Optimal. Leaf size=10 \[ -1+e^x+\frac {x}{e^4} \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} \frac {x}{e^4}+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (1+e^{4+x}\right ) \, dx}{e^4}\\ &=\frac {x}{e^4}+\frac {\int e^{4+x} \, dx}{e^4}\\ &=e^x+\frac {x}{e^4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 0.90 \begin {gather*} e^x+\frac {x}{e^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 9, normalized size = 0.90 \begin {gather*} {\left (x + e^{\left (x + 4\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 9, normalized size = 0.90 \begin {gather*} {\left (x + e^{\left (x + 4\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 8, normalized size = 0.80
method | result | size |
risch | \(x \,{\mathrm e}^{-4}+{\mathrm e}^{x}\) | \(8\) |
norman | \(x \,{\mathrm e}^{-4}+{\mathrm e}^{x}\) | \(10\) |
default | \({\mathrm e}^{-4} \left (x +{\mathrm e}^{4} {\mathrm e}^{x}\right )\) | \(13\) |
derivativedivides | \({\mathrm e}^{-4} \left ({\mathrm e}^{4} {\mathrm e}^{x}+\ln \left ({\mathrm e}^{x}\right )\right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 9, normalized size = 0.90 \begin {gather*} {\left (x + e^{\left (x + 4\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.15, size = 7, normalized size = 0.70 \begin {gather*} {\mathrm {e}}^x+x\,{\mathrm {e}}^{-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.70 \begin {gather*} \frac {x}{e^{4}} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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