Optimal. Leaf size=28 \[ \frac {1}{2} \left (\frac {2 e^x}{x}-\frac {\log (3)}{1-2 x \log ^4(x)}\right ) \]
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Rubi [A]
time = 0.59, antiderivative size = 25, normalized size of antiderivative = 0.89, number of steps
used = 5, number of rules used = 4, integrand size = 89, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6873, 6874,
2228, 6818} \begin {gather*} \frac {e^x}{x}-\frac {\log (3)}{2 \left (1-2 x \log ^4(x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2228
Rule 6818
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x (-1+x)-4 x^2 \log (3) \log ^3(x)+\left (e^x \left (4 x-4 x^2\right )-x^2 \log (3)\right ) \log ^4(x)+e^x \left (-4 x^2+4 x^3\right ) \log ^8(x)}{x^2 \left (1-2 x \log ^4(x)\right )^2} \, dx\\ &=\int \left (\frac {e^x (-1+x)}{x^2}-\frac {\log (3) \log ^3(x) (4+\log (x))}{\left (-1+2 x \log ^4(x)\right )^2}\right ) \, dx\\ &=-\left (\log (3) \int \frac {\log ^3(x) (4+\log (x))}{\left (-1+2 x \log ^4(x)\right )^2} \, dx\right )+\int \frac {e^x (-1+x)}{x^2} \, dx\\ &=\frac {e^x}{x}-\frac {\log (3)}{2 \left (1-2 x \log ^4(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.15, size = 22, normalized size = 0.79 \begin {gather*} \frac {e^x}{x}+\frac {\log (3)}{-2+4 x \log ^4(x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.94, size = 23, normalized size = 0.82
method | result | size |
risch | \(\frac {{\mathrm e}^{x}}{x}+\frac {\ln \left (3\right )}{4 x \ln \left (x \right )^{4}-2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.58, size = 35, normalized size = 1.25 \begin {gather*} \frac {2 \, {\left (2 \, x \log \left (x\right )^{4} - 1\right )} e^{x} + x \log \left (3\right )}{2 \, {\left (2 \, x^{2} \log \left (x\right )^{4} - x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 35, normalized size = 1.25 \begin {gather*} \frac {4 \, x e^{x} \log \left (x\right )^{4} + x \log \left (3\right ) - 2 \, e^{x}}{2 \, {\left (2 \, x^{2} \log \left (x\right )^{4} - x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 17, normalized size = 0.61 \begin {gather*} \frac {\log {\left (3 \right )}}{4 x \log {\left (x \right )}^{4} - 2} + \frac {e^{x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.62, size = 35, normalized size = 1.25 \begin {gather*} \frac {4 \, x e^{x} \log \left (x\right )^{4} + x \log \left (3\right ) - 2 \, e^{x}}{2 \, {\left (2 \, x^{2} \log \left (x\right )^{4} - x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.56, size = 21, normalized size = 0.75 \begin {gather*} \frac {{\mathrm {e}}^x}{x}+\frac {\ln \left (3\right )}{2\,\left (2\,x\,{\ln \left (x\right )}^4-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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