Optimal. Leaf size=25 \[ (-225+x)^{\frac {e^4}{e^{2/x}-e^{5+x}}} \]
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Rubi [F] time = 8.68, 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 {(-225+x)^{-\frac {e^4}{-e^{2/x}+e^{5+x}}} \left (e^{4+\frac {2}{x}} x^2-e^{9+x} x^2+\left (e^{4+\frac {2}{x}} (-450+2 x)+e^{9+x} \left (-225 x^2+x^3\right )\right ) \log (-225+x)\right )}{e^{5+\frac {2}{x}+x} \left (450 x^2-2 x^3\right )+e^{4/x} \left (-225 x^2+x^3\right )+e^{10+2 x} \left (-225 x^2+x^3\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 {e^4 (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (\left (e^{2/x}-e^{5+x}\right ) x^2+(-225+x) \left (2 e^{2/x}+e^{5+x} x^2\right ) \log (-225+x)\right )}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (\left (e^{2/x}-e^{5+x}\right ) x^2+(-225+x) \left (2 e^{2/x}+e^{5+x} x^2\right ) \log (-225+x)\right )}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \left (\frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (-450+2 x-225 x^2+x^3\right ) \log (-225+x)}{\left (e^{2/x}-e^{5+x}\right )^2 x^2}-\frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} (-1-225 \log (-225+x)+x \log (-225+x))}{e^{2/x}-e^{5+x}}\right ) \, dx\\ &=e^4 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \left (-450+2 x-225 x^2+x^3\right ) \log (-225+x)}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx-e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} (-1-225 \log (-225+x)+x \log (-225+x))}{e^{2/x}-e^{5+x}} \, dx\\ &=-\left (e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} (-1+(-225+x) \log (-225+x))}{e^{2/x}-e^{5+x}} \, dx\right )-e^4 \int \frac {-225 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-450 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx+\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=-\left (e^4 \int \left (-\frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}}-\frac {225 (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \log (-225+x)}{e^{2/x}-e^{5+x}}+\frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x \log (-225+x)}{e^{2/x}-e^{5+x}}\right ) \, dx\right )-e^4 \int \left (\frac {-225 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-450 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x}+\frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x}\right ) \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x \log (-225+x)}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {-225 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-450 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} \log (-225+x)}{e^{2/x}-e^{5+x}} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \left (-\frac {225 \left (\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\right )}{-225+x}+\frac {2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x}\right ) \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (2 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (2 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \left (\frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x}+\frac {2 \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx}{-225+x}\right ) \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ &=e^4 \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-e^4 \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx+e^4 \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx-\left (2 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx}{-225+x} \, dx+\left (225 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx}{-225+x} \, dx-\left (225 e^4\right ) \int \frac {\int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx}{-225+x} \, dx+\left (450 e^4\right ) \int \frac {\int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx}{-225+x} \, dx+\left (e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx-\left (e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}} x}{e^{2/x}-e^{5+x}} \, dx+\left (2 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x} \, dx-\left (225 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2} \, dx+\left (225 e^4 \log (-225+x)\right ) \int \frac {(-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{e^{2/x}-e^{5+x}} \, dx-\left (450 e^4 \log (-225+x)\right ) \int \frac {e^{2/x} (-225+x)^{-1+\frac {e^4}{e^{2/x}-e^{5+x}}}}{\left (e^{2/x}-e^{5+x}\right )^2 x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 26, normalized size = 1.04 \begin {gather*} (-225+x)^{-\frac {e^4}{-e^{2/x}+e^{5+x}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 37, normalized size = 1.48 \begin {gather*} \frac {1}{{\left (x - 225\right )}^{\frac {e^{\left (x + 17\right )}}{e^{\left (2 \, x + 18\right )} - e^{\left (\frac {x^{2} + 5 \, x + 2}{x} + 8\right )}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 24, normalized size = 0.96
method | result | size |
risch | \(\left (x -225\right )^{-\frac {{\mathrm e}^{4}}{{\mathrm e}^{5+x}-{\mathrm e}^{\frac {2}{x}}}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{{\left (x - 225\right )}^{\frac {e^{4}}{e^{\left (x + 5\right )} - e^{\frac {2}{x}}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.00, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{{\left (x-225\right )}^{\frac {{\mathrm {e}}^4}{{\mathrm {e}}^{x+5}-{\mathrm {e}}^{2/x}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 12.64, size = 20, normalized size = 0.80 \begin {gather*} e^{- \frac {e^{4} \log {\left (x - 225 \right )}}{- e^{\frac {2}{x}} + e^{x + 5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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