Optimal. Leaf size=35 \[ \frac {3}{x}+\left (-e+x-x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right )^2 \]
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Rubi [F] time = 10.06, 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 {-3 x-2 e x^3+2 x^4+e^{2 x^2} \left (-27-18 e x^2+18 x^3\right )+\left (-8 x^4+16 x^6+e^{2 x^2} \left (36 e x^2-36 x^3\right )+e \left (8 x^3-16 x^5\right )\right ) \log \left (\frac {1}{9} e^{-2 x^2} \left (9 e^{2 x^2} x+x^2\right )\right )+\left (2 e x^3-4 x^4+e^{2 x^2} \left (18 e x^2-36 x^3\right )\right ) \log ^2\left (\frac {1}{9} e^{-2 x^2} \left (9 e^{2 x^2} x+x^2\right )\right )+\left (36 e^{2 x^2} x^3+8 x^4-16 x^6\right ) \log ^3\left (\frac {1}{9} e^{-2 x^2} \left (9 e^{2 x^2} x+x^2\right )\right )+\left (18 e^{2 x^2} x^3+2 x^4\right ) \log ^4\left (\frac {1}{9} e^{-2 x^2} \left (9 e^{2 x^2} x+x^2\right )\right )}{9 e^{2 x^2} x^2+x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {4 x \left (-1+4 x^2\right ) \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \left (e-x+x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right )}{9 e^{2 x^2}+x}+\frac {-3-2 e x^2+2 x^3+4 e x^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )-4 x^3 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 e x^2 \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )-4 x^3 \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+4 x^3 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 x^3 \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{x^2}\right ) \, dx\\ &=-\left (4 \int \frac {x \left (-1+4 x^2\right ) \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \left (e-x+x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right )}{9 e^{2 x^2}+x} \, dx\right )+\int \frac {-3-2 e x^2+2 x^3+4 e x^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )-4 x^3 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 e x^2 \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )-4 x^3 \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+4 x^3 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 x^3 \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{x^2} \, dx\\ &=-\left (4 \int \left (-\frac {x \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \left (e-x+x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right )}{9 e^{2 x^2}+x}+\frac {4 x^3 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \left (e-x+x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right )}{9 e^{2 x^2}+x}\right ) \, dx\right )+\int \left (\frac {-3-2 e x^2+2 x^3}{x^2}+4 (e-x) \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 (e-2 x) \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+4 x \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 x \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \, dx\\ &=2 \int (e-2 x) \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+2 \int x \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int (e-x) \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int x \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int \frac {x \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \left (e-x+x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right )}{9 e^{2 x^2}+x} \, dx-16 \int \frac {x^3 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \left (e-x+x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right )}{9 e^{2 x^2}+x} \, dx+\int \frac {-3-2 e x^2+2 x^3}{x^2} \, dx\\ &=-2 (e-x)^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 \int \frac {(e-x)^2 \left (9 e^{2 x^2}+2 x-4 x^3\right )}{x \left (9 e^{2 x^2}+x\right )} \, dx+2 \int x \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+2 \int \left (e \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )-2 x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \, dx+4 \int x \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int \left (\frac {e x \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x}-\frac {x^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x}+\frac {x^2 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x}\right ) \, dx-16 \int \left (\frac {e x^3 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x}-\frac {x^4 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x}+\frac {x^4 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x}\right ) \, dx+\int \left (-2 e-\frac {3}{x^2}+2 x\right ) \, dx\\ &=\frac {3}{x}-2 e x+x^2-2 (e-x)^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 \int \left (\frac {(e-x)^2}{x}-\frac {(e-x)^2 \left (-1+4 x^2\right )}{9 e^{2 x^2}+x}\right ) \, dx+2 \int x \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx-4 \int \frac {x^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx-4 \int x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int x \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int \frac {x^2 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx+16 \int \frac {x^4 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx-16 \int \frac {x^4 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx+(2 e) \int \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+(4 e) \int \frac {x \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx-(16 e) \int \frac {x^3 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx\\ &=\frac {3}{x}-2 e x+x^2-2 (e-x)^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 \int \frac {(e-x)^2}{x} \, dx-2 \int \frac {(e-x)^2 \left (-1+4 x^2\right )}{9 e^{2 x^2}+x} \, dx+2 \int x \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx-4 \int x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int x \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int \frac {x^2 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx+4 \int \frac {\left (9 e^{2 x^2}+2 x-4 x^3\right ) \int \frac {x^2}{9 e^{2 x^2}+x} \, dx}{x \left (9 e^{2 x^2}+x\right )} \, dx-16 \int \frac {x^4 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx-16 \int \frac {\left (9 e^{2 x^2}+2 x-4 x^3\right ) \int \frac {x^4}{9 e^{2 x^2}+x} \, dx}{x \left (9 e^{2 x^2}+x\right )} \, dx+(2 e) \int \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx-(4 e) \int \frac {\left (9 e^{2 x^2}+2 x-4 x^3\right ) \int \frac {x}{9 e^{2 x^2}+x} \, dx}{x \left (9 e^{2 x^2}+x\right )} \, dx+(16 e) \int \frac {\left (9 e^{2 x^2}+2 x-4 x^3\right ) \int \frac {x^3}{9 e^{2 x^2}+x} \, dx}{x \left (9 e^{2 x^2}+x\right )} \, dx-\left (4 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^2}{9 e^{2 x^2}+x} \, dx+\left (16 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^4}{9 e^{2 x^2}+x} \, dx+\left (4 e \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x}{9 e^{2 x^2}+x} \, dx-\left (16 e \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^3}{9 e^{2 x^2}+x} \, dx\\ &=\frac {3}{x}-2 e x+x^2-2 (e-x)^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 \int \left (-2 e+\frac {e^2}{x}+x\right ) \, dx-2 \int \left (-\frac {e^2}{9 e^{2 x^2}+x}+\frac {2 e x}{9 e^{2 x^2}+x}+\frac {\left (-1+4 e^2\right ) x^2}{9 e^{2 x^2}+x}-\frac {8 e x^3}{9 e^{2 x^2}+x}+\frac {4 x^4}{9 e^{2 x^2}+x}\right ) \, dx+2 \int x \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx-4 \int x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int x \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int \frac {x^2 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx+4 \int \left (\frac {\int \frac {x^2}{9 e^{2 x^2}+x} \, dx}{x}-\frac {\left (-1+4 x^2\right ) \int \frac {x^2}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x}\right ) \, dx-16 \int \frac {x^4 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx-16 \int \left (\frac {\int \frac {x^4}{9 e^{2 x^2}+x} \, dx}{x}-\frac {\left (-1+4 x^2\right ) \int \frac {x^4}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x}\right ) \, dx+(2 e) \int \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx-(4 e) \int \left (\frac {\int \frac {x}{9 e^{2 x^2}+x} \, dx}{x}-\frac {\left (-1+4 x^2\right ) \int \frac {x}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x}\right ) \, dx+(16 e) \int \left (\frac {\int \frac {x^3}{9 e^{2 x^2}+x} \, dx}{x}-\frac {\left (-1+4 x^2\right ) \int \frac {x^3}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x}\right ) \, dx-\left (4 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^2}{9 e^{2 x^2}+x} \, dx+\left (16 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^4}{9 e^{2 x^2}+x} \, dx+\left (4 e \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x}{9 e^{2 x^2}+x} \, dx-\left (16 e \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^3}{9 e^{2 x^2}+x} \, dx\\ &=\frac {3}{x}-6 e x+2 x^2+2 e^2 \log (x)-2 (e-x)^2 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+2 \int x \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx-4 \int x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int x \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx+4 \int \frac {x^2 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx+4 \int \frac {\int \frac {x^2}{9 e^{2 x^2}+x} \, dx}{x} \, dx-4 \int \frac {\left (-1+4 x^2\right ) \int \frac {x^2}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x} \, dx-8 \int \frac {x^4}{9 e^{2 x^2}+x} \, dx-16 \int \frac {x^4 \log ^3\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )}{9 e^{2 x^2}+x} \, dx-16 \int \frac {\int \frac {x^4}{9 e^{2 x^2}+x} \, dx}{x} \, dx+16 \int \frac {\left (-1+4 x^2\right ) \int \frac {x^4}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x} \, dx+(2 e) \int \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \, dx-(4 e) \int \frac {x}{9 e^{2 x^2}+x} \, dx-(4 e) \int \frac {\int \frac {x}{9 e^{2 x^2}+x} \, dx}{x} \, dx+(4 e) \int \frac {\left (-1+4 x^2\right ) \int \frac {x}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x} \, dx+(16 e) \int \frac {x^3}{9 e^{2 x^2}+x} \, dx+(16 e) \int \frac {\int \frac {x^3}{9 e^{2 x^2}+x} \, dx}{x} \, dx-(16 e) \int \frac {\left (-1+4 x^2\right ) \int \frac {x^3}{9 e^{2 x^2}+x} \, dx}{9 e^{2 x^2}+x} \, dx+\left (2 e^2\right ) \int \frac {1}{9 e^{2 x^2}+x} \, dx+\left (2 \left (1-4 e^2\right )\right ) \int \frac {x^2}{9 e^{2 x^2}+x} \, dx-\left (4 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^2}{9 e^{2 x^2}+x} \, dx+\left (16 \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^4}{9 e^{2 x^2}+x} \, dx+\left (4 e \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x}{9 e^{2 x^2}+x} \, dx-\left (16 e \log \left (x+\frac {1}{9} e^{-2 x^2} x^2\right )\right ) \int \frac {x^3}{9 e^{2 x^2}+x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 63, normalized size = 1.80 \begin {gather*} \frac {3}{x}-2 e x+x^2+2 (e-x) x \log ^2\left (x+\frac {1}{9} e^{-2 x^2} x^2\right )+x^2 \log ^4\left (x+\frac {1}{9} e^{-2 x^2} x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.75, size = 81, normalized size = 2.31 \begin {gather*} \frac {x^{3} \log \left (\frac {1}{9} \, {\left (x^{2} + 9 \, x e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-2 \, x^{2}\right )}\right )^{4} + x^{3} - 2 \, x^{2} e - 2 \, {\left (x^{3} - x^{2} e\right )} \log \left (\frac {1}{9} \, {\left (x^{2} + 9 \, x e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-2 \, x^{2}\right )}\right )^{2} + 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 24.30, size = 104, normalized size = 2.97 \begin {gather*} \frac {x^{3} \log \left (\frac {1}{9} \, {\left (x^{2} + 9 \, x e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-2 \, x^{2}\right )}\right )^{4} - 2 \, x^{3} \log \left (\frac {1}{9} \, {\left (x^{2} + 9 \, x e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-2 \, x^{2}\right )}\right )^{2} + 2 \, x^{2} e \log \left (\frac {1}{9} \, {\left (x^{2} + 9 \, x e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-2 \, x^{2}\right )}\right )^{2} + x^{3} - 2 \, x^{2} e + 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 51.75, size = 190125, normalized size = 5432.14
method | result | size |
risch | \(\text {Expression too large to display}\) | \(190125\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.17, size = 467, normalized size = 13.34 \begin {gather*} \frac {16 \, x^{11} + 64 \, x^{9} \log \relax (3) + 8 \, {\left (12 \, \log \relax (3)^{2} - 1\right )} x^{7} + 8 \, x^{6} e + x^{3} \log \left (x + 9 \, e^{\left (2 \, x^{2}\right )}\right )^{4} + x^{3} \log \relax (x)^{4} + 16 \, {\left (4 \, \log \relax (3)^{3} - \log \relax (3)\right )} x^{5} + 16 \, x^{4} e \log \relax (3) + {\left (16 \, \log \relax (3)^{4} - 8 \, \log \relax (3)^{2} + 1\right )} x^{3} + 2 \, {\left (4 \, \log \relax (3)^{2} - 1\right )} x^{2} e - 4 \, {\left (2 \, x^{5} + 2 \, x^{3} \log \relax (3) - x^{3} \log \relax (x)\right )} \log \left (x + 9 \, e^{\left (2 \, x^{2}\right )}\right )^{3} - 8 \, {\left (x^{5} + x^{3} \log \relax (3)\right )} \log \relax (x)^{3} + 2 \, {\left (12 \, x^{7} + 24 \, x^{5} \log \relax (3) + 3 \, x^{3} \log \relax (x)^{2} + {\left (12 \, \log \relax (3)^{2} - 1\right )} x^{3} + x^{2} e - 12 \, {\left (x^{5} + x^{3} \log \relax (3)\right )} \log \relax (x)\right )} \log \left (x + 9 \, e^{\left (2 \, x^{2}\right )}\right )^{2} + 2 \, {\left (12 \, x^{7} + 24 \, x^{5} \log \relax (3) + {\left (12 \, \log \relax (3)^{2} - 1\right )} x^{3} + x^{2} e\right )} \log \relax (x)^{2} - 4 \, {\left (8 \, x^{9} + 24 \, x^{7} \log \relax (3) + 2 \, {\left (12 \, \log \relax (3)^{2} - 1\right )} x^{5} - x^{3} \log \relax (x)^{3} + 2 \, x^{4} e + 2 \, {\left (4 \, \log \relax (3)^{3} - \log \relax (3)\right )} x^{3} + 2 \, x^{2} e \log \relax (3) + 6 \, {\left (x^{5} + x^{3} \log \relax (3)\right )} \log \relax (x)^{2} - {\left (12 \, x^{7} + 24 \, x^{5} \log \relax (3) + {\left (12 \, \log \relax (3)^{2} - 1\right )} x^{3} + x^{2} e\right )} \log \relax (x)\right )} \log \left (x + 9 \, e^{\left (2 \, x^{2}\right )}\right ) - 8 \, {\left (4 \, x^{9} + 12 \, x^{7} \log \relax (3) + {\left (12 \, \log \relax (3)^{2} - 1\right )} x^{5} + x^{4} e + {\left (4 \, \log \relax (3)^{3} - \log \relax (3)\right )} x^{3} + x^{2} e \log \relax (3)\right )} \log \relax (x) + 3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.84, size = 76, normalized size = 2.17 \begin {gather*} x^2\,{\ln \left (x+\frac {x^2\,{\mathrm {e}}^{-2\,x^2}}{9}\right )}^4-2\,x^2\,{\ln \left (x+\frac {x^2\,{\mathrm {e}}^{-2\,x^2}}{9}\right )}^2-2\,x\,\mathrm {e}+\frac {3}{x}+x^2+2\,x\,{\ln \left (x+\frac {x^2\,{\mathrm {e}}^{-2\,x^2}}{9}\right )}^2\,\mathrm {e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.65, size = 75, normalized size = 2.14 \begin {gather*} x^{2} \log {\left (\left (\frac {x^{2}}{9} + x e^{2 x^{2}}\right ) e^{- 2 x^{2}} \right )}^{4} + x^{2} - 2 e x + \left (- 2 x^{2} + 2 e x\right ) \log {\left (\left (\frac {x^{2}}{9} + x e^{2 x^{2}}\right ) e^{- 2 x^{2}} \right )}^{2} + \frac {3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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