Optimal. Leaf size=22 \[ -\frac {1}{8 x^8}+\frac {1}{8} \log \left (x^8+1\right )-\log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, 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} \[ -\frac {1}{8 x^8}+\frac {1}{8} \log \left (x^8+1\right )-\log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 44
Rule 266
Rubi steps
\begin {align*} \int \frac {1}{x^9 \left (1+x^8\right )} \, dx &=\frac {1}{8} \operatorname {Subst}\left (\int \frac {1}{x^2 (1+x)} \, dx,x,x^8\right )\\ &=\frac {1}{8} \operatorname {Subst}\left (\int \left (\frac {1}{x^2}-\frac {1}{x}+\frac {1}{1+x}\right ) \, dx,x,x^8\right )\\ &=-\frac {1}{8 x^8}-\log (x)+\frac {1}{8} \log \left (1+x^8\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ -\frac {1}{8 x^8}+\frac {1}{8} \log \left (x^8+1\right )-\log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.84, size = 24, normalized size = 1.09 \[ \frac {x^{8} \log \left (x^{8} + 1\right ) - 8 \, x^{8} \log \relax (x) - 1}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 25, normalized size = 1.14 \[ \frac {x^{8} - 1}{8 \, x^{8}} + \frac {1}{8} \, \log \left (x^{8} + 1\right ) - \frac {1}{8} \, \log \left (x^{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 19, normalized size = 0.86 \[ -\ln \relax (x )+\frac {\ln \left (x^{8}+1\right )}{8}-\frac {1}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.01, size = 20, normalized size = 0.91 \[ -\frac {1}{8 \, x^{8}} + \frac {1}{8} \, \log \left (x^{8} + 1\right ) - \frac {1}{8} \, \log \left (x^{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 18, normalized size = 0.82 \[ \frac {\ln \left (x^8+1\right )}{8}-\ln \relax (x)-\frac {1}{8\,x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 17, normalized size = 0.77 \[ - \log {\relax (x )} + \frac {\log {\left (x^{8} + 1 \right )}}{8} - \frac {1}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________