Optimal. Leaf size=22 \[ \left (4 x+x^3-\frac {25}{3} x^2 (-x+\log (2))\right )^2 \]
________________________________________________________________________________________
Rubi [B] time = 0.02, antiderivative size = 46, normalized size of antiderivative = 2.09, number of steps used = 4, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {6, 12} \begin {gather*} \frac {784 x^6}{9}-\frac {1400}{9} x^5 \log (2)+\frac {1}{9} x^4 \left (672+625 \log ^2(2)\right )-\frac {200}{3} x^3 \log (2)+16 x^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{9} \left (288 x+4704 x^5+\left (-1800 x^2-7000 x^4\right ) \log (2)+x^3 \left (2688+2500 \log ^2(2)\right )\right ) \, dx\\ &=\frac {1}{9} \int \left (288 x+4704 x^5+\left (-1800 x^2-7000 x^4\right ) \log (2)+x^3 \left (2688+2500 \log ^2(2)\right )\right ) \, dx\\ &=16 x^2+\frac {784 x^6}{9}+\frac {1}{9} x^4 \left (672+625 \log ^2(2)\right )+\frac {1}{9} \log (2) \int \left (-1800 x^2-7000 x^4\right ) \, dx\\ &=16 x^2+\frac {784 x^6}{9}-\frac {200}{3} x^3 \log (2)-\frac {1400}{9} x^5 \log (2)+\frac {1}{9} x^4 \left (672+625 \log ^2(2)\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 21, normalized size = 0.95 \begin {gather*} \frac {1}{9} x^2 \left (12+28 x^2-25 x \log (2)\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 40, normalized size = 1.82 \begin {gather*} \frac {784}{9} \, x^{6} + \frac {625}{9} \, x^{4} \log \relax (2)^{2} + \frac {224}{3} \, x^{4} + 16 \, x^{2} - \frac {200}{9} \, {\left (7 \, x^{5} + 3 \, x^{3}\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.31, size = 40, normalized size = 1.82 \begin {gather*} \frac {784}{9} \, x^{6} + \frac {625}{9} \, x^{4} \log \relax (2)^{2} + \frac {224}{3} \, x^{4} + 16 \, x^{2} - \frac {200}{9} \, {\left (7 \, x^{5} + 3 \, x^{3}\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 20, normalized size = 0.91
method | result | size |
gosper | \(\frac {x^{2} \left (25 x \ln \relax (2)-28 x^{2}-12\right )^{2}}{9}\) | \(20\) |
norman | \(\left (\frac {625 \ln \relax (2)^{2}}{9}+\frac {224}{3}\right ) x^{4}+16 x^{2}+\frac {784 x^{6}}{9}-\frac {200 x^{3} \ln \relax (2)}{3}-\frac {1400 x^{5} \ln \relax (2)}{9}\) | \(38\) |
risch | \(\frac {625 x^{4} \ln \relax (2)^{2}}{9}-\frac {1400 x^{5} \ln \relax (2)}{9}-\frac {200 x^{3} \ln \relax (2)}{3}+\frac {784 x^{6}}{9}+\frac {224 x^{4}}{3}+16 x^{2}\) | \(40\) |
default | \(\frac {625 x^{4} \ln \relax (2)^{2}}{9}+\frac {\ln \relax (2) \left (-1400 x^{5}-600 x^{3}\right )}{9}+\frac {784 x^{6}}{9}+\frac {224 x^{4}}{3}+16 x^{2}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.36, size = 40, normalized size = 1.82 \begin {gather*} \frac {784}{9} \, x^{6} + \frac {625}{9} \, x^{4} \log \relax (2)^{2} + \frac {224}{3} \, x^{4} + 16 \, x^{2} - \frac {200}{9} \, {\left (7 \, x^{5} + 3 \, x^{3}\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 37, normalized size = 1.68 \begin {gather*} \frac {784\,x^6}{9}-\frac {1400\,\ln \relax (2)\,x^5}{9}+\left (\frac {625\,{\ln \relax (2)}^2}{9}+\frac {224}{3}\right )\,x^4-\frac {200\,\ln \relax (2)\,x^3}{3}+16\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.06, size = 46, normalized size = 2.09 \begin {gather*} \frac {784 x^{6}}{9} - \frac {1400 x^{5} \log {\relax (2 )}}{9} + x^{4} \left (\frac {625 \log {\relax (2 )}^{2}}{9} + \frac {224}{3}\right ) - \frac {200 x^{3} \log {\relax (2 )}}{3} + 16 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________