Optimal. Leaf size=22 \[ 2-x+e^x \left (7+e^2+x+x^4-\log (2)\right ) \]
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Rubi [A] time = 0.12, antiderivative size = 34, normalized size of antiderivative = 1.55, number of steps used = 15, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2196, 2176, 2194} \begin {gather*} e^x x^4+e^x x-x-e^x+e^x \left (8+e^2-\log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^x \left (8+e^2+x+4 x^3+x^4-\log (2)\right ) \, dx\\ &=-x+\int \left (e^x x+4 e^x x^3+e^x x^4+8 e^x \left (1+\frac {1}{8} \left (e^2-\log (2)\right )\right )\right ) \, dx\\ &=-x+4 \int e^x x^3 \, dx+\left (8+e^2-\log (2)\right ) \int e^x \, dx+\int e^x x \, dx+\int e^x x^4 \, dx\\ &=-x+e^x x+4 e^x x^3+e^x x^4+e^x \left (8+e^2-\log (2)\right )-4 \int e^x x^3 \, dx-12 \int e^x x^2 \, dx-\int e^x \, dx\\ &=-e^x-x+e^x x-12 e^x x^2+e^x x^4+e^x \left (8+e^2-\log (2)\right )+12 \int e^x x^2 \, dx+24 \int e^x x \, dx\\ &=-e^x-x+25 e^x x+e^x x^4+e^x \left (8+e^2-\log (2)\right )-24 \int e^x \, dx-24 \int e^x x \, dx\\ &=-25 e^x-x+e^x x+e^x x^4+e^x \left (8+e^2-\log (2)\right )+24 \int e^x \, dx\\ &=-e^x-x+e^x x+e^x x^4+e^x \left (8+e^2-\log (2)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 21, normalized size = 0.95 \begin {gather*} -x+e^x \left (7+e^2+x+x^4-\log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 19, normalized size = 0.86 \begin {gather*} {\left (x^{4} + x + e^{2} - \log \relax (2) + 7\right )} e^{x} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 21, normalized size = 0.95 \begin {gather*} {\left (x^{4} + x - \log \relax (2) + 7\right )} e^{x} - x + e^{\left (x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 0.91
method | result | size |
risch | \({\mathrm e}^{x} \left (7+{\mathrm e}^{2}+x^{4}-\ln \relax (2)+x \right )-x\) | \(20\) |
norman | \(\left (7+{\mathrm e}^{2}-\ln \relax (2)\right ) {\mathrm e}^{x}+{\mathrm e}^{x} x +{\mathrm e}^{x} x^{4}-x\) | \(26\) |
default | \(-x +{\mathrm e}^{x} x +7 \,{\mathrm e}^{x}+{\mathrm e}^{x} x^{4}+{\mathrm e}^{2} {\mathrm e}^{x}-{\mathrm e}^{x} \ln \relax (2)\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.42, size = 62, normalized size = 2.82 \begin {gather*} {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{x} + 4 \, {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{x} + {\left (x - 1\right )} e^{x} - e^{x} \log \relax (2) - x + e^{\left (x + 2\right )} + 8 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 25, normalized size = 1.14 \begin {gather*} x^4\,{\mathrm {e}}^x-x+x\,{\mathrm {e}}^x+{\mathrm {e}}^x\,\left ({\mathrm {e}}^2-\ln \relax (2)+7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.77 \begin {gather*} - x + \left (x^{4} + x - \log {\relax (2 )} + 7 + e^{2}\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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