Optimal. Leaf size=8 \[ \frac {\log (4+x)}{e^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 31}
\begin {gather*} \frac {\log (x+4)}{e^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 31
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {1}{4+x} \, dx}{e^3}\\ &=\frac {\log (4+x)}{e^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {\log (4+x)}{e^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.52, size = 10, normalized size = 1.25
method | result | size |
risch | \(\ln \left (4+x \right ) {\mathrm e}^{-3}\) | \(8\) |
default | \(\ln \left (4+x \right ) {\mathrm e}^{-3}\) | \(10\) |
norman | \(\ln \left (4+x \right ) {\mathrm e}^{-3}\) | \(10\) |
meijerg | \({\mathrm e}^{-3} \ln \left (1+\frac {x}{4}\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 7, normalized size = 0.88 \begin {gather*} e^{\left (-3\right )} \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 7, normalized size = 0.88 \begin {gather*} e^{\left (-3\right )} \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 14, normalized size = 1.75 \begin {gather*} \frac {\log {\left (x e^{3} + 4 e^{3} \right )}}{e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 8, normalized size = 1.00 \begin {gather*} e^{\left (-3\right )} \log \left ({\left | x + 4 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 7, normalized size = 0.88 \begin {gather*} \ln \left (x+4\right )\,{\mathrm {e}}^{-3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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