Optimal. Leaf size=22 \[ -\frac{1}{5 x^5}+\frac{1}{5} \log \left (x^5+1\right )-\log (x) \]
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Rubi [A] time = 0.0096588, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {266, 44} \[ -\frac{1}{5 x^5}+\frac{1}{5} \log \left (x^5+1\right )-\log (x) \]
Antiderivative was successfully verified.
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Rule 266
Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^6 \left (1+x^5\right )} \, dx &=\frac{1}{5} \operatorname{Subst}\left (\int \frac{1}{x^2 (1+x)} \, dx,x,x^5\right )\\ &=\frac{1}{5} \operatorname{Subst}\left (\int \left (\frac{1}{x^2}-\frac{1}{x}+\frac{1}{1+x}\right ) \, dx,x,x^5\right )\\ &=-\frac{1}{5 x^5}-\log (x)+\frac{1}{5} \log \left (1+x^5\right )\\ \end{align*}
Mathematica [A] time = 0.0032063, size = 22, normalized size = 1. \[ -\frac{1}{5 x^5}+\frac{1}{5} \log \left (x^5+1\right )-\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 36, normalized size = 1.6 \begin{align*} -{\frac{1}{5\,{x}^{5}}}-\ln \left ( x \right ) +{\frac{\ln \left ( 1+x \right ) }{5}}+{\frac{\ln \left ({x}^{4}-{x}^{3}+{x}^{2}-x+1 \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.981994, size = 27, normalized size = 1.23 \begin{align*} -\frac{1}{5 \, x^{5}} + \frac{1}{5} \, \log \left (x^{5} + 1\right ) - \frac{1}{5} \, \log \left (x^{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.65769, size = 63, normalized size = 2.86 \begin{align*} \frac{x^{5} \log \left (x^{5} + 1\right ) - 5 \, x^{5} \log \left (x\right ) - 1}{5 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.154177, size = 17, normalized size = 0.77 \begin{align*} - \log{\left (x \right )} + \frac{\log{\left (x^{5} + 1 \right )}}{5} - \frac{1}{5 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16425, size = 34, normalized size = 1.55 \begin{align*} \frac{x^{5} - 1}{5 \, x^{5}} + \frac{1}{5} \, \log \left ({\left | x^{5} + 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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