Integrand size = 32, antiderivative size = 15 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{20 e^{-2 x+9 x^3}} \]
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\[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=\int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (-40 e^{20 e^{-2 x+9 x^3}-2 x+9 x^3}+540 e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} x^2\right ) \, dx \\ & = -\left (40 \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \, dx\right )+540 \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} x^2 \, dx \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{20 e^{-2 x+9 x^3}} \]
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Time = 0.14 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93
method | result | size |
risch | \({\mathrm e}^{20 \,{\mathrm e}^{x \left (9 x^{2}-2\right )}}\) | \(14\) |
default | \({\mathrm e}^{20 \,{\mathrm e}^{9 x^{3}-2 x}}\) | \(16\) |
norman | \({\mathrm e}^{20 \,{\mathrm e}^{9 x^{3}-2 x}}\) | \(16\) |
parallelrisch | \({\mathrm e}^{20 \,{\mathrm e}^{9 x^{3}-2 x}}\) | \(16\) |
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \]
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Time = 0.12 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{20 e^{9 x^{3} - 2 x}} \]
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Time = 0.33 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \]
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\[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=\int { 20 \, {\left (27 \, x^{2} - 2\right )} e^{\left (9 \, x^{3} - 2 \, x + 20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \,d x } \]
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Time = 0.12 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx={\mathrm {e}}^{20\,{\mathrm {e}}^{9\,x^3-2\,x}} \]
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