Optimal. Leaf size=27 \[ -2+x+\frac {(-3+x) \log \left (\frac {x}{2}\right )}{3+e^{x^2}-\frac {5}{x}} \]
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Rubi [F] time = 1.89, 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 {40-44 x+12 x^2+e^{2 x^2} x^2+e^{x^2} \left (-13 x+7 x^2\right )+\left (15-10 x+3 x^2+e^{x^2} \left (x^2+6 x^3-2 x^4\right )\right ) \log \left (\frac {x}{2}\right )}{25-30 x+9 x^2+e^{2 x^2} x^2+e^{x^2} \left (-10 x+6 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {40-44 x+12 x^2+e^{2 x^2} x^2+e^{x^2} \left (-13 x+7 x^2\right )+\left (15-10 x+3 x^2+e^{x^2} \left (x^2+6 x^3-2 x^4\right )\right ) \log \left (\frac {x}{2}\right )}{\left (5-3 x-e^{x^2} x\right )^2} \, dx\\ &=\int \left (1+\frac {\left (15-5 x+30 x^2-28 x^3+6 x^4\right ) \log \left (\frac {x}{2}\right )}{\left (-5+3 x+e^{x^2} x\right )^2}-\frac {3-x-x \log \left (\frac {x}{2}\right )-6 x^2 \log \left (\frac {x}{2}\right )+2 x^3 \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x}\right ) \, dx\\ &=x+\int \frac {\left (15-5 x+30 x^2-28 x^3+6 x^4\right ) \log \left (\frac {x}{2}\right )}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\int \frac {3-x-x \log \left (\frac {x}{2}\right )-6 x^2 \log \left (\frac {x}{2}\right )+2 x^3 \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x} \, dx\\ &=x-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\int \frac {-3+x-x \left (-1-6 x+2 x^2\right ) \log \left (\frac {x}{2}\right )}{5-\left (3+e^{x^2}\right ) x} \, dx-\int \frac {15 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-5 \int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx+30 \int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-28 \int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx+6 \int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx\\ &=x-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\int \left (\frac {3}{-5+3 x+e^{x^2} x}-\frac {x}{-5+3 x+e^{x^2} x}-\frac {x \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x}-\frac {6 x^2 \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x}+\frac {2 x^3 \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x}\right ) \, dx-\int \left (\frac {15 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-5 \int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx+30 \int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-28 \int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x}+\frac {6 \int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x}\right ) \, dx\\ &=x-2 \int \frac {x^3 \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x} \, dx-3 \int \frac {1}{-5+3 x+e^{x^2} x} \, dx+6 \int \frac {x^2 \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x} \, dx-6 \int \frac {\int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\int \frac {x}{-5+3 x+e^{x^2} x} \, dx+\int \frac {x \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x} \, dx-\int \frac {15 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-5 \int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx+30 \int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-28 \int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx\\ &=x+2 \int \frac {\int \frac {x^3}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx-3 \int \frac {1}{-5+3 x+e^{x^2} x} \, dx-6 \int \frac {\int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^2}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx+\log \left (\frac {x}{2}\right ) \int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\left (2 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{-5+3 x+e^{x^2} x} \, dx-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{-5+3 x+e^{x^2} x} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\int \left (\frac {5 \left (3 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-\int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx+6 \int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx\right )}{x}-\frac {28 \int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x}\right ) \, dx-\int \frac {\int \frac {x}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx\\ &=x+2 \int \frac {\int \frac {x^3}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx-3 \int \frac {1}{-5+3 x+e^{x^2} x} \, dx-5 \int \frac {3 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-\int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx+6 \int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^2}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx+28 \int \frac {\int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx+\log \left (\frac {x}{2}\right ) \int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\left (2 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{-5+3 x+e^{x^2} x} \, dx-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{-5+3 x+e^{x^2} x} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\int \frac {\int \frac {x}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx\\ &=x+2 \int \frac {\int \frac {x^3}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx-3 \int \frac {1}{-5+3 x+e^{x^2} x} \, dx-5 \int \left (\frac {3 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-\int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x}+\frac {6 \int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x}\right ) \, dx-6 \int \frac {\int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^2}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx+28 \int \frac {\int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx+\log \left (\frac {x}{2}\right ) \int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\left (2 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{-5+3 x+e^{x^2} x} \, dx-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{-5+3 x+e^{x^2} x} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\int \frac {\int \frac {x}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx\\ &=x+2 \int \frac {\int \frac {x^3}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx-3 \int \frac {1}{-5+3 x+e^{x^2} x} \, dx-5 \int \frac {3 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx-\int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^2}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx+28 \int \frac {\int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-30 \int \frac {\int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx+\log \left (\frac {x}{2}\right ) \int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\left (2 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{-5+3 x+e^{x^2} x} \, dx-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{-5+3 x+e^{x^2} x} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\int \frac {\int \frac {x}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx\\ &=x+2 \int \frac {\int \frac {x^3}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx-3 \int \frac {1}{-5+3 x+e^{x^2} x} \, dx-5 \int \left (\frac {3 \int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x}-\frac {\int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x}\right ) \, dx-6 \int \frac {\int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^2}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx+28 \int \frac {\int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-30 \int \frac {\int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx+\log \left (\frac {x}{2}\right ) \int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\left (2 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{-5+3 x+e^{x^2} x} \, dx-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{-5+3 x+e^{x^2} x} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\int \frac {\int \frac {x}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx\\ &=x+2 \int \frac {\int \frac {x^3}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx-3 \int \frac {1}{-5+3 x+e^{x^2} x} \, dx+5 \int \frac {\int \frac {x}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^4}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-6 \int \frac {\int \frac {x^2}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx-15 \int \frac {\int \frac {1}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx+28 \int \frac {\int \frac {x^3}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx-30 \int \frac {\int \frac {x^2}{\left (-5+\left (3+e^{x^2}\right ) x\right )^2} \, dx}{x} \, dx+\log \left (\frac {x}{2}\right ) \int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\left (2 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{-5+3 x+e^{x^2} x} \, dx-\left (5 \log \left (\frac {x}{2}\right )\right ) \int \frac {x}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^4}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (6 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{-5+3 x+e^{x^2} x} \, dx+\left (15 \log \left (\frac {x}{2}\right )\right ) \int \frac {1}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx-\left (28 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^3}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\left (30 \log \left (\frac {x}{2}\right )\right ) \int \frac {x^2}{\left (-5+3 x+e^{x^2} x\right )^2} \, dx+\int \frac {x}{-5+3 x+e^{x^2} x} \, dx-\int \frac {\int \frac {x}{-5+\left (3+e^{x^2}\right ) x} \, dx}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 27, normalized size = 1.00 \begin {gather*} x+\frac {(-3+x) x \log \left (\frac {x}{2}\right )}{-5+3 x+e^{x^2} x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 43, normalized size = 1.59 \begin {gather*} \frac {x^{2} e^{\left (x^{2}\right )} + 3 \, x^{2} + {\left (x^{2} - 3 \, x\right )} \log \left (\frac {1}{2} \, x\right ) - 5 \, x}{x e^{\left (x^{2}\right )} + 3 \, x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 54, normalized size = 2.00 \begin {gather*} \frac {x^{2} e^{\left (x^{2}\right )} - x^{2} \log \relax (2) + x^{2} \log \relax (x) + 3 \, x^{2} + 3 \, x \log \relax (2) - 3 \, x \log \relax (x) - 5 \, x}{x e^{\left (x^{2}\right )} + 3 \, x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 25, normalized size = 0.93
method | result | size |
risch | \(\frac {x \left (x -3\right ) \ln \left (\frac {x}{2}\right )}{{\mathrm e}^{x^{2}} x +3 x -5}+x\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 53, normalized size = 1.96 \begin {gather*} -\frac {x^{2} {\left (\log \relax (2) - 3\right )} - x^{2} e^{\left (x^{2}\right )} - x {\left (3 \, \log \relax (2) - 5\right )} - {\left (x^{2} - 3 \, x\right )} \log \relax (x)}{x e^{\left (x^{2}\right )} + 3 \, x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.71, size = 30, normalized size = 1.11 \begin {gather*} x-\frac {\ln \left (\frac {x}{2}\right )\,\left (3\,x-x^2\right )}{3\,x+x\,{\mathrm {e}}^{x^2}-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 29, normalized size = 1.07 \begin {gather*} x + \frac {x^{2} \log {\left (\frac {x}{2} \right )} - 3 x \log {\left (\frac {x}{2} \right )}}{x e^{x^{2}} + 3 x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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