Optimal. Leaf size=12 \[ -\frac{1}{8} \log \left (1-x^8\right ) \]
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Rubi [A] time = 0.0025672, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {260} \[ -\frac{1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{x^7}{1-x^8} \, dx &=-\frac{1}{8} \log \left (1-x^8\right )\\ \end{align*}
Mathematica [A] time = 0.0029171, size = 12, normalized size = 1. \[ -\frac{1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 30, normalized size = 2.5 \begin{align*} -{\frac{\ln \left ( -1+x \right ) }{8}}-{\frac{\ln \left ( 1+x \right ) }{8}}-{\frac{\ln \left ({x}^{2}+1 \right ) }{8}}-{\frac{\ln \left ({x}^{4}+1 \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.941738, size = 11, normalized size = 0.92 \begin{align*} -\frac{1}{8} \, \log \left (x^{8} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.18963, size = 26, normalized size = 2.17 \begin{align*} -\frac{1}{8} \, \log \left (x^{8} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095827, size = 8, normalized size = 0.67 \begin{align*} - \frac{\log{\left (x^{8} - 1 \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18282, size = 12, normalized size = 1. \begin{align*} -\frac{1}{8} \, \log \left ({\left | x^{8} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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