Optimal. Leaf size=27 \[ e^{4+x}-4 x^2-\frac {\log (10)}{3}+\frac {5}{\log (x)}-\log (x) \]
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Rubi [A] time = 0.41, antiderivative size = 21, normalized size of antiderivative = 0.78, number of steps used = 10, number of rules used = 6, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.207, Rules used = {6742, 2194, 6688, 14, 2302, 30} \begin {gather*} -4 x^2+e^{x+4}-\log (x)+\frac {5}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 30
Rule 2194
Rule 2302
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{4+x}+\frac {-5-\log ^2(x)-8 x^2 \log ^2(x)}{x \log ^2(x)}\right ) \, dx\\ &=\int e^{4+x} \, dx+\int \frac {-5-\log ^2(x)-8 x^2 \log ^2(x)}{x \log ^2(x)} \, dx\\ &=e^{4+x}+\int \frac {-1-8 x^2-\frac {5}{\log ^2(x)}}{x} \, dx\\ &=e^{4+x}+\int \left (\frac {-1-8 x^2}{x}-\frac {5}{x \log ^2(x)}\right ) \, dx\\ &=e^{4+x}-5 \int \frac {1}{x \log ^2(x)} \, dx+\int \frac {-1-8 x^2}{x} \, dx\\ &=e^{4+x}-5 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )+\int \left (-\frac {1}{x}-8 x\right ) \, dx\\ &=e^{4+x}-4 x^2+\frac {5}{\log (x)}-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 21, normalized size = 0.78 \begin {gather*} e^{4+x}-4 x^2+\frac {5}{\log (x)}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 27, normalized size = 1.00 \begin {gather*} -\frac {{\left (4 \, x^{2} - e^{\left (x + 4\right )}\right )} \log \relax (x) + \log \relax (x)^{2} - 5}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 27, normalized size = 1.00 \begin {gather*} -\frac {4 \, x^{2} \log \relax (x) - e^{\left (x + 4\right )} \log \relax (x) + \log \relax (x)^{2} - 5}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 0.78
method | result | size |
default | \(\frac {5}{\ln \relax (x )}-4 x^{2}-\ln \relax (x )+{\mathrm e}^{4+x}\) | \(21\) |
risch | \(\frac {5}{\ln \relax (x )}-4 x^{2}-\ln \relax (x )+{\mathrm e}^{4+x}\) | \(21\) |
norman | \(\frac {5+{\mathrm e}^{4+x} \ln \relax (x )-4 x^{2} \ln \relax (x )}{\ln \relax (x )}-\ln \relax (x )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 20, normalized size = 0.74 \begin {gather*} -4 \, x^{2} + \frac {5}{\log \relax (x)} + e^{\left (x + 4\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.87, size = 20, normalized size = 0.74 \begin {gather*} {\mathrm {e}}^{x+4}-\ln \relax (x)+\frac {5}{\ln \relax (x)}-4\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 17, normalized size = 0.63 \begin {gather*} - 4 x^{2} + e^{x + 4} - \log {\relax (x )} + \frac {5}{\log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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