Optimal. Leaf size=20 \[ 3+e^{25 (1-2 x)}-\frac {\log ^2(x)}{x} \]
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Rubi [A] time = 0.05, antiderivative size = 27, normalized size of antiderivative = 1.35, number of steps used = 5, number of rules used = 5, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {14, 2194, 2304, 2366, 2303} \begin {gather*} e^{25-50 x}+\frac {(2-\log (x)) \log (x)}{x}-\frac {2 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rule 2303
Rule 2304
Rule 2366
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-50 e^{25-50 x}+\frac {(-2+\log (x)) \log (x)}{x^2}\right ) \, dx\\ &=-\left (50 \int e^{25-50 x} \, dx\right )+\int \frac {(-2+\log (x)) \log (x)}{x^2} \, dx\\ &=e^{25-50 x}-\frac {\log (x)}{x}+\frac {(2-\log (x)) \log (x)}{x}-\int \frac {1-\log (x)}{x^2} \, dx\\ &=e^{25-50 x}-\frac {2 \log (x)}{x}+\frac {(2-\log (x)) \log (x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 17, normalized size = 0.85 \begin {gather*} e^{25-50 x}-\frac {\log ^2(x)}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 2.51, size = 19, normalized size = 0.95 \begin {gather*} \frac {x e^{\left (-50 \, x + 25\right )} - \log \relax (x)^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 19, normalized size = 0.95 \begin {gather*} \frac {x e^{\left (-50 \, x + 25\right )} - \log \relax (x)^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.85
method | result | size |
default | \(-\frac {\ln \relax (x )^{2}}{x}+{\mathrm e}^{-50 x +25}\) | \(17\) |
risch | \(-\frac {\ln \relax (x )^{2}}{x}+{\mathrm e}^{-50 x +25}\) | \(17\) |
norman | \(\frac {x \,{\mathrm e}^{-50 x +25}-\ln \relax (x )^{2}}{x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 34, normalized size = 1.70 \begin {gather*} -\frac {\log \relax (x)^{2} + 2 \, \log \relax (x) + 2}{x} + \frac {2 \, \log \relax (x)}{x} + \frac {2}{x} + e^{\left (-50 \, x + 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.94, size = 17, normalized size = 0.85 \begin {gather*} {\mathrm {e}}^{-50\,x}\,{\mathrm {e}}^{25}-\frac {{\ln \relax (x)}^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 12, normalized size = 0.60 \begin {gather*} e^{25 - 50 x} - \frac {\log {\relax (x )}^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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