Optimal. Leaf size=25 \[ 1+(5+x) \left (5-e^x+2 x+\log ^2\left (2 \log \left (x^2\right )\right )\right ) \]
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Rubi [F] time = 0.61, 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 {\left (15 x+4 x^2+e^x \left (-6 x-x^2\right )\right ) \log \left (x^2\right )+(20+4 x) \log \left (2 \log \left (x^2\right )\right )+x \log \left (x^2\right ) \log ^2\left (2 \log \left (x^2\right )\right )}{x \log \left (x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (15+4 x-e^x (6+x)+\frac {4 (5+x) \log \left (2 \log \left (x^2\right )\right )}{x \log \left (x^2\right )}+\log ^2\left (2 \log \left (x^2\right )\right )\right ) \, dx\\ &=15 x+2 x^2+4 \int \frac {(5+x) \log \left (2 \log \left (x^2\right )\right )}{x \log \left (x^2\right )} \, dx-\int e^x (6+x) \, dx+\int \log ^2\left (2 \log \left (x^2\right )\right ) \, dx\\ &=15 x+2 x^2-e^x (6+x)+4 \int \left (\frac {\log \left (2 \log \left (x^2\right )\right )}{\log \left (x^2\right )}+\frac {5 \log \left (2 \log \left (x^2\right )\right )}{x \log \left (x^2\right )}\right ) \, dx+\int e^x \, dx+\int \log ^2\left (2 \log \left (x^2\right )\right ) \, dx\\ &=e^x+15 x+2 x^2-e^x (6+x)+4 \int \frac {\log \left (2 \log \left (x^2\right )\right )}{\log \left (x^2\right )} \, dx+20 \int \frac {\log \left (2 \log \left (x^2\right )\right )}{x \log \left (x^2\right )} \, dx+\int \log ^2\left (2 \log \left (x^2\right )\right ) \, dx\\ &=e^x+15 x+2 x^2-e^x (6+x)+4 \int \frac {\log \left (2 \log \left (x^2\right )\right )}{\log \left (x^2\right )} \, dx+10 \operatorname {Subst}\left (\int \frac {\log (2 x)}{x} \, dx,x,\log \left (x^2\right )\right )+\int \log ^2\left (2 \log \left (x^2\right )\right ) \, dx\\ &=e^x+15 x+2 x^2-e^x (6+x)+5 \log ^2\left (2 \log \left (x^2\right )\right )+4 \int \frac {\log \left (2 \log \left (x^2\right )\right )}{\log \left (x^2\right )} \, dx+\int \log ^2\left (2 \log \left (x^2\right )\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 29, normalized size = 1.16 \begin {gather*} -e^x (5+x)+x (15+2 x)+(5+x) \log ^2\left (2 \log \left (x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 29, normalized size = 1.16 \begin {gather*} {\left (x + 5\right )} \log \left (2 \, \log \left (x^{2}\right )\right )^{2} + 2 \, x^{2} - {\left (x + 5\right )} e^{x} + 15 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.76, size = 40, normalized size = 1.60 \begin {gather*} x \log \left (2 \, \log \left (x^{2}\right )\right )^{2} + 2 \, x^{2} - x e^{x} + 5 \, \log \left (2 \, \log \left (x^{2}\right )\right )^{2} + 15 \, x - 5 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.70, size = 59, normalized size = 2.36
method | result | size |
risch | \(\left (5+x \right ) \ln \left (4 \ln \relax (x )-i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}\right )^{2}+2 x^{2}-{\mathrm e}^{x} x +15 x -5 \,{\mathrm e}^{x}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.49, size = 50, normalized size = 2.00 \begin {gather*} 4 \, x \log \relax (2)^{2} + {\left (x + 5\right )} \log \left (\log \relax (x)\right )^{2} + 2 \, x^{2} - {\left (x - 1\right )} e^{x} + 4 \, {\left (x \log \relax (2) + 5 \, \log \relax (2)\right )} \log \left (\log \relax (x)\right ) + 15 \, x - 6 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.54, size = 29, normalized size = 1.16 \begin {gather*} 15\,x-{\mathrm {e}}^x\,\left (x+5\right )+{\ln \left (2\,\ln \left (x^2\right )\right )}^2\,\left (x+5\right )+2\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.49, size = 29, normalized size = 1.16 \begin {gather*} 2 x^{2} + 15 x + \left (- x - 5\right ) e^{x} + \left (x + 5\right ) \log {\left (2 \log {\left (x^{2} \right )} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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