Optimal. Leaf size=19 \[ \left (-3+2 \left (-1-2 x+x^3 \log ^2(4)\right )\right )^2 \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 36, normalized size of antiderivative = 1.89, number of steps used = 2, number of rules used = 0, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 4 x^6 \log ^4(4)-16 x^4 \log ^2(4)-20 x^3 \log ^2(4)+16 x^2+40 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=40 x+16 x^2+4 x^6 \log ^4(4)+\log ^2(4) \int \left (-60 x^2-64 x^3\right ) \, dx\\ &=40 x+16 x^2-20 x^3 \log ^2(4)-16 x^4 \log ^2(4)+4 x^6 \log ^4(4)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 36, normalized size = 1.89 \begin {gather*} 40 x+16 x^2-20 x^3 \log ^2(4)-16 x^4 \log ^2(4)+4 x^6 \log ^4(4) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.61, size = 35, normalized size = 1.84 \begin {gather*} 64 \, x^{6} \log \relax (2)^{4} - 16 \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \relax (2)^{2} + 16 \, x^{2} + 40 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.12, size = 35, normalized size = 1.84 \begin {gather*} 64 \, x^{6} \log \relax (2)^{4} - 16 \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \relax (2)^{2} + 16 \, x^{2} + 40 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.03, size = 36, normalized size = 1.89
method | result | size |
gosper | \(8 x \left (8 x^{5} \ln \relax (2)^{4}-8 x^{3} \ln \relax (2)^{2}-10 x^{2} \ln \relax (2)^{2}+2 x +5\right )\) | \(36\) |
default | \(64 x^{6} \ln \relax (2)^{4}+4 \ln \relax (2)^{2} \left (-16 x^{4}-20 x^{3}\right )+16 x^{2}+40 x\) | \(36\) |
norman | \(40 x +16 x^{2}-80 x^{3} \ln \relax (2)^{2}-64 x^{4} \ln \relax (2)^{2}+64 x^{6} \ln \relax (2)^{4}\) | \(37\) |
risch | \(40 x +16 x^{2}-80 x^{3} \ln \relax (2)^{2}-64 x^{4} \ln \relax (2)^{2}+64 x^{6} \ln \relax (2)^{4}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.35, size = 35, normalized size = 1.84 \begin {gather*} 64 \, x^{6} \log \relax (2)^{4} - 16 \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \relax (2)^{2} + 16 \, x^{2} + 40 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.99, size = 36, normalized size = 1.89 \begin {gather*} 64\,{\ln \relax (2)}^4\,x^6-64\,{\ln \relax (2)}^2\,x^4-80\,{\ln \relax (2)}^2\,x^3+16\,x^2+40\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.06, size = 37, normalized size = 1.95 \begin {gather*} 64 x^{6} \log {\relax (2 )}^{4} - 64 x^{4} \log {\relax (2 )}^{2} - 80 x^{3} \log {\relax (2 )}^{2} + 16 x^{2} + 40 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________