Optimal. Leaf size=17 \[ \frac {\log (x)}{2 \left (-5-e^{25} \log (x)\right )} \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 32} \begin {gather*} \frac {5}{2 e^{25} \left (e^{25} \log (x)+5\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 32
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (5 \int \frac {1}{50 x+20 e^{25} x \log (x)+2 e^{50} x \log ^2(x)} \, dx\right )\\ &=-\left (5 \operatorname {Subst}\left (\int \frac {1}{2 \left (5+e^{25} x\right )^2} \, dx,x,\log (x)\right )\right )\\ &=-\left (\frac {5}{2} \operatorname {Subst}\left (\int \frac {1}{\left (5+e^{25} x\right )^2} \, dx,x,\log (x)\right )\right )\\ &=\frac {5}{2 e^{25} \left (5+e^{25} \log (x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {5}{2 e^{25} \left (5+e^{25} \log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 14, normalized size = 0.82 \begin {gather*} \frac {5}{2 \, {\left (e^{50} \log \relax (x) + 5 \, e^{25}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 14, normalized size = 0.82
method | result | size |
norman | \(-\frac {\ln \relax (x )}{2 \left ({\mathrm e}^{25} \ln \relax (x )+5\right )}\) | \(14\) |
risch | \(\frac {5 \,{\mathrm e}^{-25}}{2 \left ({\mathrm e}^{25} \ln \relax (x )+5\right )}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 14, normalized size = 0.82 \begin {gather*} \frac {5}{2 \, {\left (e^{50} \log \relax (x) + 5 \, e^{25}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.41, size = 14, normalized size = 0.82 \begin {gather*} \frac {5\,{\mathrm {e}}^{-25}}{2\,{\mathrm {e}}^{25}\,\ln \relax (x)+10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.82 \begin {gather*} \frac {5}{2 e^{50} \log {\relax (x )} + 10 e^{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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