Optimal. Leaf size=18 \[ -\frac {4}{e^4}-4 e^{-3+4 x}+3 x \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.72, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2194} \begin {gather*} 3 x-4 e^{4 x-3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 x-16 \int e^{-3+4 x} \, dx\\ &=-4 e^{-3+4 x}+3 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.72 \begin {gather*} -4 e^{-3+4 x}+3 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 12, normalized size = 0.67 \begin {gather*} 3 \, x - 4 \, e^{\left (4 \, x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 12, normalized size = 0.67 \begin {gather*} 3 \, x - 4 \, e^{\left (4 \, x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 0.72
method | result | size |
default | \(3 x -4 \,{\mathrm e}^{4 x -3}\) | \(13\) |
norman | \(3 x -4 \,{\mathrm e}^{4 x -3}\) | \(13\) |
risch | \(3 x -4 \,{\mathrm e}^{4 x -3}\) | \(13\) |
derivativedivides | \(-4 \,{\mathrm e}^{4 x -3}+\frac {3 \ln \left ({\mathrm e}^{4 x -3}\right )}{4}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 12, normalized size = 0.67 \begin {gather*} 3 \, x - 4 \, e^{\left (4 \, x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 12, normalized size = 0.67 \begin {gather*} 3\,x-4\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{-3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 10, normalized size = 0.56 \begin {gather*} 3 x - 4 e^{4 x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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