Integrand size = 30, antiderivative size = 23 \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=-x+\frac {e^{10} \left (2+125 \left (e^2+\log \left (x^2\right )\right )\right )}{x^2} \]
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Time = 0.02 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.70, number of steps used = 5, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14, 2341} \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=-\frac {e^{10} \left (123-125 e^2\right )}{x^2}+\frac {125 e^{10}}{x^2}+\frac {125 e^{10} \log \left (x^2\right )}{x^2}-x \]
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Rule 14
Rule 2341
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {246 e^{10}-250 e^{12}-x^3}{x^3}-\frac {250 e^{10} \log \left (x^2\right )}{x^3}\right ) \, dx \\ & = -\left (\left (250 e^{10}\right ) \int \frac {\log \left (x^2\right )}{x^3} \, dx\right )+\int \frac {246 e^{10}-250 e^{12}-x^3}{x^3} \, dx \\ & = \frac {125 e^{10}}{x^2}+\frac {125 e^{10} \log \left (x^2\right )}{x^2}+\int \left (-1+\frac {2 e^{10} \left (123-125 e^2\right )}{x^3}\right ) \, dx \\ & = \frac {125 e^{10}}{x^2}-\frac {e^{10} \left (123-125 e^2\right )}{x^2}-x+\frac {125 e^{10} \log \left (x^2\right )}{x^2} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=\frac {2 e^{10}}{x^2}+\frac {125 e^{12}}{x^2}-x+\frac {125 e^{10} \log \left (x^2\right )}{x^2} \]
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Time = 0.06 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.35
method | result | size |
risch | \(\frac {125 \,{\mathrm e}^{10} \ln \left (x^{2}\right )}{x^{2}}+\frac {125 \,{\mathrm e}^{12}+2 \,{\mathrm e}^{10}-x^{3}}{x^{2}}\) | \(31\) |
parallelrisch | \(\frac {250 \,{\mathrm e}^{10} {\mathrm e}^{2}+250 \,{\mathrm e}^{10} \ln \left (x^{2}\right )-2 x^{3}+4 \,{\mathrm e}^{10}}{2 x^{2}}\) | \(38\) |
default | \(-x +\frac {250 \,{\mathrm e}^{12}-246 \,{\mathrm e}^{10}}{2 x^{2}}+\frac {125 \,{\mathrm e}^{10} \ln \left (x^{2}\right )}{x^{2}}+\frac {125 \,{\mathrm e}^{10}}{x^{2}}\) | \(41\) |
parts | \(-x +\frac {250 \,{\mathrm e}^{12}-246 \,{\mathrm e}^{10}}{2 x^{2}}+\frac {125 \,{\mathrm e}^{10} \ln \left (x^{2}\right )}{x^{2}}+\frac {125 \,{\mathrm e}^{10}}{x^{2}}\) | \(41\) |
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Time = 0.25 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=-\frac {x^{3} - 125 \, e^{10} \log \left (x^{2}\right ) - 125 \, e^{12} - 2 \, e^{10}}{x^{2}} \]
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Time = 0.11 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.26 \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=- x + \frac {125 e^{10} \log {\left (x^{2} \right )}}{x^{2}} - \frac {- 125 e^{12} - 2 e^{10}}{x^{2}} \]
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Time = 0.20 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.48 \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=125 \, {\left (\frac {\log \left (x^{2}\right )}{x^{2}} + \frac {1}{x^{2}}\right )} e^{10} - x + \frac {125 \, e^{12}}{x^{2}} - \frac {123 \, e^{10}}{x^{2}} \]
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Time = 0.26 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=-\frac {x^{3} - 125 \, e^{10} \log \left (x^{2}\right ) - 125 \, e^{12} - 2 \, e^{10}}{x^{2}} \]
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Time = 12.83 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13 \[ \int \frac {e^{10} \left (246-250 e^2\right )-x^3-250 e^{10} \log \left (x^2\right )}{x^3} \, dx=\frac {125\,\ln \left (x^2\right )\,{\mathrm {e}}^{10}+{\mathrm {e}}^{10}\,\left (125\,{\mathrm {e}}^2+2\right )}{x^2}-x \]
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