Optimal. Leaf size=16 \[ 2+2 \left (5-x+e^{169 x} x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.69, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2207, 2225}
\begin {gather*} -2 x-\frac {2 e^{169 x}}{169}+\frac {2}{169} e^{169 x} (169 x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-2 x+\int e^{169 x} (2+338 x) \, dx\\ &=-2 x+\frac {2}{169} e^{169 x} (1+169 x)-2 \int e^{169 x} \, dx\\ &=-\frac {2 e^{169 x}}{169}-2 x+\frac {2}{169} e^{169 x} (1+169 x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 12, normalized size = 0.75 \begin {gather*} -2 x+2 e^{169 x} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.36, size = 12, normalized size = 0.75
method | result | size |
derivativedivides | \(-2 x +2 x \,{\mathrm e}^{169 x}\) | \(12\) |
default | \(-2 x +2 x \,{\mathrm e}^{169 x}\) | \(12\) |
norman | \(-2 x +2 x \,{\mathrm e}^{169 x}\) | \(12\) |
risch | \(-2 x +2 x \,{\mathrm e}^{169 x}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 21, normalized size = 1.31 \begin {gather*} \frac {2}{169} \, {\left (169 \, x - 1\right )} e^{\left (169 \, x\right )} - 2 \, x + \frac {2}{169} \, e^{\left (169 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 11, normalized size = 0.69 \begin {gather*} 2 \, x e^{\left (169 \, x\right )} - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.62 \begin {gather*} 2 x e^{169 x} - 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 11, normalized size = 0.69 \begin {gather*} 2 \, x e^{\left (169 \, x\right )} - 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 9, normalized size = 0.56 \begin {gather*} 2\,x\,\left ({\mathrm {e}}^{169\,x}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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