Optimal. Leaf size=24 \[ -\frac {5 \left (4-\frac {2 x}{e}-5 e^{2 x} \log (4)\right )}{4 x} \]
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Rubi [A]
time = 0.03, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps
used = 4, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {12, 14, 2228}
\begin {gather*} \frac {25 e^{2 x} \log (4)}{4 x}-\frac {5}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2228
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {20+e^{2 x} (-25+50 x) \log (4)}{x^2} \, dx\\ &=\frac {1}{4} \int \left (\frac {20}{x^2}+\frac {25 e^{2 x} (-1+2 x) \log (4)}{x^2}\right ) \, dx\\ &=-\frac {5}{x}+\frac {1}{4} (25 \log (4)) \int \frac {e^{2 x} (-1+2 x)}{x^2} \, dx\\ &=-\frac {5}{x}+\frac {25 e^{2 x} \log (4)}{4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 0.75 \begin {gather*} \frac {5 \left (-4+5 e^{2 x} \log (4)\right )}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 18, normalized size = 0.75
method | result | size |
norman | \(\frac {-5+\frac {25 \ln \left (2\right ) {\mathrm e}^{2 x}}{2}}{x}\) | \(15\) |
default | \(-\frac {5}{x}+\frac {25 \ln \left (2\right ) {\mathrm e}^{2 x}}{2 x}\) | \(18\) |
risch | \(-\frac {5}{x}+\frac {25 \ln \left (2\right ) {\mathrm e}^{2 x}}{2 x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.30, size = 23, normalized size = 0.96 \begin {gather*} 25 \, {\rm Ei}\left (2 \, x\right ) \log \left (2\right ) - 25 \, \Gamma \left (-1, -2 \, x\right ) \log \left (2\right ) - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 15, normalized size = 0.62 \begin {gather*} \frac {5 \, {\left (5 \, e^{\left (2 \, x\right )} \log \left (2\right ) - 2\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 15, normalized size = 0.62 \begin {gather*} \frac {25 e^{2 x} \log {\left (2 \right )}}{2 x} - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 0.62 \begin {gather*} \frac {5 \, {\left (5 \, e^{\left (2 \, x\right )} \log \left (2\right ) - 2\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 15, normalized size = 0.62 \begin {gather*} \frac {25\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )-10}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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