Integrand size = 35, antiderivative size = 12 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=e^{\left (22+e^3+x\right )^2}+x \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {2259, 2240} \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x+e^{\left (x+e^3+22\right )^2} \]
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Rule 2240
Rule 2259
Rubi steps \begin{align*} \text {integral}& = x+\int e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right ) \, dx \\ & = x+\int e^{\left (22+e^3+x\right )^2} \left (44+2 e^3+2 x\right ) \, dx \\ & = e^{\left (22+e^3+x\right )^2}+x \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=e^{\left (22+e^3+x\right )^2}+x \]
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Leaf count of result is larger than twice the leaf count of optimal. \(22\) vs. \(2(10)=20\).
Time = 0.06 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.92
method | result | size |
risch | \(x +{\mathrm e}^{2 x \,{\mathrm e}^{3}+x^{2}+44 \,{\mathrm e}^{3}+{\mathrm e}^{6}+44 x +484}\) | \(23\) |
norman | \(x +{\mathrm e}^{{\mathrm e}^{6}+\left (2 x +44\right ) {\mathrm e}^{3}+x^{2}+44 x +484}\) | \(24\) |
parallelrisch | \(x +{\mathrm e}^{{\mathrm e}^{6}+\left (2 x +44\right ) {\mathrm e}^{3}+x^{2}+44 x +484}\) | \(24\) |
default | \(x +2 \,{\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \left (\frac {{\mathrm e}^{x^{2}+\left (2 \,{\mathrm e}^{3}+44\right ) x}}{2}+\frac {i \left (2 \,{\mathrm e}^{3}+44\right ) \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )}{4}\right )-i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} {\mathrm e}^{3} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )-22 i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )\) | \(161\) |
parts | \(x +2 \,{\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \left (\frac {{\mathrm e}^{x^{2}+\left (2 \,{\mathrm e}^{3}+44\right ) x}}{2}+\frac {i \left (2 \,{\mathrm e}^{3}+44\right ) \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )}{4}\right )-i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} {\mathrm e}^{3} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )-22 i {\mathrm e}^{{\mathrm e}^{6}} {\mathrm e}^{44 \,{\mathrm e}^{3}} {\mathrm e}^{484} \sqrt {\pi }\, {\mathrm e}^{-\frac {\left (2 \,{\mathrm e}^{3}+44\right )^{2}}{4}} \operatorname {erf}\left (i x +\frac {i \left (2 \,{\mathrm e}^{3}+44\right )}{2}\right )\) | \(161\) |
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Time = 0.29 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 22 vs. \(2 (10) = 20\).
Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{x^{2} + 44 x + \left (2 x + 44\right ) e^{3} + e^{6} + 484} \]
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Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{\left (x^{2} + 2 \, {\left (x + 22\right )} e^{3} + 44 \, x + e^{6} + 484\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 22 vs. \(2 (10) = 20\).
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x + e^{\left (x^{2} + 2 \, x e^{3} + 44 \, x + e^{6} + 44 \, e^{3} + 484\right )} \]
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Time = 7.52 (sec) , antiderivative size = 27, normalized size of antiderivative = 2.25 \[ \int \left (1+e^{484+e^6+44 x+x^2+e^3 (44+2 x)} \left (44+2 e^3+2 x\right )\right ) \, dx=x+{\mathrm {e}}^{44\,{\mathrm {e}}^3}\,{\mathrm {e}}^{44\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{484}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^3}\,{\mathrm {e}}^{{\mathrm {e}}^6} \]
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