Optimal. Leaf size=29 \[ x-\left (-5+e^{4+\frac {3}{4 e^4 x}}-e^x-x\right ) x \]
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Rubi [A] time = 0.04, antiderivative size = 42, normalized size of antiderivative = 1.45, number of steps used = 5, number of rules used = 4, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.089, Rules used = {12, 2288, 2176, 2194} \begin {gather*} x^2-e^{\frac {\frac {3}{x}+16 e^4}{4 e^4}} x+6 x-e^x+e^x (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2194
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \left (24+e^{\frac {1}{4} \left (16+\frac {3}{e^4 x}\right )} \left (-4+\frac {3}{e^4 x}\right )+8 x+e^x (4+4 x)\right ) \, dx\\ &=6 x+x^2+\frac {1}{4} \int e^{\frac {1}{4} \left (16+\frac {3}{e^4 x}\right )} \left (-4+\frac {3}{e^4 x}\right ) \, dx+\frac {1}{4} \int e^x (4+4 x) \, dx\\ &=6 x-e^{\frac {16 e^4+\frac {3}{x}}{4 e^4}} x+x^2+e^x (1+x)-\int e^x \, dx\\ &=-e^x+6 x-e^{\frac {16 e^4+\frac {3}{x}}{4 e^4}} x+x^2+e^x (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 29, normalized size = 1.00 \begin {gather*} 6 x-e^{4+\frac {3}{4 e^4 x}} x+e^x x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 29, normalized size = 1.00 \begin {gather*} x^{2} + x e^{x} - x e^{\left (\frac {{\left (16 \, x e^{4} + 3\right )} e^{\left (-4\right )}}{4 \, x}\right )} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 24, normalized size = 0.83 \begin {gather*} x^{2} + x e^{x} - x e^{\left (\frac {3 \, e^{\left (-4\right )}}{4 \, x} + 4\right )} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 25, normalized size = 0.86
method | result | size |
norman | \(x^{2}+{\mathrm e}^{x} x +6 x -x \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{-4}}{4 x}+4}\) | \(25\) |
risch | \(x^{2}+{\mathrm e}^{x} x +6 x -x \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{-4}+16 x}{4 x}}\) | \(29\) |
default | \(x^{2}+6 x +{\mathrm e}^{x} x -{\mathrm e}^{\frac {{\mathrm e}^{-4+\ln \left (\frac {3}{x}\right )+\ln \relax (x )}}{4 x}+4} x\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 24, normalized size = 0.83 \begin {gather*} x^{2} + x e^{x} - x e^{\left (\frac {3 \, e^{\left (-4\right )}}{4 \, x} + 4\right )} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.81, size = 22, normalized size = 0.76 \begin {gather*} x\,\left ({\mathrm {e}}^x-{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{-4}}{4\,x}+4}+6\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 24, normalized size = 0.83 \begin {gather*} x^{2} + x e^{x} - x e^{4 + \frac {3}{4 x e^{4}}} + 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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