Optimal. Leaf size=7 \[ \log \left (-1+e^4+x\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.57, number of steps
used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {31}
\begin {gather*} \log \left (-x-e^4+1\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (1-e^4-x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} \log \left (-1+e^4+x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 7, normalized size = 1.00
method | result | size |
default | \(\ln \left ({\mathrm e}^{4}+x -1\right )\) | \(7\) |
norman | \(\ln \left ({\mathrm e}^{4}+x -1\right )\) | \(7\) |
risch | \(\ln \left ({\mathrm e}^{4}+x -1\right )\) | \(7\) |
meijerg | \(\ln \left (1+\frac {x}{{\mathrm e}^{4}-1}\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 6, normalized size = 0.86 \begin {gather*} \log \left (x + e^{4} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 6, normalized size = 0.86 \begin {gather*} \log \left (x + e^{4} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 7, normalized size = 1.00 \begin {gather*} \log {\left (x - 1 + e^{4} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 7, normalized size = 1.00 \begin {gather*} \log \left ({\left | x + e^{4} - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 6, normalized size = 0.86 \begin {gather*} \ln \left (x+{\mathrm {e}}^4-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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