Optimal. Leaf size=22 \[ 2+x-x \left (-3-x-5 e^{-8+4 x} \log (x)\right ) \]
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Rubi [A]
time = 0.04, antiderivative size = 38, normalized size of antiderivative = 1.73, number of steps
used = 5, number of rules used = 4, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.138, Rules used = {2225, 2207,
2634, 12} \begin {gather*} x^2+4 x-\frac {5}{4} e^{4 x-8} \log (x)+\frac {5}{4} e^{4 x-8} (4 x+1) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rule 2634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 x+x^2+5 \int e^{-8+4 x} \, dx+\int e^{-8+4 x} (5+20 x) \log (x) \, dx\\ &=\frac {5}{4} e^{-8+4 x}+4 x+x^2-\frac {5}{4} e^{-8+4 x} \log (x)+\frac {5}{4} e^{-8+4 x} (1+4 x) \log (x)-\int 5 e^{-8+4 x} \, dx\\ &=\frac {5}{4} e^{-8+4 x}+4 x+x^2-\frac {5}{4} e^{-8+4 x} \log (x)+\frac {5}{4} e^{-8+4 x} (1+4 x) \log (x)-5 \int e^{-8+4 x} \, dx\\ &=4 x+x^2-\frac {5}{4} e^{-8+4 x} \log (x)+\frac {5}{4} e^{-8+4 x} (1+4 x) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 19, normalized size = 0.86 \begin {gather*} 4 x+x^2+5 e^{-8+4 x} x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 19, normalized size = 0.86
method | result | size |
default | \(4 x +5 x \,{\mathrm e}^{4 x -8} \ln \left (x \right )+x^{2}\) | \(19\) |
risch | \(4 x +5 x \,{\mathrm e}^{4 x -8} \ln \left (x \right )+x^{2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 18, normalized size = 0.82 \begin {gather*} 5 \, x e^{\left (4 \, x - 8\right )} \log \left (x\right ) + x^{2} + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 18, normalized size = 0.82 \begin {gather*} 5 \, x e^{\left (4 \, x - 8\right )} \log \left (x\right ) + x^{2} + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 19, normalized size = 0.86 \begin {gather*} x^{2} + 5 x e^{4 x - 8} \log {\left (x \right )} + 4 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 18, normalized size = 0.82 \begin {gather*} 5 \, x e^{\left (4 \, x - 8\right )} \log \left (x\right ) + x^{2} + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.15, size = 18, normalized size = 0.82 \begin {gather*} 4\,x+x^2+5\,x\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{-8}\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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