Optimal. Leaf size=18 \[ -3+\left (3+x+\frac {45}{(2+x) \log ^2(2)}\right )^2 \]
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Rubi [A] time = 0.06, antiderivative size = 29, normalized size of antiderivative = 1.61, number of steps used = 3, number of rules used = 2, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {12, 2074} \begin {gather*} x^2+6 x+\frac {2025}{(x+2)^2 \log ^4(2)}+\frac {90}{(x+2) \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-4050+(-180-90 x) \log ^2(2)+\left (48+88 x+60 x^2+18 x^3+2 x^4\right ) \log ^4(2)}{8+12 x+6 x^2+x^3} \, dx}{\log ^4(2)}\\ &=\frac {\int \left (-\frac {4050}{(2+x)^3}-\frac {90 \log ^2(2)}{(2+x)^2}+6 \log ^4(2)+2 x \log ^4(2)\right ) \, dx}{\log ^4(2)}\\ &=6 x+x^2+\frac {2025}{(2+x)^2 \log ^4(2)}+\frac {90}{(2+x) \log ^2(2)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 29, normalized size = 1.61 \begin {gather*} 6 x+x^2+\frac {2025}{(2+x)^2 \log ^4(2)}+\frac {90}{(2+x) \log ^2(2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 48, normalized size = 2.67 \begin {gather*} \frac {{\left (x^{4} + 10 \, x^{3} + 28 \, x^{2} + 24 \, x\right )} \log \relax (2)^{4} + 90 \, {\left (x + 2\right )} \log \relax (2)^{2} + 2025}{{\left (x^{2} + 4 \, x + 4\right )} \log \relax (2)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 43, normalized size = 2.39 \begin {gather*} \frac {x^{2} \log \relax (2)^{4} + 6 \, x \log \relax (2)^{4} + \frac {45 \, {\left (2 \, x \log \relax (2)^{2} + 4 \, \log \relax (2)^{2} + 45\right )}}{{\left (x + 2\right )}^{2}}}{\log \relax (2)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 38, normalized size = 2.11
method | result | size |
risch | \(x^{2}+6 x +\frac {90 x \ln \relax (2)^{2}+180 \ln \relax (2)^{2}+2025}{\ln \relax (2)^{4} \left (x^{2}+4 x +4\right )}\) | \(38\) |
default | \(\frac {x^{2} \ln \relax (2)^{4}+6 x \ln \relax (2)^{4}+\frac {90 \ln \relax (2)^{2}}{2+x}+\frac {2025}{\left (2+x \right )^{2}}}{\ln \relax (2)^{4}}\) | \(40\) |
gosper | \(\frac {\ln \relax (2)^{4} x^{4}+10 x^{3} \ln \relax (2)^{4}-88 x \ln \relax (2)^{4}-112 \ln \relax (2)^{4}+90 x \ln \relax (2)^{2}+180 \ln \relax (2)^{2}+2025}{\ln \relax (2)^{4} \left (x^{2}+4 x +4\right )}\) | \(61\) |
norman | \(\frac {x^{4} \ln \relax (2)^{3}-2 \ln \relax (2) \left (44 \ln \relax (2)^{2}-45\right ) x +10 x^{3} \ln \relax (2)^{3}-\frac {112 \ln \relax (2)^{4}-180 \ln \relax (2)^{2}-2025}{\ln \relax (2)}}{\left (2+x \right )^{2} \ln \relax (2)^{3}}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 48, normalized size = 2.67 \begin {gather*} \frac {x^{2} \log \relax (2)^{4} + 6 \, x \log \relax (2)^{4} + \frac {45 \, {\left (2 \, x \log \relax (2)^{2} + 4 \, \log \relax (2)^{2} + 45\right )}}{x^{2} + 4 \, x + 4}}{\log \relax (2)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 58, normalized size = 3.22 \begin {gather*} \frac {28\,x^2\,{\ln \relax (2)}^4+10\,x^3\,{\ln \relax (2)}^4+x^4\,{\ln \relax (2)}^4+90\,x\,{\ln \relax (2)}^2+24\,x\,{\ln \relax (2)}^4+180\,{\ln \relax (2)}^2+2025}{{\ln \relax (2)}^4\,{\left (x+2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.30, size = 46, normalized size = 2.56 \begin {gather*} x^{2} + 6 x + \frac {90 x \log {\relax (2 )}^{2} + 180 \log {\relax (2 )}^{2} + 2025}{x^{2} \log {\relax (2 )}^{4} + 4 x \log {\relax (2 )}^{4} + 4 \log {\relax (2 )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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