Optimal. Leaf size=21 \[ \frac {2 e^3}{x}-\log \left (-\frac {2}{x \log (2)}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.52, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} \frac {2 e^3}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 e^3}{x^2}+\frac {1}{x}\right ) \, dx\\ &=\frac {2 e^3}{x}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.52 \begin {gather*} \frac {2 e^3}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 11, normalized size = 0.52
method | result | size |
default | \(\frac {2 \,{\mathrm e}^{3}}{x}+\ln \left (x \right )\) | \(11\) |
norman | \(\frac {2 \,{\mathrm e}^{3}}{x}+\ln \left (x \right )\) | \(11\) |
risch | \(\frac {2 \,{\mathrm e}^{3}}{x}+\ln \left (x \right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 10, normalized size = 0.48 \begin {gather*} \frac {2 \, e^{3}}{x} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 13, normalized size = 0.62 \begin {gather*} \frac {x \log \left (x\right ) + 2 \, e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 8, normalized size = 0.38 \begin {gather*} \log {\left (x \right )} + \frac {2 e^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 11, normalized size = 0.52 \begin {gather*} \frac {2 \, e^{3}}{x} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 10, normalized size = 0.48 \begin {gather*} \ln \left (x\right )+\frac {2\,{\mathrm {e}}^3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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