Optimal. Leaf size=23 \[ -x+x^2+\left (-3-16 x^2-\log (\log (3+x))\right )^2 \]
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Rubi [F] time = 0.39, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {6+32 x^2+\left (-3+581 x+194 x^2+3072 x^3+1024 x^4\right ) \log (3+x)+\left (2+\left (192 x+64 x^2\right ) \log (3+x)\right ) \log (\log (3+x))}{(3+x) \log (3+x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+194 x+1024 x^3+64 x \log (\log (3+x))+\frac {2 \left (3+16 x^2+\log (\log (3+x))\right )}{(3+x) \log (3+x)}\right ) \, dx\\ &=-x+97 x^2+256 x^4+2 \int \frac {3+16 x^2+\log (\log (3+x))}{(3+x) \log (3+x)} \, dx+64 \int x \log (\log (3+x)) \, dx\\ &=-x+97 x^2+256 x^4+2 \int \left (\frac {3+16 x^2}{(3+x) \log (3+x)}+\frac {\log (\log (3+x))}{(3+x) \log (3+x)}\right ) \, dx+64 \int x \log (\log (3+x)) \, dx\\ &=-x+97 x^2+256 x^4+2 \int \frac {3+16 x^2}{(3+x) \log (3+x)} \, dx+2 \int \frac {\log (\log (3+x))}{(3+x) \log (3+x)} \, dx+64 \int x \log (\log (3+x)) \, dx\\ &=-x+97 x^2+256 x^4+\log ^2(\log (3+x))+2 \int \left (-\frac {48}{\log (3+x)}+\frac {16 x}{\log (3+x)}+\frac {147}{(3+x) \log (3+x)}\right ) \, dx+64 \int x \log (\log (3+x)) \, dx\\ &=-x+97 x^2+256 x^4+\log ^2(\log (3+x))+32 \int \frac {x}{\log (3+x)} \, dx+64 \int x \log (\log (3+x)) \, dx-96 \int \frac {1}{\log (3+x)} \, dx+294 \int \frac {1}{(3+x) \log (3+x)} \, dx\\ &=-x+97 x^2+256 x^4+\log ^2(\log (3+x))+32 \int \left (-\frac {3}{\log (3+x)}+\frac {3+x}{\log (3+x)}\right ) \, dx+64 \int x \log (\log (3+x)) \, dx-96 \operatorname {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,3+x\right )+294 \operatorname {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,3+x\right )\\ &=-x+97 x^2+256 x^4+\log ^2(\log (3+x))-96 \text {li}(3+x)+32 \int \frac {3+x}{\log (3+x)} \, dx+64 \int x \log (\log (3+x)) \, dx-96 \int \frac {1}{\log (3+x)} \, dx+294 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (3+x)\right )\\ &=-x+97 x^2+256 x^4+294 \log (\log (3+x))+\log ^2(\log (3+x))-96 \text {li}(3+x)+32 \operatorname {Subst}\left (\int \frac {x}{\log (x)} \, dx,x,3+x\right )+64 \int x \log (\log (3+x)) \, dx-96 \operatorname {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,3+x\right )\\ &=-x+97 x^2+256 x^4+294 \log (\log (3+x))+\log ^2(\log (3+x))-192 \text {li}(3+x)+32 \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (3+x)\right )+64 \int x \log (\log (3+x)) \, dx\\ &=-x+97 x^2+256 x^4+32 \text {Ei}(2 \log (3+x))+294 \log (\log (3+x))+\log ^2(\log (3+x))-192 \text {li}(3+x)+64 \int x \log (\log (3+x)) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 41, normalized size = 1.78 \begin {gather*} -x+97 x^2+256 x^4+294 \log (\log (3+x))+32 (-3+x) (3+x) \log (\log (3+x))+\log ^2(\log (3+x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.12, size = 35, normalized size = 1.52 \begin {gather*} 256 \, x^{4} + 97 \, x^{2} + 2 \, {\left (16 \, x^{2} + 3\right )} \log \left (\log \left (x + 3\right )\right ) + \log \left (\log \left (x + 3\right )\right )^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 38, normalized size = 1.65 \begin {gather*} 256 \, x^{4} + 32 \, x^{2} \log \left (\log \left (x + 3\right )\right ) + 97 \, x^{2} + \log \left (\log \left (x + 3\right )\right )^{2} - x + 6 \, \log \left (\log \left (x + 3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.37, size = 39, normalized size = 1.70
method | result | size |
risch | \(\ln \left (\ln \left (3+x \right )\right )^{2}+32 x^{2} \ln \left (\ln \left (3+x \right )\right )+256 x^{4}+97 x^{2}-x +6 \ln \left (\ln \left (3+x \right )\right )\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 38, normalized size = 1.65 \begin {gather*} 256 \, x^{4} + 32 \, x^{2} \log \left (\log \left (x + 3\right )\right ) + 97 \, x^{2} + \log \left (\log \left (x + 3\right )\right )^{2} - x + 6 \, \log \left (\log \left (x + 3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.30, size = 38, normalized size = 1.65 \begin {gather*} 256\,x^4+32\,x^2\,\ln \left (\ln \left (x+3\right )\right )+97\,x^2-x+{\ln \left (\ln \left (x+3\right )\right )}^2+6\,\ln \left (\ln \left (x+3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 39, normalized size = 1.70 \begin {gather*} 256 x^{4} + 32 x^{2} \log {\left (\log {\left (x + 3 \right )} \right )} + 97 x^{2} - x + \log {\left (\log {\left (x + 3 \right )} \right )}^{2} + 6 \log {\left (\log {\left (x + 3 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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