Optimal. Leaf size=31 \[ -1+e^{\left (-e^{5 x^2}+x \log \left (\frac {1}{x+4 x^2}\right )\right )^2}-x \]
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Rubi [F] time = 41.15, 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 {-1-4 x+\exp \left (e^{10 x^2}-2 e^{5 x^2} x \log \left (\frac {1}{x+4 x^2}\right )+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )\right ) \left (e^{5 x^2} (2+16 x)+e^{10 x^2} \left (20 x+80 x^2\right )+\left (-2 x-16 x^2+e^{5 x^2} \left (-2-8 x-20 x^2-80 x^3\right )\right ) \log \left (\frac {1}{x+4 x^2}\right )+\left (2 x+8 x^2\right ) \log ^2\left (\frac {1}{x+4 x^2}\right )\right )}{1+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 \left (-1+\frac {2 e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \left (1+8 x+10 e^{5 x^2} x+40 e^{5 x^2} x^2-\log \left (\frac {1}{x+4 x^2}\right )-4 x \log \left (\frac {1}{x+4 x^2}\right )\right ) \left (e^{5 x^2}-x \log \left (\frac {1}{x+4 x^2}\right )\right )}{1+4 x}\right ) \, dx\\ &=-x+2 \int \frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \left (1+8 x+10 e^{5 x^2} x+40 e^{5 x^2} x^2-\log \left (\frac {1}{x+4 x^2}\right )-4 x \log \left (\frac {1}{x+4 x^2}\right )\right ) \left (e^{5 x^2}-x \log \left (\frac {1}{x+4 x^2}\right )\right )}{1+4 x} \, dx\\ &=-x+2 \int \left (10 e^{e^{10 x^2}+10 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x}+\frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \left (-1-8 x+\log \left (\frac {1}{x+4 x^2}\right )+4 x \log \left (\frac {1}{x+4 x^2}\right )\right )}{1+4 x}-\frac {e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \left (-1-8 x+\log \left (\frac {1}{x+4 x^2}\right )+4 x \log \left (\frac {1}{x+4 x^2}\right )+10 x^2 \log \left (\frac {1}{x+4 x^2}\right )+40 x^3 \log \left (\frac {1}{x+4 x^2}\right )\right )}{1+4 x}\right ) \, dx\\ &=-x+2 \int \frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \left (-1-8 x+\log \left (\frac {1}{x+4 x^2}\right )+4 x \log \left (\frac {1}{x+4 x^2}\right )\right )}{1+4 x} \, dx-2 \int \frac {e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \left (-1-8 x+\log \left (\frac {1}{x+4 x^2}\right )+4 x \log \left (\frac {1}{x+4 x^2}\right )+10 x^2 \log \left (\frac {1}{x+4 x^2}\right )+40 x^3 \log \left (\frac {1}{x+4 x^2}\right )\right )}{1+4 x} \, dx+20 \int e^{e^{10 x^2}+10 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \, dx\\ &=-x+2 \int \left (\frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} (-1-8 x) x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )}{1+4 x}+e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log ^2\left (\frac {1}{x (1+4 x)}\right )\right ) \, dx-2 \int \frac {e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \left (-1-8 x+\left (1+4 x+10 x^2+40 x^3\right ) \log \left (\frac {1}{x+4 x^2}\right )\right )}{1+4 x} \, dx+20 \int e^{e^{10 x^2}+10 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \, dx\\ &=-x+2 \int \frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} (-1-8 x) x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )}{1+4 x} \, dx+2 \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log ^2\left (\frac {1}{x (1+4 x)}\right ) \, dx-2 \int \left (\frac {e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} (-1-8 x) \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x}}{1+4 x}+e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \left (1+10 x^2\right ) \log \left (\frac {1}{x (1+4 x)}\right )\right ) \, dx+20 \int e^{e^{10 x^2}+10 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \, dx\\ &=-x-2 \int \frac {e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} (-1-8 x) \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x}}{1+4 x} \, dx-2 \int e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \left (1+10 x^2\right ) \log \left (\frac {1}{x (1+4 x)}\right ) \, dx+2 \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log ^2\left (\frac {1}{x (1+4 x)}\right ) \, dx+2 \int \left (\frac {1}{4} e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )+\frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )}{4 (-1-4 x)}-2 e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )\right ) \, dx+20 \int e^{e^{10 x^2}+10 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \, dx\\ &=-x+\frac {1}{2} \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \, dx+\frac {1}{2} \int \frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )}{-1-4 x} \, dx-2 \int \left (-2 e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x}+\frac {e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x}}{1+4 x}\right ) \, dx+2 \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log ^2\left (\frac {1}{x (1+4 x)}\right ) \, dx-2 \int \left (e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )+10 e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x^2 \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )\right ) \, dx-4 \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \, dx+20 \int e^{e^{10 x^2}+10 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \, dx\\ &=-x+\frac {1}{2} \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \, dx+\frac {1}{2} \int \frac {e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right )}{-1-4 x} \, dx-2 \int \frac {e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x}}{1+4 x} \, dx-2 \int e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \, dx+2 \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log ^2\left (\frac {1}{x (1+4 x)}\right ) \, dx+4 \int e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \, dx-4 \int e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \, dx+20 \int e^{e^{10 x^2}+10 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \, dx-20 \int e^{e^{10 x^2}+5 x^2+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} x^2 \left (\frac {1}{x (1+4 x)}\right )^{-2 e^{5 x^2} x} \log \left (\frac {1}{x (1+4 x)}\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.32, size = 51, normalized size = 1.65 \begin {gather*} -x+e^{e^{10 x^2}+x^2 \log ^2\left (\frac {1}{x+4 x^2}\right )} \left (\frac {1}{x+4 x^2}\right )^{-2 e^{5 x^2} x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 47, normalized size = 1.52 \begin {gather*} -x + e^{\left (x^{2} \log \left (\frac {1}{4 \, x^{2} + x}\right )^{2} - 2 \, x e^{\left (5 \, x^{2}\right )} \log \left (\frac {1}{4 \, x^{2} + x}\right ) + e^{\left (10 \, x^{2}\right )}\right )} \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*} \int \frac {2 \, {\left ({\left (4 \, x^{2} + x\right )} \log \left (\frac {1}{4 \, x^{2} + x}\right )^{2} + 10 \, {\left (4 \, x^{2} + x\right )} e^{\left (10 \, x^{2}\right )} + {\left (8 \, x + 1\right )} e^{\left (5 \, x^{2}\right )} - {\left (8 \, x^{2} + {\left (40 \, x^{3} + 10 \, x^{2} + 4 \, x + 1\right )} e^{\left (5 \, x^{2}\right )} + x\right )} \log \left (\frac {1}{4 \, x^{2} + x}\right )\right )} e^{\left (x^{2} \log \left (\frac {1}{4 \, x^{2} + x}\right )^{2} - 2 \, x e^{\left (5 \, x^{2}\right )} \log \left (\frac {1}{4 \, x^{2} + x}\right ) + e^{\left (10 \, x^{2}\right )}\right )} - 4 \, x - 1}{4 \, x + 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.68, size = 863, normalized size = 27.84
method | result | size |
risch | \(-x +x^{4 x^{2} \ln \relax (2)} \left (x +\frac {1}{4}\right )^{4 x^{2} \ln \relax (2)} \left (x +\frac {1}{4}\right )^{2 x^{2} \ln \relax (x )} 2^{-2 i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x}\right )} x^{i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x \left (4 x +1\right )}\right ) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i}{4 x +1}\right )} \left (x +\frac {1}{4}\right )^{-i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{4 x +1}\right )} x^{-i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x}\right )} 2^{2 i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x \left (4 x +1\right )}\right ) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i}{4 x +1}\right )} x^{-i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{4 x +1}\right )} \left (x +\frac {1}{4}\right )^{-i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x}\right )} \left (x +\frac {1}{4}\right )^{i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x \left (4 x +1\right )}\right ) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i}{4 x +1}\right )} 2^{2 i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x \left (4 x +1\right )}\right )} x^{i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x \left (4 x +1\right )}\right )} 16^{x \,{\mathrm e}^{5 x^{2}}} x^{2 x \,{\mathrm e}^{5 x^{2}}} \left (x +\frac {1}{4}\right )^{2 x \,{\mathrm e}^{5 x^{2}}} 2^{-2 i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{4 x +1}\right )} \left (x +\frac {1}{4}\right )^{i x^{2} \pi \,\mathrm {csgn}\left (\frac {i}{x \left (4 x +1\right )}\right )} {\mathrm e}^{x^{2} \ln \relax (x )^{2}+4 x^{2} \ln \relax (2)^{2}+x^{2} \ln \left (x +\frac {1}{4}\right )^{2}+{\mathrm e}^{10 x^{2}}} {\mathrm e}^{\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{5} \mathrm {csgn}\left (\frac {i}{x}\right )}{2}} {\mathrm e}^{\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{5} \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )}{2}} {\mathrm e}^{-\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{4} \mathrm {csgn}\left (\frac {i}{x}\right )^{2}}{4}} {\mathrm e}^{-\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{4} \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )^{2}}{4}} {\mathrm e}^{i x \,{\mathrm e}^{5 x^{2}} \pi \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{3}} {\mathrm e}^{-i x \,{\mathrm e}^{5 x^{2}} \pi \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )} {\mathrm e}^{-i x \,{\mathrm e}^{5 x^{2}} \pi \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{2} \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )} {\mathrm e}^{\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{3} \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )}{2}} {\mathrm e}^{-\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )^{2}}{4}} {\mathrm e}^{-x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{4} \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )} {\mathrm e}^{\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{3} \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )}{2}} {\mathrm e}^{i x \,{\mathrm e}^{5 x^{2}} \pi \,\mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right ) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i}{x +\frac {1}{4}}\right )} {\mathrm e}^{-\frac {x^{2} \pi ^{2} \mathrm {csgn}\left (\frac {i}{x \left (x +\frac {1}{4}\right )}\right )^{6}}{4}}\) | \(863\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.53, size = 71, normalized size = 2.29 \begin {gather*} -x + e^{\left (x^{2} \log \left (4 \, x + 1\right )^{2} + 2 \, x^{2} \log \left (4 \, x + 1\right ) \log \relax (x) + x^{2} \log \relax (x)^{2} + 2 \, x e^{\left (5 \, x^{2}\right )} \log \left (4 \, x + 1\right ) + 2 \, x e^{\left (5 \, x^{2}\right )} \log \relax (x) + e^{\left (10 \, x^{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.51, size = 50, normalized size = 1.61 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{10\,x^2}}\,{\mathrm {e}}^{x^2\,{\ln \left (\frac {1}{4\,x^2+x}\right )}^2}}{{\left (\frac {1}{4\,x^2+x}\right )}^{2\,x\,{\mathrm {e}}^{5\,x^2}}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.56, size = 44, normalized size = 1.42 \begin {gather*} - x + e^{x^{2} \log {\left (\frac {1}{4 x^{2} + x} \right )}^{2} - 2 x e^{5 x^{2}} \log {\left (\frac {1}{4 x^{2} + x} \right )} + e^{10 x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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