Optimal. Leaf size=33 \[ \left (e^3+x\right ) \left (-e^{\left (5-e^x\right )^2+2 x}+x-\log \left (4+e^4\right )\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(33)=66\).
time = 0.43, antiderivative size = 77, normalized size of antiderivative = 2.33, number of steps
used = 2, number of rules used = 1, integrand size = 71, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {2326}
\begin {gather*} x^2-\frac {e^{2 x-10 e^x+e^{2 x}+25} \left (x-5 e^x \left (x+e^3\right )+e^{2 x} \left (x+e^3\right )+e^3\right )}{-5 e^x+e^{2 x}+1}+x \left (e^3-\log \left (4+e^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x^2+x \left (e^3-\log \left (4+e^4\right )\right )+\int e^{25-10 e^x+e^{2 x}+2 x} \left (-1-2 e^3+e^{2 x} \left (-2 e^3-2 x\right )-2 x+e^x \left (10 e^3+10 x\right )\right ) \, dx\\ &=x^2-\frac {e^{25-10 e^x+e^{2 x}+2 x} \left (e^3+x-5 e^x \left (e^3+x\right )+e^{2 x} \left (e^3+x\right )\right )}{1-5 e^x+e^{2 x}}+x \left (e^3-\log \left (4+e^4\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.45, size = 57, normalized size = 1.73 \begin {gather*} -e^{28-10 e^x+e^{2 x}+2 x}+e^3 x-e^{25-10 e^x+e^{2 x}+2 x} x+x \left (x-\log \left (4+e^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.78, size = 52, normalized size = 1.58
method | result | size |
risch | \(\left (-{\mathrm e}^{3}-x \right ) {\mathrm e}^{{\mathrm e}^{2 x}-10 \,{\mathrm e}^{x}+2 x +25}-x \ln \left (4+{\mathrm e}^{4}\right )+x^{2}+x \,{\mathrm e}^{3}\) | \(40\) |
default | \(-{\mathrm e}^{{\mathrm e}^{2 x}-10 \,{\mathrm e}^{x}+2 x +25} x -{\mathrm e}^{3} {\mathrm e}^{{\mathrm e}^{2 x}-10 \,{\mathrm e}^{x}+2 x +25}+x^{2}-x \ln \left (4+{\mathrm e}^{4}\right )+x \,{\mathrm e}^{3}\) | \(52\) |
norman | \(x^{2}+\left ({\mathrm e}^{3}-\ln \left (4+{\mathrm e}^{4}\right )\right ) x -{\mathrm e}^{3} {\mathrm e}^{{\mathrm e}^{2 x}-10 \,{\mathrm e}^{x}+2 x +25}-{\mathrm e}^{{\mathrm e}^{2 x}-10 \,{\mathrm e}^{x}+2 x +25} x\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 38, normalized size = 1.15 \begin {gather*} x^{2} + x e^{3} - {\left (x e^{25} + e^{28}\right )} e^{\left (2 \, x + e^{\left (2 \, x\right )} - 10 \, e^{x}\right )} - x \log \left (e^{4} + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 36, normalized size = 1.09 \begin {gather*} x^{2} + x e^{3} - {\left (x + e^{3}\right )} e^{\left (2 \, x + e^{\left (2 \, x\right )} - 10 \, e^{x} + 25\right )} - x \log \left (e^{4} + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 37, normalized size = 1.12 \begin {gather*} x^{2} + x \left (- \log {\left (4 + e^{4} \right )} + e^{3}\right ) + \left (- x - e^{3}\right ) e^{2 x + e^{2 x} - 10 e^{x} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 49, normalized size = 1.48 \begin {gather*} x^{2} + x e^{3} - x e^{\left (2 \, x + e^{\left (2 \, x\right )} - 10 \, e^{x} + 25\right )} - x \log \left (e^{4} + 4\right ) - e^{\left (2 \, x + e^{\left (2 \, x\right )} - 10 \, e^{x} + 28\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.18, size = 49, normalized size = 1.48 \begin {gather*} x\,{\mathrm {e}}^3-x\,\ln \left ({\mathrm {e}}^4+4\right )-{\mathrm {e}}^{2\,x+{\mathrm {e}}^{2\,x}-10\,{\mathrm {e}}^x+28}+x^2-x\,{\mathrm {e}}^{2\,x+{\mathrm {e}}^{2\,x}-10\,{\mathrm {e}}^x+25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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