Optimal. Leaf size=24 \[ \frac {x}{1+e^{16-x}-x+\log (x)-\log \left (x^2\right )} \]
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Rubi [F] time = 9.41, 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 {2+e^{16-x} (1+x)+\log (x)-\log \left (x^2\right )}{1+e^{32-2 x}+e^{16-x} (2-2 x)-2 x+x^2+\left (2+2 e^{16-x}-2 x\right ) \log (x)+\log ^2(x)+\left (-2-2 e^{16-x}+2 x-2 \log (x)\right ) \log \left (x^2\right )+\log ^2\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 \frac {e^x \left (e^{16}+2 e^x+e^{16} x+e^x \log (x)-e^x \log \left (x^2\right )\right )}{\left (e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )\right )^2} \, dx\\ &=\int \left (\frac {e^x \left (2+\log (x)-\log \left (x^2\right )\right )}{\left (1-x+\log (x)-\log \left (x^2\right )\right ) \left (e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )\right )}+\frac {e^{16+x} \left (1+x^2-x \log (x)+x \log \left (x^2\right )\right )}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )\right )^2}\right ) \, dx\\ &=\int \frac {e^x \left (2+\log (x)-\log \left (x^2\right )\right )}{\left (1-x+\log (x)-\log \left (x^2\right )\right ) \left (e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )\right )} \, dx+\int \frac {e^{16+x} \left (1+x^2-x \log (x)+x \log \left (x^2\right )\right )}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )\right )^2} \, dx\\ &=\int \left (\frac {e^{16+x}}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2}+\frac {e^{16+x} x^2}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2}-\frac {e^{16+x} x \log (x)}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2}+\frac {e^{16+x} x \log \left (x^2\right )}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2}\right ) \, dx+\int \left (\frac {e^x \log (x)}{\left (1-x+\log (x)-\log \left (x^2\right )\right ) \left (e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )\right )}+\frac {2 e^x}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )}-\frac {e^x \log \left (x^2\right )}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )}\right ) \, dx\\ &=2 \int \frac {e^x}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )} \, dx+\int \frac {e^x \log (x)}{\left (1-x+\log (x)-\log \left (x^2\right )\right ) \left (e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )\right )} \, dx+\int \frac {e^{16+x}}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2} \, dx+\int \frac {e^{16+x} x^2}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2} \, dx-\int \frac {e^{16+x} x \log (x)}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2} \, dx+\int \frac {e^{16+x} x \log \left (x^2\right )}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )^2} \, dx-\int \frac {e^x \log \left (x^2\right )}{\left (-1+x-\log (x)+\log \left (x^2\right )\right ) \left (-e^{16}-e^x+e^x x-e^x \log (x)+e^x \log \left (x^2\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 2.56, size = 35, normalized size = 1.46 \begin {gather*} \frac {e^x x}{e^{16}+e^x-e^x x+e^x \log (x)-e^x \log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 18, normalized size = 0.75 \begin {gather*} -\frac {x}{x - e^{\left (-x + 16\right )} + \log \relax (x) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 18, normalized size = 0.75 \begin {gather*} -\frac {x}{x - e^{\left (-x + 16\right )} + \log \relax (x) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.08, size = 72, normalized size = 3.00
method | result | size |
risch | \(-\frac {2 x}{-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 x -2 \,{\mathrm e}^{16-x}+2 \ln \relax (x )-2}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 20, normalized size = 0.83 \begin {gather*} -\frac {x e^{x}}{{\left (x + \log \relax (x) - 1\right )} e^{x} - e^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.17, size = 38, normalized size = 1.58 \begin {gather*} \frac {x\,{\mathrm {e}}^{x-16}}{{\mathrm {e}}^{x-16}-x\,{\mathrm {e}}^{x-16}+{\mathrm {e}}^{x-16}\,\ln \relax (x)-\ln \left (x^2\right )\,{\mathrm {e}}^{x-16}+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 12, normalized size = 0.50 \begin {gather*} \frac {x}{- x + e^{16 - x} - \log {\relax (x )} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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