Integrand size = 42, antiderivative size = 23 \[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx=e^{\frac {1}{4} x \left (10-7 \left (-1+e^x\right )+2 x\right )}-x \]
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Time = 0.08 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {12, 6838} \[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx=e^{\frac {1}{4} \left (2 x^2-7 e^x x+17 x\right )}-x \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{4} \int \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx \\ & = -x+\frac {1}{4} \int e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right ) \, dx \\ & = e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )}-x \\ \end{align*}
Time = 0.94 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx=e^{\frac {17 x}{4}-\frac {7 e^x x}{4}+\frac {x^2}{2}}-x \]
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Time = 0.07 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.78
method | result | size |
risch | \(-x +{\mathrm e}^{-\frac {x \left (7 \,{\mathrm e}^{x}-2 x -17\right )}{4}}\) | \(18\) |
parallelrisch | \(-x +{\mathrm e}^{-\frac {x \left (7 \,{\mathrm e}^{x}-2 x -17\right )}{4}}\) | \(18\) |
default | \(-x +{\mathrm e}^{-\frac {7 \,{\mathrm e}^{x} x}{4}+\frac {x^{2}}{2}+\frac {17 x}{4}}\) | \(20\) |
norman | \(-x +{\mathrm e}^{-\frac {7 \,{\mathrm e}^{x} x}{4}+\frac {x^{2}}{2}+\frac {17 x}{4}}\) | \(20\) |
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx=-x + e^{\left (\frac {1}{2} \, x^{2} - \frac {7}{4} \, x e^{x} + \frac {17}{4} \, x\right )} \]
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Time = 0.10 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx=- x + e^{\frac {x^{2}}{2} - \frac {7 x e^{x}}{4} + \frac {17 x}{4}} \]
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\[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx=\int { -\frac {1}{4} \, {\left (7 \, {\left (x + 1\right )} e^{x} - 4 \, x - 17\right )} e^{\left (\frac {1}{2} \, x^{2} - \frac {7}{4} \, x e^{x} + \frac {17}{4} \, x\right )} - 1 \,d x } \]
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Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx=-x + e^{\left (\frac {1}{2} \, x^{2} - \frac {7}{4} \, x e^{x} + \frac {17}{4} \, x\right )} \]
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Time = 0.11 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{4} \left (-4+e^{\frac {1}{4} \left (17 x-7 e^x x+2 x^2\right )} \left (17+e^x (-7-7 x)+4 x\right )\right ) \, dx={\mathrm {e}}^{\frac {17\,x}{4}-\frac {7\,x\,{\mathrm {e}}^x}{4}+\frac {x^2}{2}}-x \]
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