Optimal. Leaf size=22 \[ \log \left (\frac {1}{5} e^{-2-2 e^{2 x}} (1+e)^2 x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 10, normalized size of antiderivative = 0.45, number of steps
used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {14, 2225}
\begin {gather*} \log (x)-2 e^{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4 e^{2 x}+\frac {1}{x}\right ) \, dx\\ &=\log (x)-4 \int e^{2 x} \, dx\\ &=-2 e^{2 x}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 10, normalized size = 0.45 \begin {gather*} -2 e^{2 x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 10, normalized size = 0.45
method | result | size |
default | \(\ln \left (x \right )-2 \,{\mathrm e}^{2 x}\) | \(10\) |
norman | \(\ln \left (x \right )-2 \,{\mathrm e}^{2 x}\) | \(10\) |
risch | \(\ln \left (x \right )-2 \,{\mathrm e}^{2 x}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 9, normalized size = 0.41 \begin {gather*} -2 \, e^{\left (2 \, x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.51, size = 9, normalized size = 0.41 \begin {gather*} -2 \, e^{\left (2 \, x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.36 \begin {gather*} - 2 e^{2 x} + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 9, normalized size = 0.41 \begin {gather*} -2 \, e^{\left (2 \, x\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.33, size = 9, normalized size = 0.41 \begin {gather*} \ln \left (x\right )-2\,{\mathrm {e}}^{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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