Integrand size = 45, antiderivative size = 23 \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=-e^{-2+e^{x^2}+x+\frac {3 x^3}{2}}+3 x \]
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Time = 0.15 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 6820, 6838} \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=3 x-e^{\frac {3 x^3}{2}+e^{x^2}+x-2} \]
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Rule 12
Rule 6820
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx \\ & = 3 x+\frac {1}{2} \int e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right ) \, dx \\ & = 3 x+\frac {1}{2} \int e^{-2+e^{x^2}+x+\frac {3 x^3}{2}} \left (-2-4 e^{x^2} x-9 x^2\right ) \, dx \\ & = -e^{-2+e^{x^2}+x+\frac {3 x^3}{2}}+3 x \\ \end{align*}
Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=-e^{-2+e^{x^2}+x+\frac {3 x^3}{2}}+3 x \]
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Time = 0.09 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87
method | result | size |
default | \(3 x -{\mathrm e}^{{\mathrm e}^{x^{2}}+\frac {3 x^{3}}{2}+x -2}\) | \(20\) |
norman | \(3 x -{\mathrm e}^{{\mathrm e}^{x^{2}}+\frac {3 x^{3}}{2}+x -2}\) | \(20\) |
risch | \(3 x -{\mathrm e}^{{\mathrm e}^{x^{2}}+\frac {3 x^{3}}{2}+x -2}\) | \(20\) |
parallelrisch | \(3 x -{\mathrm e}^{{\mathrm e}^{x^{2}}+\frac {3 x^{3}}{2}+x -2}\) | \(20\) |
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=3 \, x - e^{\left (\frac {3}{2} \, x^{3} + x + e^{\left (x^{2}\right )} - 2\right )} \]
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Time = 0.12 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=3 x - e^{\frac {3 x^{3}}{2} + x + e^{x^{2}} - 2} \]
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Time = 0.19 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=3 \, x - e^{\left (\frac {3}{2} \, x^{3} + x + e^{\left (x^{2}\right )} - 2\right )} \]
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=3 \, x - e^{\left (\frac {3}{2} \, x^{3} + x + e^{\left (x^{2}\right )} - 2\right )} \]
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Time = 0.13 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {1}{2} \left (6+e^{\frac {1}{2} \left (-4+2 e^{x^2}+2 x+3 x^3\right )} \left (-2-4 e^{x^2} x-9 x^2\right )\right ) \, dx=3\,x-{\mathrm {e}}^{x+{\mathrm {e}}^{x^2}+\frac {3\,x^3}{2}-2} \]
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