Optimal. Leaf size=35 \[ 8-\left (-2-x+e^{-1-x} x+\log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )^2 \]
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Rubi [F]
time = 15.15, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-8 x+10 x^2-2 x^3+e^{2+2 x} \left (-20-6 x+2 x^2\right )+e^{1+x} \left (16-2 x-8 x^2+2 x^3\right )+e^{\frac {x^2}{4}} \left (-2 x+2 x^2+e^{1+x} \left (4-3 x^2\right )+e^{2+2 x} \left (-4+x^2\right )\right )+\left (e^{2+2 x} (10-2 x)+e^{1+x} \left (-8+10 x-2 x^2\right )+e^{\frac {x^2}{4}} \left (e^{2+2 x} (2-x)+e^{1+x} (-2+2 x)\right )\right ) \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{e^{2+2 x+\frac {x^2}{4}}+e^{2+2 x} (4-x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-2-2 x} \left (2 e^{1+x} (-5+x)+e^{\frac {1}{4} (2+x)^2} (-2+x)-2 e^{\frac {x^2}{4}} (-1+x)+2 \left (4-5 x+x^2\right )\right ) \left (-x+e^{1+x} (2+x)-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\\ &=\int \left (\frac {e^{-2-2 x+\frac {1}{4} (2+x)^2} (-2+x) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x}-\frac {2 e^{-2-2 x} \left (-4-e^{\frac {x^2}{4}}+5 e^{1+x}+5 x+e^{\frac {x^2}{4}} x-e^{1+x} x-x^2\right ) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx\\ &=-\left (2 \int \frac {e^{-2-2 x} \left (-4-e^{\frac {x^2}{4}}+5 e^{1+x}+5 x+e^{\frac {x^2}{4}} x-e^{1+x} x-x^2\right ) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\right )+\int \frac {e^{-2-2 x+\frac {1}{4} (2+x)^2} (-2+x) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\\ &=-\left (2 \int \frac {e^{-2-2 x} \left (4+e^{1+x} (-5+x)-e^{\frac {x^2}{4}} (-1+x)-5 x+x^2\right ) \left (x-e^{1+x} (2+x)+e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\right )+\int \frac {e^{-1-x+\frac {x^2}{4}} (2-x) \left (-2 e^{1+x}+x-e^{1+x} x+e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\\ &=-\left (2 \int \left (-\frac {e^{-1-x} (-5+x) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x}+e^{-2-2 x} (-1+x) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )\right ) \, dx\right )+\int \left (-\frac {2 e^{-1-x+\frac {x^2}{4}} \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x}+\frac {e^{-1-x+\frac {x^2}{4}} x \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx\\ &=-\left (2 \int \frac {e^{-1-x+\frac {x^2}{4}} \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\right )+2 \int \frac {e^{-1-x} (-5+x) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx-2 \int e^{-2-2 x} (-1+x) \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \, dx+\int \frac {e^{-1-x+\frac {x^2}{4}} x \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\\ &=-\left (2 \int \left (-e^{-2-2 x} (-1+x) x+e^{-1-x} (-1+x) \left (2+x-\log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )\right ) \, dx\right )-2 \int \left (\frac {2 e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x}+\frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x}-\frac {e^{-1-x+\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x}-\frac {e^{\frac {x^2}{4}} \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx+2 \int \left (-\frac {5 e^{-1-x} \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x}+\frac {e^{-1-x} x \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx+\int \left (\frac {2 e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x}+\frac {e^{\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x}-\frac {e^{-1-x+\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x}-\frac {e^{\frac {x^2}{4}} x \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx\\ &=2 \int \frac {e^{-1-x+\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int e^{-2-2 x} (-1+x) x \, dx-2 \int e^{-1-x} (-1+x) \left (2+x-\log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \, dx+2 \int \frac {e^{\frac {x^2}{4}} \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int \frac {e^{-1-x} x \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx-4 \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx-10 \int \frac {e^{-1-x} \left (2 e^{1+x}-x+e^{1+x} x-e^{1+x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx+\int \frac {e^{\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {e^{-1-x+\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {e^{\frac {x^2}{4}} x \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x} \, dx\\ &=2 \int \frac {e^{-1-x+\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int \left (-e^{-2-2 x} x+e^{-2-2 x} x^2\right ) \, dx+2 \int \frac {x \left (2+x-e^{-1-x} x-\log \left (-4-e^{\frac {x^2}{4}}+x\right )\right )}{4+e^{\frac {x^2}{4}}-x} \, dx-2 \int \left (-2 e^{-1-x}+e^{-1-x} x+e^{-1-x} x^2-e^{-1-x} (-1+x) \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \, dx-2 \int \frac {\left (-2+e^{\frac {x^2}{4}} x\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx}{2 \left (4+e^{\frac {x^2}{4}}-x\right )} \, dx-4 \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx-10 \int \frac {2+x-e^{-1-x} x-\log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x} \, dx-\log \left (-4-e^{\frac {x^2}{4}}+x\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+\left (2 \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx+\int \frac {e^{\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {e^{-1-x+\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx+\int \frac {\left (-2+e^{\frac {x^2}{4}} x\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx}{2 \left (4+e^{\frac {x^2}{4}}-x\right )} \, dx\\ &=\frac {1}{2} \int \frac {\left (-2+e^{\frac {x^2}{4}} x\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx}{4+e^{\frac {x^2}{4}}-x} \, dx-2 \int e^{-2-2 x} x \, dx-2 \int e^{-1-x} x \, dx+2 \int \frac {e^{-1-x+\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int e^{-2-2 x} x^2 \, dx-2 \int e^{-1-x} x^2 \, dx+2 \int e^{-1-x} (-1+x) \log \left (-4-e^{\frac {x^2}{4}}+x\right ) \, dx+2 \int \left (\frac {2 x}{4+e^{\frac {x^2}{4}}-x}+\frac {x^2}{4+e^{\frac {x^2}{4}}-x}-\frac {e^{-1-x} x^2}{4+e^{\frac {x^2}{4}}-x}-\frac {x \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx+4 \int e^{-1-x} \, dx-4 \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx-10 \int \left (\frac {2}{4+e^{\frac {x^2}{4}}-x}+\frac {x}{4+e^{\frac {x^2}{4}}-x}-\frac {e^{-1-x} x}{4+e^{\frac {x^2}{4}}-x}-\frac {\log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx-\log \left (-4-e^{\frac {x^2}{4}}+x\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+\left (2 \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx+\int \frac {e^{\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {e^{-1-x+\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {\left (-2+e^{\frac {x^2}{4}} x\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx}{4+e^{\frac {x^2}{4}}-x} \, dx\\ &=-4 e^{-1-x}+e^{-2-2 x} x+2 e^{-1-x} x-e^{-2-2 x} x^2+2 e^{-1-x} x^2-2 e^{-1-x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )+2 e^{-1-x} (1-x) \log \left (-4-e^{\frac {x^2}{4}}+x\right )+\frac {1}{2} \int \left (x \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+\frac {\left (-2-4 x+x^2\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx-2 \int e^{-1-x} \, dx+2 \int e^{-2-2 x} x \, dx+2 \int \frac {e^{-1-x+\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int \frac {x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-2 \int \frac {e^{-1-x} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-2 \int \frac {e^{-1-x} x \left (2-e^{\frac {x^2}{4}} x\right )}{2 \left (4+e^{\frac {x^2}{4}}-x\right )} \, dx-2 \int \frac {x \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x} \, dx-4 \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx-4 \int e^{-1-x} x \, dx+4 \int \frac {x}{4+e^{\frac {x^2}{4}}-x} \, dx-10 \int \frac {x}{4+e^{\frac {x^2}{4}}-x} \, dx+10 \int \frac {e^{-1-x} x}{4+e^{\frac {x^2}{4}}-x} \, dx+10 \int \frac {\log \left (-4-e^{\frac {x^2}{4}}+x\right )}{4+e^{\frac {x^2}{4}}-x} \, dx-20 \int \frac {1}{4+e^{\frac {x^2}{4}}-x} \, dx-\log \left (-4-e^{\frac {x^2}{4}}+x\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+\left (2 \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx-\int e^{-2-2 x} \, dx+\int \frac {e^{\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {e^{-1-x+\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \left (x \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx+\frac {\left (-2-4 x+x^2\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx}{4+e^{\frac {x^2}{4}}-x}\right ) \, dx\\ &=\frac {1}{2} e^{-2-2 x}-2 e^{-1-x}+6 e^{-1-x} x-e^{-2-2 x} x^2+2 e^{-1-x} x^2-2 e^{-1-x} \log \left (-4-e^{\frac {x^2}{4}}+x\right )+2 e^{-1-x} (1-x) \log \left (-4-e^{\frac {x^2}{4}}+x\right )+\frac {1}{2} \int x \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx \, dx+\frac {1}{2} \int \frac {\left (-2-4 x+x^2\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int \frac {e^{-1-x+\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int \frac {x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-2 \int \frac {e^{-1-x} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx+2 \int \frac {\left (-2+e^{\frac {x^2}{4}} x\right ) \int \frac {x}{4+e^{\frac {x^2}{4}}-x} \, dx}{2 \left (4+e^{\frac {x^2}{4}}-x\right )} \, dx-4 \int e^{-1-x} \, dx-4 \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx+4 \int \frac {x}{4+e^{\frac {x^2}{4}}-x} \, dx-10 \int \frac {x}{4+e^{\frac {x^2}{4}}-x} \, dx+10 \int \frac {e^{-1-x} x}{4+e^{\frac {x^2}{4}}-x} \, dx-10 \int \frac {\left (-2+e^{\frac {x^2}{4}} x\right ) \int \frac {1}{4+e^{\frac {x^2}{4}}-x} \, dx}{2 \left (4+e^{\frac {x^2}{4}}-x\right )} \, dx-20 \int \frac {1}{4+e^{\frac {x^2}{4}}-x} \, dx-\log \left (-4-e^{\frac {x^2}{4}}+x\right ) \int \frac {e^{\frac {x^2}{4}} x}{4+e^{\frac {x^2}{4}}-x} \, dx+\left (2 \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx-\left (2 \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \int \frac {x}{4+e^{\frac {x^2}{4}}-x} \, dx+\left (10 \log \left (-4-e^{\frac {x^2}{4}}+x\right )\right ) \int \frac {1}{4+e^{\frac {x^2}{4}}-x} \, dx+\int e^{-2-2 x} \, dx+\int \frac {e^{\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {e^{-1-x+\frac {x^2}{4}} x^2}{4+e^{\frac {x^2}{4}}-x} \, dx-\int \frac {e^{-1-x} x \left (2-e^{\frac {x^2}{4}} x\right )}{4+e^{\frac {x^2}{4}}-x} \, dx-\int x \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx \, dx-\int \frac {\left (-2-4 x+x^2\right ) \int \frac {e^{\frac {x^2}{4}}}{4+e^{\frac {x^2}{4}}-x} \, dx}{4+e^{\frac {x^2}{4}}-x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [F]
time = 1.87, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-8 x+10 x^2-2 x^3+e^{2+2 x} \left (-20-6 x+2 x^2\right )+e^{1+x} \left (16-2 x-8 x^2+2 x^3\right )+e^{\frac {x^2}{4}} \left (-2 x+2 x^2+e^{1+x} \left (4-3 x^2\right )+e^{2+2 x} \left (-4+x^2\right )\right )+\left (e^{2+2 x} (10-2 x)+e^{1+x} \left (-8+10 x-2 x^2\right )+e^{\frac {x^2}{4}} \left (e^{2+2 x} (2-x)+e^{1+x} (-2+2 x)\right )\right ) \log \left (-4-e^{\frac {x^2}{4}}+x\right )}{e^{2+2 x+\frac {x^2}{4}}+e^{2+2 x} (4-x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(113\) vs.
\(2(31)=62\).
time = 0.32, size = 114, normalized size = 3.26
method | result | size |
risch | \(-\ln \left (-{\mathrm e}^{\frac {x^{2}}{4}}+x -4\right )^{2}+2 x \left ({\mathrm e}^{x +1}-1\right ) {\mathrm e}^{-x -1} \ln \left (-{\mathrm e}^{\frac {x^{2}}{4}}+x -4\right )+\left (-x^{2} {\mathrm e}^{2 x +2}+4 \ln \left ({\mathrm e}^{\frac {x^{2}}{4}}-x +4\right ) {\mathrm e}^{2 x +2}+2 x^{2} {\mathrm e}^{x +1}-4 x \,{\mathrm e}^{2 x +2}-x^{2}+4 x \,{\mathrm e}^{x +1}\right ) {\mathrm e}^{-2 x -2}\) | \(114\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 132 vs.
\(2 (31) = 62\).
time = 0.39, size = 132, normalized size = 3.77 \begin {gather*} -{\left (e^{\left (2 \, x + 2\right )} \log \left ({\left ({\left (x - 4\right )} e^{\left (2 \, x + 2\right )} - e^{\left (\frac {1}{4} \, x^{2} + 2 \, x + 2\right )}\right )} e^{\left (-2 \, x - 2\right )}\right )^{2} + x^{2} + {\left (x^{2} + 4 \, x\right )} e^{\left (2 \, x + 2\right )} - 2 \, {\left (x^{2} + 2 \, x\right )} e^{\left (x + 1\right )} - 2 \, {\left ({\left (x + 2\right )} e^{\left (2 \, x + 2\right )} - x e^{\left (x + 1\right )}\right )} \log \left ({\left ({\left (x - 4\right )} e^{\left (2 \, x + 2\right )} - e^{\left (\frac {1}{4} \, x^{2} + 2 \, x + 2\right )}\right )} e^{\left (-2 \, x - 2\right )}\right )\right )} e^{\left (-2 \, x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {8\,x+\ln \left (x-{\mathrm {e}}^{\frac {x^2}{4}}-4\right )\,\left ({\mathrm {e}}^{x+1}\,\left (2\,x^2-10\,x+8\right )-{\mathrm {e}}^{\frac {x^2}{4}}\,\left ({\mathrm {e}}^{x+1}\,\left (2\,x-2\right )-{\mathrm {e}}^{2\,x+2}\,\left (x-2\right )\right )+{\mathrm {e}}^{2\,x+2}\,\left (2\,x-10\right )\right )+{\mathrm {e}}^{x+1}\,\left (-2\,x^3+8\,x^2+2\,x-16\right )+{\mathrm {e}}^{2\,x+2}\,\left (-2\,x^2+6\,x+20\right )+{\mathrm {e}}^{\frac {x^2}{4}}\,\left (2\,x+{\mathrm {e}}^{x+1}\,\left (3\,x^2-4\right )-{\mathrm {e}}^{2\,x+2}\,\left (x^2-4\right )-2\,x^2\right )-10\,x^2+2\,x^3}{{\mathrm {e}}^{2\,x+2}\,{\mathrm {e}}^{\frac {x^2}{4}}-{\mathrm {e}}^{2\,x+2}\,\left (x-4\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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