Optimal. Leaf size=26 \[ -5-x+\log (2)-x \log \left (x-\left (-4+e^{3+x} x\right ) \log (x)\right ) \]
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Rubi [F]
time = 0.85, 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 {4+2 x-e^{3+x} x+\left (4+e^{3+x} \left (-2 x-x^2\right )\right ) \log (x)+\left (x+\left (4-e^{3+x} x\right ) \log (x)\right ) \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right )}{-x+\left (-4+e^{3+x} x\right ) \log (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 (-\frac {x+x^2 \log (x)+4 \log ^2(x)+4 x \log ^2(x)}{\log (x) \left (-x-4 \log (x)+e^{3+x} x \log (x)\right )}+\frac {-1-2 \log (x)-x \log (x)-\log (x) \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right )}{\log (x)}\right ) \, dx\\ &=-\int \frac {x+x^2 \log (x)+4 \log ^2(x)+4 x \log ^2(x)}{\log (x) \left (-x-4 \log (x)+e^{3+x} x \log (x)\right )} \, dx+\int \frac {-1-2 \log (x)-x \log (x)-\log (x) \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right )}{\log (x)} \, dx\\ &=-\int \left (\frac {x^2}{-x-4 \log (x)+e^{3+x} x \log (x)}+\frac {x}{\log (x) \left (-x-4 \log (x)+e^{3+x} x \log (x)\right )}+\frac {4 \log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)}+\frac {4 x \log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)}\right ) \, dx+\int \left (\frac {-1-2 \log (x)-x \log (x)}{\log (x)}-\log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right )\right ) \, dx\\ &=-\left (4 \int \frac {\log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx\right )-4 \int \frac {x \log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx+\int \frac {-1-2 \log (x)-x \log (x)}{\log (x)} \, dx-\int \frac {x^2}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-\int \frac {x}{\log (x) \left (-x-4 \log (x)+e^{3+x} x \log (x)\right )} \, dx-\int \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right ) \, dx\\ &=-\left (4 \int \frac {\log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx\right )-4 \int \frac {x \log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx+\int \left (-2-x-\frac {1}{\log (x)}\right ) \, dx-\int \frac {x^2}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-\int \frac {x}{\log (x) \left (-x-4 \log (x)+e^{3+x} x \log (x)\right )} \, dx-\int \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right ) \, dx\\ &=-2 x-\frac {x^2}{2}-4 \int \frac {\log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-4 \int \frac {x \log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-\int \frac {1}{\log (x)} \, dx-\int \frac {x^2}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-\int \frac {x}{\log (x) \left (-x-4 \log (x)+e^{3+x} x \log (x)\right )} \, dx-\int \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right ) \, dx\\ &=-2 x-\frac {x^2}{2}-\text {li}(x)-4 \int \frac {\log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-4 \int \frac {x \log (x)}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-\int \frac {x^2}{-x-4 \log (x)+e^{3+x} x \log (x)} \, dx-\int \frac {x}{\log (x) \left (-x-4 \log (x)+e^{3+x} x \log (x)\right )} \, dx-\int \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 23, normalized size = 0.88 \begin {gather*} -x-x \log \left (x+\left (4-e^{3+x} x\right ) \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 23, normalized size = 0.88
method | result | size |
risch | \(-x \ln \left (\left (-{\mathrm e}^{3+x} x +4\right ) \ln \left (x \right )+x \right )-x\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 22, normalized size = 0.85 \begin {gather*} -x \log \left (-{\left (x e^{\left (x + 3\right )} - 4\right )} \log \left (x\right ) + x\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.60, size = 22, normalized size = 0.85 \begin {gather*} -x \log \left (-{\left (x e^{\left (x + 3\right )} - 4\right )} \log \left (x\right ) + x\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.54, size = 19, normalized size = 0.73 \begin {gather*} - x \log {\left (x + \left (- x e^{x + 3} + 4\right ) \log {\left (x \right )} \right )} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 23, normalized size = 0.88 \begin {gather*} -x \log \left (-x e^{\left (x + 3\right )} \log \left (x\right ) + x + 4 \, \log \left (x\right )\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.90, size = 20, normalized size = 0.77 \begin {gather*} -x\,\left (\ln \left (x-\ln \left (x\right )\,\left (x\,{\mathrm {e}}^3\,{\mathrm {e}}^x-4\right )\right )+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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