Optimal. Leaf size=17 \[ e^{\frac {3}{4}+5 e^{1+x}}-x \]
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Rubi [A]
time = 0.02, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2320, 2225}
\begin {gather*} e^{5 e^{x+1}+\frac {3}{4}}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+5 \int e^{1+\frac {1}{4} \left (3+20 e^{1+x}\right )+x} \, dx\\ &=-x+5 \text {Subst}\left (\int e^{\frac {7}{4}+5 e x} \, dx,x,e^x\right )\\ &=e^{\frac {3}{4}+5 e^{1+x}}-x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} e^{\frac {3}{4}+5 e^{1+x}}-x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.82
method | result | size |
default | \({\mathrm e}^{5 \,{\mathrm e}^{x +1}+\frac {3}{4}}-x\) | \(14\) |
norman | \({\mathrm e}^{5 \,{\mathrm e}^{x +1}+\frac {3}{4}}-x\) | \(14\) |
risch | \({\mathrm e}^{5 \,{\mathrm e}^{x +1}+\frac {3}{4}}-x\) | \(14\) |
derivativedivides | \({\mathrm e}^{5 \,{\mathrm e}^{x +1}+\frac {3}{4}}-\ln \left (20 \,{\mathrm e}^{x +1}\right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.76 \begin {gather*} -x + e^{\left (5 \, e^{\left (x + 1\right )} + \frac {3}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 27 vs.
\(2 (13) = 26\).
time = 0.35, size = 27, normalized size = 1.59 \begin {gather*} -{\left (x e^{\left (x + 1\right )} - e^{\left (x + 5 \, e^{\left (x + 1\right )} + \frac {7}{4}\right )}\right )} e^{\left (-x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 12, normalized size = 0.71 \begin {gather*} - x + e^{5 e^{x + 1} + \frac {3}{4}} \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 = 0.76 \begin {gather*} -x + e^{\left (5 \, e^{\left (x + 1\right )} + \frac {3}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 14, normalized size = 0.82 \begin {gather*} {\mathrm {e}}^{5\,{\mathrm {e}}^{x+1}}\,{\mathrm {e}}^{3/4}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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