right )}}{4 b} + \frac{\log{\left (x^{5} + 2 \right )}}{20 b} - \frac{1}{10 b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**6/(b*x**5+2*b),x)
[Out]
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GIAC/XCAS [A] time = 0.239208, size = 46, normalized size = 1.39 \[ \frac{{\rm ln}\left ({\left | x^{5} + 2 \right |}\right )}{20 \, b} - \frac{{\rm ln}\left ({\left | x \right |}\right )}{4 \, b} + \frac{x^{5} - 2}{20 \, b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + 2*b)*x^6),x, algorithm="giac")
[Out]