Optimal. Leaf size=17 \[ 2-e^{-4 x}+7 e^x+2 x \]
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Rubi [A]
time = 0.03, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps
used = 3, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2320, 14}
\begin {gather*} 2 x-e^{-4 x}+7 e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\text {Subst}\left (\int \frac {2+\frac {4}{x^4}+7 x}{x} \, dx,x,e^x\right )\\ &=\text {Subst}\left (\int \left (7+\frac {4}{x^5}+\frac {2}{x}\right ) \, dx,x,e^x\right )\\ &=-e^{-4 x}+7 e^x+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 0.94 \begin {gather*} -e^{-4 x}+7 e^x+2 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 15, normalized size = 0.88
method | result | size |
default | \(2 x -{\mathrm e}^{-4 x}+7 \,{\mathrm e}^{x}\) | \(15\) |
risch | \(2 x -{\mathrm e}^{-4 x}+7 \,{\mathrm e}^{x}\) | \(15\) |
norman | \(\left (-1+7 \,{\mathrm e}^{5 x}+2 x \,{\mathrm e}^{4 x}\right ) {\mathrm e}^{-4 x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 14, normalized size = 0.82 \begin {gather*} 2 \, x - e^{\left (-4 \, x\right )} + 7 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 20, normalized size = 1.18 \begin {gather*} {\left (2 \, x e^{\left (4 \, x\right )} + 7 \, e^{\left (5 \, x\right )} - 1\right )} e^{\left (-4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.82 \begin {gather*} 2 x + 7 e^{x} - e^{- 4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 14, normalized size = 0.82 \begin {gather*} 2 \, x - e^{\left (-4 \, x\right )} + 7 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.75, size = 14, normalized size = 0.82 \begin {gather*} 2\,x-{\mathrm {e}}^{-4\,x}+7\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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