Optimal. Leaf size=24 \[ \frac {e^{x^2} \log (x) \left (x+\log \left (1+e^{-2+2 x}+x\right )\right )}{x} \]
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Rubi [A] time = 14.17, antiderivative size = 31, normalized size of antiderivative = 1.29, number of steps used = 91, number of rules used = 18, integrand size = 127, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.142, Rules used = {6742, 2554, 14, 6688, 2210, 2199, 2194, 2178, 12, 6483, 6475, 2288, 2214, 2204, 6351, 6360, 2557, 6715} \begin {gather*} e^{x^2} \log (x)+\frac {e^{x^2} \log \left (x+e^{2 x-2}+1\right ) \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2178
Rule 2194
Rule 2199
Rule 2204
Rule 2210
Rule 2214
Rule 2288
Rule 2554
Rule 2557
Rule 6351
Rule 6360
Rule 6475
Rule 6483
Rule 6688
Rule 6715
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {e^{2+x^2} (1+2 x) \log (x)}{x \left (e^2+e^{2 x}+e^2 x\right )}+\frac {e^{x^2} \left (x+2 x \log (x)+2 x^3 \log (x)+\log \left (1+e^{-2+2 x}+x\right )-\log (x) \log \left (1+e^{-2+2 x}+x\right )+2 x^2 \log (x) \log \left (1+e^{-2+2 x}+x\right )\right )}{x^2}\right ) \, dx\\ &=-\int \frac {e^{2+x^2} (1+2 x) \log (x)}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx+\int \frac {e^{x^2} \left (x+2 x \log (x)+2 x^3 \log (x)+\log \left (1+e^{-2+2 x}+x\right )-\log (x) \log \left (1+e^{-2+2 x}+x\right )+2 x^2 \log (x) \log \left (1+e^{-2+2 x}+x\right )\right )}{x^2} \, dx\\ &=-\left (\log (x) \int \frac {e^{2+x^2}}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx\right )-(2 \log (x)) \int \frac {e^{2+x^2}}{e^2+e^{2 x}+e^2 x} \, dx+\int \frac {e^{x^2} \left (x+\log \left (1+e^{-2+2 x}+x\right )+\log (x) \left (2 \left (x+x^3\right )+\left (-1+2 x^2\right ) \log \left (1+e^{-2+2 x}+x\right )\right )\right )}{x^2} \, dx+\int \frac {2 \int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx+\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx\\ &=-\left (\log (x) \int \frac {e^{2+x^2}}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx\right )-(2 \log (x)) \int \frac {e^{2+x^2}}{e^2+e^{2 x}+e^2 x} \, dx+\int \left (\frac {e^{x^2} \left (1+2 \log (x)+2 x^2 \log (x)\right )}{x}+\frac {e^{x^2} \left (1-\log (x)+2 x^2 \log (x)\right ) \log \left (1+e^{-2+2 x}+x\right )}{x^2}\right ) \, dx+\int \left (\frac {2 \int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x}+\frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x}\right ) \, dx\\ &=2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\log (x) \int \frac {e^{2+x^2}}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx-(2 \log (x)) \int \frac {e^{2+x^2}}{e^2+e^{2 x}+e^2 x} \, dx+\int \frac {e^{x^2} \left (1+2 \log (x)+2 x^2 \log (x)\right )}{x} \, dx+\int \frac {e^{x^2} \left (1-\log (x)+2 x^2 \log (x)\right ) \log \left (1+e^{-2+2 x}+x\right )}{x^2} \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx\\ &=2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\log (x) \int \frac {e^{2+x^2}}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx-(2 \log (x)) \int \frac {e^{2+x^2}}{e^2+e^{2 x}+e^2 x} \, dx+\int \left (\frac {e^{x^2}}{x}+\frac {2 e^{x^2} \left (1+x^2\right ) \log (x)}{x}\right ) \, dx+\int \left (\frac {e^{x^2} \log \left (1+e^{-2+2 x}+x\right )}{x^2}+2 e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )-\frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x^2}\right ) \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx\\ &=2 \int \frac {e^{x^2} \left (1+x^2\right ) \log (x)}{x} \, dx+2 \int e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right ) \, dx+2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\log (x) \int \frac {e^{2+x^2}}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx-(2 \log (x)) \int \frac {e^{2+x^2}}{e^2+e^{2 x}+e^2 x} \, dx+\int \frac {e^{x^2}}{x} \, dx+\int \frac {e^{x^2} \log \left (1+e^{-2+2 x}+x\right )}{x^2} \, dx-\int \frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x^2} \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx\\ &=\frac {\text {Ei}\left (x^2\right )}{2}+e^{x^2} \log (x)+\text {Ei}\left (x^2\right ) \log (x)-\frac {e^{x^2} \log \left (1+e^{-2+2 x}+x\right )}{x}+\sqrt {\pi } \text {erfi}(x) \log \left (1+e^{-2+2 x}+x\right )+\frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x}-2 \int \frac {e^{x^2}+\text {Ei}\left (x^2\right )}{2 x} \, dx-2 \int \frac {\left (1+2 e^{-2+2 x}\right ) \sqrt {\pi } \text {erfi}(x) \log (x)}{2 \left (1+e^{-2+2 x}+x\right )} \, dx-2 \int \frac {\sqrt {\pi } \text {erfi}(x) \log \left (1+e^{-2+2 x}+x\right )}{2 x} \, dx+2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\log (x) \int \frac {e^{2+x^2}}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx-(2 \log (x)) \int \frac {e^{2+x^2}}{e^2+e^{2 x}+e^2 x} \, dx-\int \frac {\left (1+2 e^{-2+2 x}\right ) \left (-\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x)\right )}{1+e^{-2+2 x}+x} \, dx+\int \frac {\left (1+2 e^{-2+2 x}\right ) \left (-\frac {e^{x^2}}{x}+\sqrt {\pi } \text {erfi}(x)\right ) \log (x)}{1+e^{-2+2 x}+x} \, dx+\int \frac {\left (-e^{x^2}+\sqrt {\pi } x \text {erfi}(x)\right ) \log \left (1+e^{-2+2 x}+x\right )}{x^2} \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx\\ &=\frac {\text {Ei}\left (x^2\right )}{2}-e^{x^2} \log (x)+2 \sqrt {\pi } x \text {erfi}(x) \log (x)+2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right ) \log \left (1+e^{-2+2 x}+x\right )+\frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x}+2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\sqrt {\pi } \int \frac {\left (1+2 e^{-2+2 x}\right ) \text {erfi}(x) \log (x)}{1+e^{-2+2 x}+x} \, dx-\sqrt {\pi } \int \frac {\text {erfi}(x) \log \left (1+e^{-2+2 x}+x\right )}{x} \, dx-\left (e^2 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(x)}{e^2+e^{2 x}+e^2 x} \, dx-\left (2 e^2 \sqrt {\pi } \log (x)\right ) \int \frac {x \text {erfi}(x)}{e^2+e^{2 x}+e^2 x} \, dx-\int \left (-\frac {e^{x^2} \left (e^2+2 e^{2 x}\right )}{x \left (e^2+e^{2 x}+e^2 x\right )}+\frac {\left (e^2+2 e^{2 x}\right ) \sqrt {\pi } \text {erfi}(x)}{e^2+e^{2 x}+e^2 x}\right ) \, dx-\int \frac {e^{x^2}+\text {Ei}\left (x^2\right )}{x} \, dx-\int \frac {\left (1+2 e^{-2+2 x}\right ) \left (\frac {e^{x^2}}{x}-\sqrt {\pi } \text {erfi}(x)+2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )\right )}{1+e^{-2+2 x}+x} \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx-\int \frac {-2 e^{x^2}+2 \sqrt {\pi } x \text {erfi}(x)-\text {Ei}\left (x^2\right )+2 \int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx+\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx-e^2 \sqrt {\pi } \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx-2 e^2 \sqrt {\pi } \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx\\ &=\frac {\text {Ei}\left (x^2\right )}{2}+e^{x^2} \log (x)+\frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x}+2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\sqrt {\pi } \int \frac {\left (e^2+2 e^{2 x}\right ) \text {erfi}(x)}{e^2+e^{2 x}+e^2 x} \, dx+\sqrt {\pi } \int \frac {2 \left (1+2 e^{-2+2 x}\right ) x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )}{\sqrt {\pi } \left (1+e^{-2+2 x}+x\right )} \, dx+\sqrt {\pi } \int \frac {-\frac {2 e^{x^2}}{\sqrt {\pi }}+2 x \text {erfi}(x)-e^2 \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx-2 e^2 \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx+\int \frac {e^{x^2} \left (e^2+2 e^{2 x}\right )}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx-\int \left (\frac {e^{x^2}}{x}+\frac {\text {Ei}\left (x^2\right )}{x}\right ) \, dx-\int \left (\frac {e^{x^2} \left (e^2+2 e^{2 x}\right )}{x \left (e^2+e^{2 x}+e^2 x\right )}+\frac {\left (e^2+2 e^{2 x}\right ) \left (-\sqrt {\pi } \text {erfi}(x)+2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )\right )}{e^2+e^{2 x}+e^2 x}\right ) \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx-\int \left (-\frac {2 e^{x^2}}{x}+\frac {2 \sqrt {\pi } x \text {erfi}(x)-\text {Ei}\left (x^2\right )+2 \int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx+\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx-e^2 \sqrt {\pi } \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx-2 e^2 \sqrt {\pi } \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x}\right ) \, dx\\ &=\frac {\text {Ei}\left (x^2\right )}{2}+e^{x^2} \log (x)+\frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x}+2 \int \frac {e^{x^2}}{x} \, dx+2 \int \frac {\left (1+2 e^{-2+2 x}\right ) x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )}{1+e^{-2+2 x}+x} \, dx+2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\sqrt {\pi } \int \left (2 \text {erfi}(x)-\frac {e^2 (1+2 x) \text {erfi}(x)}{e^2+e^{2 x}+e^2 x}\right ) \, dx+\sqrt {\pi } \int \left (-\frac {2 e^{x^2}}{\sqrt {\pi } x}+\frac {2 x \text {erfi}(x)-e^2 \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx-2 e^2 \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x}\right ) \, dx-\int \frac {e^{x^2}}{x} \, dx-\int \frac {e^{x^2} \left (e^2+2 e^{2 x}\right )}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx+\int \left (\frac {2 e^{x^2}}{x}-\frac {e^{2+x^2} (1+2 x)}{x \left (e^2+e^{2 x}+e^2 x\right )}\right ) \, dx-\int \frac {\text {Ei}\left (x^2\right )}{x} \, dx-\int \frac {\left (e^2+2 e^{2 x}\right ) \left (-\sqrt {\pi } \text {erfi}(x)+2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )\right )}{e^2+e^{2 x}+e^2 x} \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx-\int \frac {2 \sqrt {\pi } x \text {erfi}(x)-\text {Ei}\left (x^2\right )+2 \int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx+\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx-e^2 \sqrt {\pi } \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx-2 e^2 \sqrt {\pi } \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx\\ &=\text {Ei}\left (x^2\right )+e^{x^2} \log (x)+\frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x}-\frac {1}{2} \operatorname {Subst}\left (\int \frac {\text {Ei}(x)}{x} \, dx,x,x^2\right )+2 \int \left (2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )-\frac {e^2 x (1+2 x) \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )}{e^2+e^{2 x}+e^2 x}\right ) \, dx+2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx+\sqrt {\pi } \int \frac {2 x \text {erfi}(x)-e^2 \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx-2 e^2 \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx-\left (2 \sqrt {\pi }\right ) \int \text {erfi}(x) \, dx+\left (e^2 \sqrt {\pi }\right ) \int \frac {(1+2 x) \text {erfi}(x)}{e^2+e^{2 x}+e^2 x} \, dx-\int \frac {e^{2+x^2} (1+2 x)}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx-\int \left (\frac {2 e^{x^2}}{x}-\frac {e^{2+x^2} (1+2 x)}{x \left (e^2+e^{2 x}+e^2 x\right )}\right ) \, dx-\int \left (-2 \left (\sqrt {\pi } \text {erfi}(x)-2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )\right )-\frac {e^2 (1+2 x) \left (-\sqrt {\pi } \text {erfi}(x)+2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )\right )}{e^2+e^{2 x}+e^2 x}\right ) \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx-\int \left (\frac {2 \sqrt {\pi } x \text {erfi}(x)-\text {Ei}\left (x^2\right )+2 \int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx+\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx-e^2 \sqrt {\pi } \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x}-\frac {2 e^2 \sqrt {\pi } \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x}\right ) \, dx\\ &=2 e^{x^2}-2 \sqrt {\pi } x \text {erfi}(x)+\text {Ei}\left (x^2\right )+e^{x^2} \log (x)-\frac {1}{2} \left (E_1\left (-x^2\right )+\text {Ei}\left (x^2\right )\right ) \log \left (x^2\right )+\frac {e^{x^2} \log (x) \log \left (1+e^{-2+2 x}+x\right )}{x}+\frac {1}{2} \operatorname {Subst}\left (\int \frac {E_1(-x)}{x} \, dx,x,x^2\right )-2 \int \frac {e^{x^2}}{x} \, dx+2 \int \left (\sqrt {\pi } \text {erfi}(x)-2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )\right ) \, dx+2 \int \frac {\int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx+4 \int x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right ) \, dx+e^2 \int \frac {(1+2 x) \left (-\sqrt {\pi } \text {erfi}(x)+2 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )\right )}{e^2+e^{2 x}+e^2 x} \, dx-\left (2 e^2\right ) \int \frac {x (1+2 x) \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )}{e^2+e^{2 x}+e^2 x} \, dx+\sqrt {\pi } \int \left (\frac {2 x \text {erfi}(x)-e^2 \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x}-\frac {2 e^2 \int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x}\right ) \, dx+\left (e^2 \sqrt {\pi }\right ) \int \left (\frac {\text {erfi}(x)}{e^2+e^{2 x}+e^2 x}+\frac {2 x \text {erfi}(x)}{e^2+e^{2 x}+e^2 x}\right ) \, dx+\left (2 e^2 \sqrt {\pi }\right ) \int \frac {\int \frac {x \text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx+\int \frac {e^{2+x^2} (1+2 x)}{x \left (e^2+e^{2 x}+e^2 x\right )} \, dx-\int \left (\frac {2 e^{2+x^2}}{e^2+e^{2 x}+e^2 x}+\frac {e^{2+x^2}}{x \left (e^2+e^{2 x}+e^2 x\right )}\right ) \, dx+\int \frac {\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx}{x} \, dx-\int \frac {2 \sqrt {\pi } x \text {erfi}(x)-\text {Ei}\left (x^2\right )+2 \int \frac {e^{2+x^2}}{e^{2 x}+e^2 (1+x)} \, dx+\int \frac {e^{2+x^2}}{x \left (e^{2 x}+e^2 (1+x)\right )} \, dx-e^2 \sqrt {\pi } \int \frac {\text {erfi}(x)}{e^{2 x}+e^2 (1+x)} \, dx}{x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 24, normalized size = 1.00 \begin {gather*} \frac {e^{x^2} \log (x) \left (x+\log \left (1+e^{-2+2 x}+x\right )\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 24, normalized size = 1.00 \begin {gather*} \frac {{\left (x + \log \left (x + e^{\left (2 \, x - 2\right )} + 1\right )\right )} e^{\left (x^{2} + \log \left (\log \relax (x)\right )\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 40, normalized size = 1.67 \begin {gather*} \frac {x e^{\left (x^{2}\right )} \log \relax (x) + e^{\left (x^{2}\right )} \log \left (x e^{2} + e^{2} + e^{\left (2 \, x\right )}\right ) \log \relax (x) - 2 \, e^{\left (x^{2}\right )} \log \relax (x)}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 23, normalized size = 0.96
method | result | size |
risch | \(\frac {\left (\ln \left ({\mathrm e}^{2 x -2}+x +1\right )+x \right ) {\mathrm e}^{x^{2}} \ln \relax (x )}{x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 34, normalized size = 1.42 \begin {gather*} \frac {{\left (x - 2\right )} e^{\left (x^{2}\right )} \log \relax (x) + e^{\left (x^{2}\right )} \log \left (x e^{2} + e^{2} + e^{\left (2 \, x\right )}\right ) \log \relax (x)}{x} \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 = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{\ln \left (\ln \relax (x)\right )+x^2}\,\left (x+\ln \left (x+{\mathrm {e}}^{2\,x-2}+1\right )\,\left (x+{\mathrm {e}}^{2\,x-2}+\ln \relax (x)\,\left ({\mathrm {e}}^{2\,x-2}\,\left (2\,x^2-1\right )-x+2\,x^2+2\,x^3-1\right )+1\right )+x\,{\mathrm {e}}^{2\,x-2}+x^2+\ln \relax (x)\,\left (x+{\mathrm {e}}^{2\,x-2}\,\left (2\,x^3+2\,x\right )+2\,x^3+2\,x^4\right )\right )}{\ln \relax (x)\,\left (x^2\,{\mathrm {e}}^{2\,x-2}+x^2+x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] 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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