Optimal. Leaf size=27 \[ \left (x^2+4 \left (2 x+\frac {\log ^2(2)}{5 (3+3 x)}\right )\right )^2 \]
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Rubi [A] time = 0.10, antiderivative size = 49, normalized size of antiderivative = 1.81, number of steps used = 2, number of rules used = 1, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {2074} \begin {gather*} x^4+16 x^3+64 x^2+\frac {16 \log ^4(2)}{225 (x+1)^2}+\frac {8}{15} x \log ^2(2)-\frac {56 \log ^2(2)}{15 (x+1)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (128 x+48 x^2+4 x^3+\frac {8 \log ^2(2)}{15}+\frac {56 \log ^2(2)}{15 (1+x)^2}-\frac {32 \log ^4(2)}{225 (1+x)^3}\right ) \, dx\\ &=64 x^2+16 x^3+x^4+\frac {8}{15} x \log ^2(2)-\frac {56 \log ^2(2)}{15 (1+x)}+\frac {16 \log ^4(2)}{225 (1+x)^2}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.05, size = 57, normalized size = 2.11 \begin {gather*} \frac {4}{225} \left (-\frac {11025}{4}+3600 x^2+900 x^3+\frac {225 x^4}{4}+30 x \log ^2(2)+\frac {30 (-6+x) \log ^2(2)}{1+x}+\frac {4 \log ^4(2)}{(1+x)^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.52, size = 63, normalized size = 2.33 \begin {gather*} \frac {225 \, x^{6} + 4050 \, x^{5} + 21825 \, x^{4} + 16 \, \log \relax (2)^{4} + 32400 \, x^{3} + 120 \, {\left (x^{3} + 2 \, x^{2} - 6 \, x - 7\right )} \log \relax (2)^{2} + 14400 \, x^{2}}{225 \, {\left (x^{2} + 2 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 48, normalized size = 1.78 \begin {gather*} x^{4} + 16 \, x^{3} + \frac {8}{15} \, x \log \relax (2)^{2} + 64 \, x^{2} + \frac {8 \, {\left (2 \, \log \relax (2)^{4} - 105 \, x \log \relax (2)^{2} - 105 \, \log \relax (2)^{2}\right )}}{225 \, {\left (x + 1\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 44, normalized size = 1.63
method | result | size |
default | \(x^{4}+16 x^{3}+64 x^{2}+\frac {8 x \ln \relax (2)^{2}}{15}+\frac {16 \ln \relax (2)^{4}}{225 \left (x +1\right )^{2}}-\frac {56 \ln \relax (2)^{2}}{15 \left (x +1\right )}\) | \(44\) |
risch | \(x^{4}+\frac {8 x \ln \relax (2)^{2}}{15}+16 x^{3}+64 x^{2}+\frac {-\frac {56 x \ln \relax (2)^{2}}{15}+\frac {16 \ln \relax (2)^{4}}{225}-\frac {56 \ln \relax (2)^{2}}{15}}{x^{2}+2 x +1}\) | \(53\) |
norman | \(\frac {x^{6}+\left (144+\frac {8 \ln \relax (2)^{2}}{15}\right ) x^{3}+\left (-128-\frac {16 \ln \relax (2)^{2}}{3}\right ) x +97 x^{4}+18 x^{5}-64-\frac {24 \ln \relax (2)^{2}}{5}+\frac {16 \ln \relax (2)^{4}}{225}}{\left (x +1\right )^{2}}\) | \(56\) |
gosper | \(\frac {225 x^{6}+120 x^{3} \ln \relax (2)^{2}+4050 x^{5}+16 \ln \relax (2)^{4}+21825 x^{4}-1200 x \ln \relax (2)^{2}+32400 x^{3}-1080 \ln \relax (2)^{2}-28800 x -14400}{225 x^{2}+450 x +225}\) | \(66\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.35, size = 53, normalized size = 1.96 \begin {gather*} x^{4} + 16 \, x^{3} + \frac {8}{15} \, x \log \relax (2)^{2} + 64 \, x^{2} + \frac {8 \, {\left (2 \, \log \relax (2)^{4} - 105 \, x \log \relax (2)^{2} - 105 \, \log \relax (2)^{2}\right )}}{225 \, {\left (x^{2} + 2 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.24, size = 55, normalized size = 2.04 \begin {gather*} \frac {8\,x\,{\ln \relax (2)}^2}{15}-\frac {840\,x\,{\ln \relax (2)}^2+840\,{\ln \relax (2)}^2-16\,{\ln \relax (2)}^4}{225\,x^2+450\,x+225}+64\,x^2+16\,x^3+x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.23, size = 54, normalized size = 2.00 \begin {gather*} x^{4} + 16 x^{3} + 64 x^{2} + \frac {8 x \log {\relax (2 )}^{2}}{15} + \frac {- 840 x \log {\relax (2 )}^{2} - 840 \log {\relax (2 )}^{2} + 16 \log {\relax (2 )}^{4}}{225 x^{2} + 450 x + 225} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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