Optimal. Leaf size=26 \[ 2-e^x+x-(-3+x) x-x^{\frac {4}{\log \left (x^2\right )}} \]
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Rubi [F] time = 0.53, 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 {x^{\frac {4}{\log \left (x^2\right )}} \left (8 \log (x)-4 \log \left (x^2\right )\right )+\left (4 x-e^x x-2 x^2\right ) \log ^2\left (x^2\right )}{x \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 \left (4-e^x-2 x-\frac {4 x^{-1+\frac {4}{\log \left (x^2\right )}} \left (-2 \log (x)+\log \left (x^2\right )\right )}{\log ^2\left (x^2\right )}\right ) \, dx\\ &=4 x-x^2-4 \int \frac {x^{-1+\frac {4}{\log \left (x^2\right )}} \left (-2 \log (x)+\log \left (x^2\right )\right )}{\log ^2\left (x^2\right )} \, dx-\int e^x \, dx\\ &=-e^x+4 x-x^2-4 \int \left (-\frac {2 x^{-1+\frac {4}{\log \left (x^2\right )}} \log (x)}{\log ^2\left (x^2\right )}+\frac {x^{-1+\frac {4}{\log \left (x^2\right )}}}{\log \left (x^2\right )}\right ) \, dx\\ &=-e^x+4 x-x^2-4 \int \frac {x^{-1+\frac {4}{\log \left (x^2\right )}}}{\log \left (x^2\right )} \, dx+8 \int \frac {x^{-1+\frac {4}{\log \left (x^2\right )}} \log (x)}{\log ^2\left (x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 26, normalized size = 1.00 \begin {gather*} -e^x+4 x-x^2-x^{\frac {4}{\log \left (x^2\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 13, normalized size = 0.50 \begin {gather*} -x^{2} + 4 \, x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 13, normalized size = 0.50 \begin {gather*} -x^{2} + 4 \, x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 36, normalized size = 1.38
method | result | size |
default | \(4 x -{\mathrm e}^{2-\frac {2 \left (\ln \left (x^{2}\right )-2 \ln \relax (x )\right )}{\ln \left (x^{2}\right )}}-x^{2}-{\mathrm e}^{x}\) | \(36\) |
risch | \(-x^{2}+4 x -{\mathrm e}^{x}-x^{\frac {4}{i \pi \,\mathrm {csgn}\left (i x \right )-i \pi \,\mathrm {csgn}\left (i x^{2}\right )+2 \ln \relax (x )}}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 0.65 \begin {gather*} -x^{2} + 4 \, x - 2 \, e^{2} - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.25, size = 25, normalized size = 0.96 \begin {gather*} 4\,x-{\mathrm {e}}^x-x^2-x^{\frac {4}{\ln \left (x^2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 8, normalized size = 0.31 \begin {gather*} - x^{2} + 4 x - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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