Optimal. Leaf size=26 \[ 3+e^{\frac {e^{4 x}}{x^4}}-\log \left (3-\frac {e^x}{x}\right ) \]
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Rubi [F] time = 1.27, 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 {e^x \left (x^4-x^5\right )+e^{\frac {e^{4 x}}{x^4}} \left (e^{5 x} (-4+4 x)+e^{4 x} \left (12 x-12 x^2\right )\right )}{e^x x^5-3 x^6} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x (1-x) \left (-4 e^{\frac {e^{4 x}}{x^4}+4 x}+12 e^{\frac {e^{4 x}}{x^4}+3 x} x+x^4\right )}{e^x x^5-3 x^6} \, dx\\ &=\int \left (\frac {4 e^{\frac {e^{4 x}}{x^4}+4 x} (-1+x)}{x^5}-\frac {e^x (-1+x)}{\left (e^x-3 x\right ) x}\right ) \, dx\\ &=4 \int \frac {e^{\frac {e^{4 x}}{x^4}+4 x} (-1+x)}{x^5} \, dx-\int \frac {e^x (-1+x)}{\left (e^x-3 x\right ) x} \, dx\\ &=4 \int \left (-\frac {e^{\frac {e^{4 x}}{x^4}+4 x}}{x^5}+\frac {e^{\frac {e^{4 x}}{x^4}+4 x}}{x^4}\right ) \, dx-\operatorname {Subst}\left (\int \frac {1}{-3+x} \, dx,x,\frac {e^x}{x}\right )\\ &=-\log \left (3-\frac {e^x}{x}\right )-4 \int \frac {e^{\frac {e^{4 x}}{x^4}+4 x}}{x^5} \, dx+4 \int \frac {e^{\frac {e^{4 x}}{x^4}+4 x}}{x^4} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.61, size = 24, normalized size = 0.92 \begin {gather*} e^{\frac {e^{4 x}}{x^4}}-\log \left (e^x-3 x\right )+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 21, normalized size = 0.81 \begin {gather*} e^{\left (\frac {e^{\left (4 \, x\right )}}{x^{4}}\right )} + \log \relax (x) - \log \left (-3 \, x + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 46, normalized size = 1.77 \begin {gather*} -{\left (e^{\left (4 \, x\right )} \log \left (3 \, x - e^{x}\right ) - e^{\left (4 \, x\right )} \log \relax (x) - e^{\left (\frac {4 \, x^{5} + e^{\left (4 \, x\right )}}{x^{4}}\right )}\right )} e^{\left (-4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 22, normalized size = 0.85
method | result | size |
risch | \(\ln \relax (x )-\ln \left ({\mathrm e}^{x}-3 x \right )+{\mathrm e}^{\frac {{\mathrm e}^{4 x}}{x^{4}}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 21, normalized size = 0.81 \begin {gather*} e^{\left (\frac {e^{\left (4 \, x\right )}}{x^{4}}\right )} + \log \relax (x) - \log \left (-3 \, x + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.24, size = 21, normalized size = 0.81 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{4\,x}}{x^4}}-\ln \left ({\mathrm {e}}^x-3\,x\right )+\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 20, normalized size = 0.77 \begin {gather*} e^{\frac {e^{4 x}}{x^{4}}} + \log {\relax (x )} - \log {\left (- 3 x + e^{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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