Optimal. Leaf size=24 \[ \frac {x+\frac {4}{e^4 \left (e^{\log ^2(x)}+x\right )}}{4 x} \]
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Rubi [A]
time = 0.19, antiderivative size = 17, normalized size of antiderivative = 0.71, number of steps
used = 3, number of rules used = 3, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {6820, 12, 6819}
\begin {gather*} \frac {1}{e^4 x \left (x+e^{\log ^2(x)}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6819
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{\log ^2(x)}-2 x-2 e^{\log ^2(x)} \log (x)}{e^4 x^2 \left (e^{\log ^2(x)}+x\right )^2} \, dx\\ &=\frac {\int \frac {-e^{\log ^2(x)}-2 x-2 e^{\log ^2(x)} \log (x)}{x^2 \left (e^{\log ^2(x)}+x\right )^2} \, dx}{e^4}\\ &=\frac {1}{e^4 x \left (e^{\log ^2(x)}+x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 17, normalized size = 0.71 \begin {gather*} \frac {1}{e^4 x \left (e^{\log ^2(x)}+x\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 16, normalized size = 0.67
method | result | size |
risch | \(\frac {{\mathrm e}^{-4}}{x \left (x +{\mathrm e}^{\ln \left (x \right )^{2}}\right )}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 18, normalized size = 0.75 \begin {gather*} \frac {1}{x^{2} e^{4} + x e^{\left (\log \left (x\right )^{2} + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 18, normalized size = 0.75 \begin {gather*} \frac {1}{x^{2} e^{4} + x e^{\left (\log \left (x\right )^{2} + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 19, normalized size = 0.79 \begin {gather*} \frac {1}{x^{2} e^{4} + x e^{4} e^{\log {\left (x \right )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 18, normalized size = 0.75 \begin {gather*} \frac {1}{x^{2} e^{4} + x e^{\left (\log \left (x\right )^{2} + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.32, size = 18, normalized size = 0.75 \begin {gather*} \frac {1}{x^2\,{\mathrm {e}}^4+x\,{\mathrm {e}}^4\,{\mathrm {e}}^{{\ln \left (x\right )}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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