Optimal. Leaf size=12 \[ -\frac {1}{8} \log \left (1-x^8\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, 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 = {266}
\begin {gather*} -\frac {1}{8} \log \left (1-x^8\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 266
Rubi steps
\begin {align*} \int \frac {x^7}{1-x^8} \, dx &=-\frac {1}{8} \log \left (1-x^8\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -\frac {1}{8} \log \left (1-x^8\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(29\) vs.
\(2(10)=20\).
time = 0.20, size = 30, normalized size = 2.50
method | result | size |
risch | \(-\frac {\ln \left (x^{8}-1\right )}{8}\) | \(9\) |
derivativedivides | \(-\frac {\ln \left (-x^{8}+1\right )}{8}\) | \(11\) |
meijerg | \(-\frac {\ln \left (-x^{8}+1\right )}{8}\) | \(11\) |
default | \(-\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x +1\right )}{8}-\frac {\ln \left (x^{2}+1\right )}{8}-\frac {\ln \left (x^{4}+1\right )}{8}\) | \(30\) |
norman | \(-\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x +1\right )}{8}-\frac {\ln \left (x^{2}+1\right )}{8}-\frac {\ln \left (x^{4}+1\right )}{8}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{8} \, \log \left (x^{8} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{8} \, \log \left (x^{8} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.67 \begin {gather*} - \frac {\log {\left (x^{8} - 1 \right )}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.94, size = 9, normalized size = 0.75 \begin {gather*} -\frac {1}{8} \, \log \left ({\left | x^{8} - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 8, normalized size = 0.67 \begin {gather*} -\frac {\ln \left (x^8-1\right )}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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