Optimal. Leaf size=23 \[ \log \left (1+e^{10}+5 \left (2+\frac {4}{x^2}-x\right )-x+\log (4)\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.34, antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 6, number of rules used = 4, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.108, Rules used = {6, 1594, 6742, 1587} \begin {gather*} \log \left (-6 x^3+x^2 \left (11+e^{10}+\log (4)\right )+20\right )-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 1587
Rule 1594
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-40-6 x^3}{20 x+\left (11+e^{10}\right ) x^3-6 x^4+x^3 \log (4)} \, dx\\ &=\int \frac {-40-6 x^3}{20 x-6 x^4+x^3 \left (11+e^{10}+\log (4)\right )} \, dx\\ &=\int \frac {-40-6 x^3}{x \left (20-6 x^3+x^2 \left (11+e^{10}+\log (4)\right )\right )} \, dx\\ &=\int \left (-\frac {2}{x}+\frac {2 x \left (11+e^{10}-9 x+\log (4)\right )}{20-6 x^3+x^2 \left (11+e^{10}+\log (4)\right )}\right ) \, dx\\ &=-2 \log (x)+2 \int \frac {x \left (11+e^{10}-9 x+\log (4)\right )}{20-6 x^3+x^2 \left (11+e^{10}+\log (4)\right )} \, dx\\ &=-2 \log (x)+\log \left (20-6 x^3+x^2 \left (11+e^{10}+\log (4)\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 31, normalized size = 1.35 \begin {gather*} -2 \log (x)+\log \left (20+11 x^2+e^{10} x^2-6 x^3+x^2 \log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.67, size = 32, normalized size = 1.39 \begin {gather*} \log \left (6 \, x^{3} - x^{2} e^{10} - 2 \, x^{2} \log \relax (2) - 11 \, x^{2} - 20\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.27, size = 34, normalized size = 1.48 \begin {gather*} \log \left ({\left | 6 \, x^{3} - x^{2} e^{10} - 2 \, x^{2} \log \relax (2) - 11 \, x^{2} - 20 \right |}\right ) - 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 30, normalized size = 1.30
method | result | size |
risch | \(-2 \ln \left (-x \right )+\ln \left (-20+6 x^{3}+\left (-2 \ln \relax (2)-{\mathrm e}^{10}-11\right ) x^{2}\right )\) | \(30\) |
norman | \(-2 \ln \relax (x )+\ln \left (2 x^{2} \ln \relax (2)+x^{2} {\mathrm e}^{10}-6 x^{3}+11 x^{2}+20\right )\) | \(32\) |
default | \(-2 \ln \relax (x )+\ln \left (-2 x^{2} \ln \relax (2)-x^{2} {\mathrm e}^{10}+6 x^{3}-11 x^{2}-20\right )\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.39, size = 26, normalized size = 1.13 \begin {gather*} \log \left (6 \, x^{3} - x^{2} {\left (e^{10} + 2 \, \log \relax (2) + 11\right )} - 20\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.22, size = 32, normalized size = 1.39 \begin {gather*} \ln \left (3\,x^2\,{\mathrm {e}}^{10}+6\,x^2\,\ln \relax (2)+33\,x^2-18\,x^3+60\right )-2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 3.15, size = 31, normalized size = 1.35 \begin {gather*} - 2 \log {\relax (x )} + \log {\left (x^{3} + x^{2} \left (- \frac {e^{10}}{6} - \frac {11}{6} - \frac {\log {\relax (2 )}}{3}\right ) - \frac {10}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________