Optimal. Leaf size=27 \[ \log \left (1+x+x \left (\left (8-\frac {e^3}{x^3}-x\right ) x-\log (\log (3))\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.13, antiderivative size = 33, normalized size of antiderivative = 1.22, number of steps used = 5, number of rules used = 3, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {6, 2074, 1587} \begin {gather*} \log \left (x^4-8 x^3-x^2 (1-\log (\log (3)))-x+e^3\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^3-16 x^3+3 x^4+x^2 (-1+\log (\log (3)))}{e^3 x-x^2-x^3-8 x^4+x^5+x^3 \log (\log (3))} \, dx\\ &=\int \frac {-e^3-16 x^3+3 x^4+x^2 (-1+\log (\log (3)))}{e^3 x-x^2-8 x^4+x^5+x^3 (-1+\log (\log (3)))} \, dx\\ &=\int \left (-\frac {1}{x}+\frac {-1-24 x^2+4 x^3-2 x (1-\log (\log (3)))}{e^3-x-8 x^3+x^4-x^2 (1-\log (\log (3)))}\right ) \, dx\\ &=-\log (x)+\int \frac {-1-24 x^2+4 x^3-2 x (1-\log (\log (3)))}{e^3-x-8 x^3+x^4-x^2 (1-\log (\log (3)))} \, dx\\ &=-\log (x)+\log \left (e^3-x-8 x^3+x^4-x^2 (1-\log (\log (3)))\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 33, normalized size = 1.22 \begin {gather*} -\log (x)+\log \left (e^3-x-x^2-8 x^3+x^4+x^2 \log (\log (3))\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.67, size = 32, normalized size = 1.19 \begin {gather*} \log \left (x^{4} - 8 \, x^{3} + x^{2} \log \left (\log \relax (3)\right ) - x^{2} - x + e^{3}\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.35, size = 34, normalized size = 1.26 \begin {gather*} \log \left ({\left | x^{4} - 8 \, x^{3} + x^{2} \log \left (\log \relax (3)\right ) - x^{2} - x + e^{3} \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 32, normalized size = 1.19
method | result | size |
risch | \(-\ln \left (-x \right )+\ln \left (x^{4}-8 x^{3}+\left (\ln \left (\ln \relax (3)\right )-1\right ) x^{2}-x +{\mathrm e}^{3}\right )\) | \(32\) |
default | \(-\ln \relax (x )+\ln \left (x^{4}+x^{2} \ln \left (\ln \relax (3)\right )-8 x^{3}-x^{2}+{\mathrm e}^{3}-x \right )\) | \(33\) |
norman | \(-\ln \relax (x )+\ln \left (x^{4}+x^{2} \ln \left (\ln \relax (3)\right )-8 x^{3}-x^{2}+{\mathrm e}^{3}-x \right )\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 29, normalized size = 1.07 \begin {gather*} \log \left (x^{4} - 8 \, x^{3} + x^{2} {\left (\log \left (\log \relax (3)\right ) - 1\right )} - x + e^{3}\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.60, size = 32, normalized size = 1.19 \begin {gather*} \ln \left ({\mathrm {e}}^3-x+x^2\,\ln \left (\ln \relax (3)\right )-x^2-8\,x^3+x^4\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 3.95, size = 27, normalized size = 1.00 \begin {gather*} - \log {\relax (x )} + \log {\left (x^{4} - 8 x^{3} + x^{2} \left (-1 + \log {\left (\log {\relax (3 )} \right )}\right ) - x + e^{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________