Optimal. Leaf size=16 \[ -3-e^{4 e^{-x}}+3 x \]
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Rubi [A]
time = 0.03, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps
used = 4, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {2320, 14, 2240}
\begin {gather*} 3 x-e^{4 e^{-x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2240
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\text {Subst}\left (\int \frac {3+\frac {4 e^{4/x}}{x}}{x} \, dx,x,e^x\right )\\ &=\text {Subst}\left (\int \left (\frac {4 e^{4/x}}{x^2}+\frac {3}{x}\right ) \, dx,x,e^x\right )\\ &=3 x+4 \text {Subst}\left (\int \frac {e^{4/x}}{x^2} \, dx,x,e^x\right )\\ &=-e^{4 e^{-x}}+3 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 15, normalized size = 0.94 \begin {gather*} -e^{4 e^{-x}}+3 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.38, size = 18, normalized size = 1.12
method | result | size |
risch | \(3 x -{\mathrm e}^{4 \,{\mathrm e}^{-x}}\) | \(14\) |
derivativedivides | \(-3 \ln \left ({\mathrm e}^{-x}\right )-{\mathrm e}^{4 \,{\mathrm e}^{-x}}\) | \(18\) |
default | \(-3 \ln \left ({\mathrm e}^{-x}\right )-{\mathrm e}^{4 \,{\mathrm e}^{-x}}\) | \(18\) |
norman | \(\left (3 \,{\mathrm e}^{x} x -{\mathrm e}^{x} {\mathrm e}^{4 \,{\mathrm e}^{-x}}\right ) {\mathrm e}^{-x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.81 \begin {gather*} 3 \, x - e^{\left (4 \, e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 13, normalized size = 0.81 \begin {gather*} 3 \, x - e^{\left (4 \, e^{\left (-x\right )}\right )} \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 = 0.50 \begin {gather*} 3 x - e^{4 e^{- x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 13, normalized size = 0.81 \begin {gather*} 3 \, x - e^{\left (4 \, e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.34, size = 13, normalized size = 0.81 \begin {gather*} 3\,x-{\mathrm {e}}^{4\,{\mathrm {e}}^{-x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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