Optimal. Leaf size=15 \[ \log (x)-\frac {1}{8} \log \left (1-x^8\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.308, Rules used = {266, 36, 31, 29} \[ \log (x)-\frac {1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 31
Rule 36
Rule 266
Rubi steps
\begin {align*} \int \frac {1}{x \left (1-x^8\right )} \, dx &=\frac {1}{8} \operatorname {Subst}\left (\int \frac {1}{(1-x) x} \, dx,x,x^8\right )\\ &=\frac {1}{8} \operatorname {Subst}\left (\int \frac {1}{1-x} \, dx,x,x^8\right )+\frac {1}{8} \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,x^8\right )\\ &=\log (x)-\frac {1}{8} \log \left (1-x^8\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \log (x)-\frac {1}{8} \log \left (1-x^8\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.72, size = 11, normalized size = 0.73 \[ -\frac {1}{8} \, \log \left (x^{8} - 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 16, normalized size = 1.07 \[ \frac {1}{8} \, \log \left (x^{8}\right ) - \frac {1}{8} \, \log \left ({\left | x^{8} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.01, size = 32, normalized size = 2.13 \[ \ln \relax (x )-\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x +1\right )}{8}-\frac {\ln \left (x^{2}+1\right )}{8}-\frac {\ln \left (x^{4}+1\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.09, size = 15, normalized size = 1.00 \[ -\frac {1}{8} \, \log \left (x^{8} - 1\right ) + \frac {1}{8} \, \log \left (x^{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.07, size = 11, normalized size = 0.73 \[ \ln \relax (x)-\frac {\ln \left (x^8-1\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.29, size = 10, normalized size = 0.67 \[ \log {\relax (x )} - \frac {\log {\left (x^{8} - 1 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________