Optimal. Leaf size=15 \[ -9-e^{5 \log ^4(x)}-4 x \]
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Rubi [A] time = 0.07, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 4, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14, 2209} \begin {gather*} -4 x-e^{5 \log ^4(x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4-\frac {20 e^{5 \log ^4(x)} \log ^3(x)}{x}\right ) \, dx\\ &=-4 x-20 \int \frac {e^{5 \log ^4(x)} \log ^3(x)}{x} \, dx\\ &=-4 x-20 \operatorname {Subst}\left (\int e^{5 x^4} x^3 \, dx,x,\log (x)\right )\\ &=-e^{5 \log ^4(x)}-4 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 1.07 \begin {gather*} -4 \left (\frac {1}{4} e^{5 \log ^4(x)}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 13, normalized size = 0.87 \begin {gather*} -4 \, x - e^{\left (5 \, \log \relax (x)^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 13, normalized size = 0.87 \begin {gather*} -4 \, x - e^{\left (5 \, \log \relax (x)^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.93
method | result | size |
default | \(-4 x -{\mathrm e}^{5 \ln \relax (x )^{4}}\) | \(14\) |
norman | \(-4 x -{\mathrm e}^{5 \ln \relax (x )^{4}}\) | \(14\) |
risch | \(-4 x -{\mathrm e}^{5 \ln \relax (x )^{4}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 13, normalized size = 0.87 \begin {gather*} -4 \, x - e^{\left (5 \, \log \relax (x)^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.27, size = 13, normalized size = 0.87 \begin {gather*} -4\,x-{\mathrm {e}}^{5\,{\ln \relax (x)}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 12, normalized size = 0.80 \begin {gather*} - 4 x - e^{5 \log {\relax (x )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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