Integrand size = 42, antiderivative size = 22 \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx=3+e^x-\frac {16}{5} e^{15 (-4+x (2+x))^2} \]
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Time = 0.05 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2225, 6838} \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx=e^x-\frac {16}{5} e^{15 x^4+60 x^3-60 x^2-240 x+240} \]
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Rule 2225
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int e^x \, dx+\int e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right ) \, dx \\ & = e^x-\frac {16}{5} e^{240-240 x-60 x^2+60 x^3+15 x^4} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx=e^x-\frac {16}{5} e^{15 \left (-4+2 x+x^2\right )^2} \]
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Time = 0.08 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86
method | result | size |
risch | \(-\frac {16 \,{\mathrm e}^{15 \left (x^{2}+2 x -4\right )^{2}}}{5}+{\mathrm e}^{x}\) | \(19\) |
default | \(-\frac {16 \,{\mathrm e}^{15 x^{4}+60 x^{3}-60 x^{2}-240 x +240}}{5}+{\mathrm e}^{x}\) | \(27\) |
norman | \(-\frac {16 \,{\mathrm e}^{15 x^{4}+60 x^{3}-60 x^{2}-240 x +240}}{5}+{\mathrm e}^{x}\) | \(27\) |
parallelrisch | \(-\frac {16 \,{\mathrm e}^{15 x^{4}+60 x^{3}-60 x^{2}-240 x +240}}{5}+{\mathrm e}^{x}\) | \(27\) |
parts | \(-\frac {16 \,{\mathrm e}^{15 x^{4}+60 x^{3}-60 x^{2}-240 x +240}}{5}+{\mathrm e}^{x}\) | \(27\) |
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none
Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx=-\frac {16}{5} \, e^{\left (15 \, x^{4} + 60 \, x^{3} - 60 \, x^{2} - 240 \, x + 240\right )} + e^{x} \]
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Time = 0.09 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.23 \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx=e^{x} - \frac {16 e^{15 x^{4} + 60 x^{3} - 60 x^{2} - 240 x + 240}}{5} \]
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none
Time = 0.18 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx=-\frac {16}{5} \, e^{\left (15 \, x^{4} + 60 \, x^{3} - 60 \, x^{2} - 240 \, x + 240\right )} + e^{x} \]
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none
Time = 0.28 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx=-\frac {16}{5} \, e^{\left (15 \, x^{4} + 60 \, x^{3} - 60 \, x^{2} - 240 \, x + 240\right )} + e^{x} \]
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Time = 14.75 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.32 \[ \int \left (e^x+e^{240-240 x-60 x^2+60 x^3+15 x^4} \left (768+384 x-576 x^2-192 x^3\right )\right ) \, dx={\mathrm {e}}^x-\frac {16\,{\mathrm {e}}^{-240\,x}\,{\mathrm {e}}^{240}\,{\mathrm {e}}^{15\,x^4}\,{\mathrm {e}}^{-60\,x^2}\,{\mathrm {e}}^{60\,x^3}}{5} \]
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