Optimal. Leaf size=17 \[ -1+\frac {2 x}{e^{25 e^2}+\log (x)} \]
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Rubi [A] time = 0.18, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 9, number of rules used = 6, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.146, Rules used = {6688, 12, 2360, 2297, 2299, 2178} \begin {gather*} \frac {2 x}{\log (x)+e^{25 e^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2178
Rule 2297
Rule 2299
Rule 2360
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-1+e^{25 e^2}+\log (x)\right )}{\left (e^{25 e^2}+\log (x)\right )^2} \, dx\\ &=2 \int \frac {-1+e^{25 e^2}+\log (x)}{\left (e^{25 e^2}+\log (x)\right )^2} \, dx\\ &=2 \int \left (-\frac {1}{\left (e^{25 e^2}+\log (x)\right )^2}+\frac {1}{e^{25 e^2}+\log (x)}\right ) \, dx\\ &=-\left (2 \int \frac {1}{\left (e^{25 e^2}+\log (x)\right )^2} \, dx\right )+2 \int \frac {1}{e^{25 e^2}+\log (x)} \, dx\\ &=\frac {2 x}{e^{25 e^2}+\log (x)}-2 \int \frac {1}{e^{25 e^2}+\log (x)} \, dx+2 \operatorname {Subst}\left (\int \frac {e^x}{e^{25 e^2}+x} \, dx,x,\log (x)\right )\\ &=2 e^{-e^{25 e^2}} \text {Ei}\left (e^{25 e^2}+\log (x)\right )+\frac {2 x}{e^{25 e^2}+\log (x)}-2 \operatorname {Subst}\left (\int \frac {e^x}{e^{25 e^2}+x} \, dx,x,\log (x)\right )\\ &=\frac {2 x}{e^{25 e^2}+\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 15, normalized size = 0.88 \begin {gather*} \frac {2 x}{e^{25 e^2}+\log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 13, normalized size = 0.76 \begin {gather*} \frac {2 \, x}{e^{\left (25 \, e^{2}\right )} + \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 13, normalized size = 0.76 \begin {gather*} \frac {2 \, x}{e^{\left (25 \, e^{2}\right )} + \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.52, size = 14, normalized size = 0.82
method | result | size |
risch | \(\frac {2 x}{{\mathrm e}^{25 \,{\mathrm e}^{2}}+\ln \relax (x )}\) | \(14\) |
default | \(\frac {2 x}{{\mathrm e}^{25 \,{\mathrm e}^{2}}+\ln \relax (x )}\) | \(16\) |
norman | \(\frac {2 x}{{\mathrm e}^{25 \,{\mathrm e}^{2}}+\ln \relax (x )}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 13, normalized size = 0.76 \begin {gather*} \frac {2 \, x}{e^{\left (25 \, e^{2}\right )} + \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.31, size = 13, normalized size = 0.76 \begin {gather*} \frac {2\,x}{{\mathrm {e}}^{25\,{\mathrm {e}}^2}+\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.71 \begin {gather*} \frac {2 x}{\log {\relax (x )} + e^{25 e^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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