Optimal. Leaf size=17 \[ -13-e^x+2 x-\log (x)+\log (\log (x)) \]
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Rubi [A]
time = 0.30, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps
used = 9, number of rules used = 5, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.208, Rules used = {6874, 2225, 45,
2339, 29} \begin {gather*} 2 x-e^x-\log (x)+\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 45
Rule 2225
Rule 2339
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^x+\frac {1-\log (x)+2 x \log (x)}{x \log (x)}\right ) \, dx\\ &=-\int e^x \, dx+\int \frac {1-\log (x)+2 x \log (x)}{x \log (x)} \, dx\\ &=-e^x+\int \left (\frac {-1+2 x}{x}+\frac {1}{x \log (x)}\right ) \, dx\\ &=-e^x+\int \frac {-1+2 x}{x} \, dx+\int \frac {1}{x \log (x)} \, dx\\ &=-e^x+\int \left (2-\frac {1}{x}\right ) \, dx+\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-e^x+2 x-\log (x)+\log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 16, normalized size = 0.94 \begin {gather*} -e^x+2 x-\log (x)+\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 16, normalized size = 0.94
method | result | size |
default | \(\ln \left (\ln \left (x \right )\right )+2 x -\ln \left (x \right )-{\mathrm e}^{x}\) | \(16\) |
norman | \(\ln \left (\ln \left (x \right )\right )+2 x -\ln \left (x \right )-{\mathrm e}^{x}\) | \(16\) |
risch | \(\ln \left (\ln \left (x \right )\right )+2 x -\ln \left (x \right )-{\mathrm e}^{x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 15, normalized size = 0.88 \begin {gather*} 2 \, x - e^{x} - \log \left (x\right ) + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 15, normalized size = 0.88 \begin {gather*} 2 \, x - e^{x} - \log \left (x\right ) + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 14, normalized size = 0.82 \begin {gather*} 2 x - e^{x} - \log {\left (x \right )} + \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 15, normalized size = 0.88 \begin {gather*} 2 \, x - e^{x} - \log \left (x\right ) + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 9.26, size = 15, normalized size = 0.88 \begin {gather*} 2\,x+\ln \left (\ln \left (x\right )\right )-{\mathrm {e}}^x-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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