Integrand size = 38, antiderivative size = 20 \[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=1+\frac {25}{2} \left (3+e^{\frac {e^x}{x^2}}\right ) x^2 \]
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\[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=\int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{x} \, dx \\ & = \frac {1}{2} \int \left (\frac {25 e^{\frac {e^x}{x^2}+x} (-2+x)}{x}+50 \left (3+e^{\frac {e^x}{x^2}}\right ) x\right ) \, dx \\ & = \frac {25}{2} \int \frac {e^{\frac {e^x}{x^2}+x} (-2+x)}{x} \, dx+25 \int \left (3+e^{\frac {e^x}{x^2}}\right ) x \, dx \\ & = \frac {25}{2} \int \left (e^{\frac {e^x}{x^2}+x}-\frac {2 e^{\frac {e^x}{x^2}+x}}{x}\right ) \, dx+25 \int \left (3 x+e^{\frac {e^x}{x^2}} x\right ) \, dx \\ & = \frac {75 x^2}{2}+\frac {25}{2} \int e^{\frac {e^x}{x^2}+x} \, dx-25 \int \frac {e^{\frac {e^x}{x^2}+x}}{x} \, dx+25 \int e^{\frac {e^x}{x^2}} x \, dx \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=\frac {25}{2} \left (3+e^{\frac {e^x}{x^2}}\right ) x^2 \]
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Time = 0.28 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95
method | result | size |
norman | \(\frac {75 x^{2}}{2}+\frac {25 \,{\mathrm e}^{\frac {{\mathrm e}^{x}}{x^{2}}} x^{2}}{2}\) | \(19\) |
risch | \(\frac {75 x^{2}}{2}+\frac {25 \,{\mathrm e}^{\frac {{\mathrm e}^{x}}{x^{2}}} x^{2}}{2}\) | \(19\) |
parallelrisch | \(\frac {75 x^{2}}{2}+\frac {25 \,{\mathrm e}^{\frac {{\mathrm e}^{x}}{x^{2}}} x^{2}}{2}\) | \(19\) |
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Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=\frac {25}{2} \, x^{2} e^{\left (\frac {e^{x}}{x^{2}}\right )} + \frac {75}{2} \, x^{2} \]
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Time = 0.61 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=\frac {25 x^{2} e^{\frac {e^{x}}{x^{2}}}}{2} + \frac {75 x^{2}}{2} \]
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Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=\frac {25}{2} \, x^{2} e^{\left (\frac {e^{x}}{x^{2}}\right )} + \frac {75}{2} \, x^{2} \]
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Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.45 \[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=\frac {25}{2} \, {\left (3 \, x^{2} e^{x} + x^{2} e^{\left (\frac {x^{3} + e^{x}}{x^{2}}\right )}\right )} e^{\left (-x\right )} \]
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Time = 11.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int \frac {150 x^2+e^{\frac {e^x}{x^2}} \left (50 x^2+e^x (-50+25 x)\right )}{2 x} \, dx=\frac {25\,x^2\,\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x^2}}+3\right )}{2} \]
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