Optimal. Leaf size=20 \[ e^{e^3}+\frac {e^x}{\log ^2(x)}-\log ^2(x) \]
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Rubi [A] time = 0.28, antiderivative size = 15, normalized size of antiderivative = 0.75, number of steps used = 4, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {6742, 2301, 2202} \begin {gather*} \frac {e^x}{\log ^2(x)}-\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2202
Rule 2301
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 \log (x)}{x}+\frac {e^x (-2+x \log (x))}{x \log ^3(x)}\right ) \, dx\\ &=-\left (2 \int \frac {\log (x)}{x} \, dx\right )+\int \frac {e^x (-2+x \log (x))}{x \log ^3(x)} \, dx\\ &=\frac {e^x}{\log ^2(x)}-\log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 15, normalized size = 0.75 \begin {gather*} \frac {e^x}{\log ^2(x)}-\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 17, normalized size = 0.85 \begin {gather*} -\log \relax (x)^{2} + e^{\left (x - \log \left (\log \relax (x)^{2}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 15, normalized size = 0.75 \begin {gather*} -\frac {\log \relax (x)^{4} - e^{x}}{\log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 18, normalized size = 0.90
method | result | size |
default | \({\mathrm e}^{-\ln \left (\ln \relax (x )^{2}\right )+x}-\ln \relax (x )^{2}\) | \(18\) |
risch | \(-\ln \relax (x )^{2}-\frac {{\mathrm e}^{x} {\mathrm e}^{\frac {i \pi \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{3}}{2}} {\mathrm e}^{\frac {i \pi \,\mathrm {csgn}\left (i \ln \relax (x )^{2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right )^{2}}{2}}}{\ln \relax (x )^{2}}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 15, normalized size = 0.75 \begin {gather*} -\frac {\log \relax (x)^{4} - e^{x}}{\log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.23, size = 14, normalized size = 0.70 \begin {gather*} \frac {{\mathrm {e}}^x-{\ln \relax (x)}^4}{{\ln \relax (x)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 12, normalized size = 0.60 \begin {gather*} \frac {e^{x}}{\log {\relax (x )}^{2}} - \log {\relax (x )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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