Integrand size = 133, antiderivative size = 28 \[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\frac {3+\frac {25 e^{e^{\left (2+e^2 (3+x)^2\right )^2}}}{x^2}}{x} \]
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\[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\int \frac {-3 x^2+\exp \left (\exp \left (4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )\right )\right ) \left (-75+\exp \left (4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )\right ) \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {3 \left (25 e^{e^{\left (2+e^2 (3+x)^2\right )^2}}+x^2\right )}{x^4}+\frac {100 \exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right ) (3+x) \left (2+9 e^2+6 e^2 x+e^2 x^2\right )}{x^3}\right ) \, dx \\ & = -\left (3 \int \frac {25 e^{e^{\left (2+e^2 (3+x)^2\right )^2}}+x^2}{x^4} \, dx\right )+100 \int \frac {\exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right ) (3+x) \left (2+9 e^2+6 e^2 x+e^2 x^2\right )}{x^3} \, dx \\ & = -\left (3 \int \left (\frac {25 e^{e^{\left (2+9 e^2+6 e^2 x+e^2 x^2\right )^2}}}{x^4}+\frac {1}{x^2}\right ) \, dx\right )+100 \int \left (\exp \left (8+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )+\frac {3 \exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right ) \left (2+9 e^2\right )}{x^3}+\frac {\exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right ) \left (2+27 e^2\right )}{x^2}+\frac {9 \exp \left (8+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )}{x}\right ) \, dx \\ & = \frac {3}{x}-75 \int \frac {e^{e^{\left (2+9 e^2+6 e^2 x+e^2 x^2\right )^2}}}{x^4} \, dx+100 \int \exp \left (8+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right ) \, dx+900 \int \frac {\exp \left (8+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )}{x} \, dx+\left (300 \left (2+9 e^2\right )\right ) \int \frac {\exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )}{x^3} \, dx+\left (100 \left (2+27 e^2\right )\right ) \int \frac {\exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )}{x^2} \, dx \\ & = \frac {3}{x}-75 \int \frac {e^{e^{\left (2+9 e^2+6 e^2 x+e^2 x^2\right )^2}}}{x^4} \, dx+100 \text {Subst}\left (\int e^{8+e^{\left (2+e^2 x^2\right )^2}+4 e^2 x^2+e^4 x^4} \, dx,x,3+x\right )+900 \int \frac {\exp \left (8+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )}{x} \, dx+\left (300 \left (2+9 e^2\right )\right ) \int \frac {\exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )}{x^3} \, dx+\left (100 \left (2+27 e^2\right )\right ) \int \frac {\exp \left (6+e^{\left (2+e^2 (3+x)^2\right )^2}+4 e^2 (3+x)^2+e^4 (3+x)^4\right )}{x^2} \, dx \\ \end{align*}
Time = 4.32 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\frac {25 e^{e^{\left (2+e^2 (3+x)^2\right )^2}}+3 x^2}{x^3} \]
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Time = 0.80 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.96
method | result | size |
norman | \(\frac {3 x^{2}+25 \,{\mathrm e}^{{\mathrm e}^{\left (x^{4}+12 x^{3}+54 x^{2}+108 x +81\right ) {\mathrm e}^{4}+\left (4 x^{2}+24 x +36\right ) {\mathrm e}^{2}+4}}}{x^{3}}\) | \(55\) |
parallelrisch | \(\frac {3 x^{2}+25 \,{\mathrm e}^{{\mathrm e}^{\left (x^{4}+12 x^{3}+54 x^{2}+108 x +81\right ) {\mathrm e}^{4}+\left (4 x^{2}+24 x +36\right ) {\mathrm e}^{2}+4}}}{x^{3}}\) | \(55\) |
risch | \(\frac {3}{x}+\frac {25 \,{\mathrm e}^{{\mathrm e}^{x^{4} {\mathrm e}^{4}+12 x^{3} {\mathrm e}^{4}+4 x^{2} {\mathrm e}^{2}+54 x^{2} {\mathrm e}^{4}+24 \,{\mathrm e}^{2} x +108 x \,{\mathrm e}^{4}+36 \,{\mathrm e}^{2}+81 \,{\mathrm e}^{4}+4}}}{x^{3}}\) | \(61\) |
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Time = 0.25 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75 \[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\frac {3 \, x^{2} + 25 \, e^{\left (e^{\left ({\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )} e^{4} + 4 \, {\left (x^{2} + 6 \, x + 9\right )} e^{2} + 4\right )}\right )}}{x^{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (22) = 44\).
Time = 0.18 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.71 \[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\frac {3}{x} + \frac {25 e^{e^{\left (4 x^{2} + 24 x + 36\right ) e^{2} + \left (x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81\right ) e^{4} + 4}}}{x^{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.14 \[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\frac {3}{x} + \frac {25 \, e^{\left (e^{\left (x^{4} e^{4} + 12 \, x^{3} e^{4} + 54 \, x^{2} e^{4} + 4 \, x^{2} e^{2} + 108 \, x e^{4} + 24 \, x e^{2} + 81 \, e^{4} + 36 \, e^{2} + 4\right )}\right )}}{x^{3}} \]
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\[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\int { -\frac {3 \, x^{2} - 25 \, {\left (4 \, {\left ({\left (x^{4} + 9 \, x^{3} + 27 \, x^{2} + 27 \, x\right )} e^{4} + 2 \, {\left (x^{2} + 3 \, x\right )} e^{2}\right )} e^{\left ({\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )} e^{4} + 4 \, {\left (x^{2} + 6 \, x + 9\right )} e^{2} + 4\right )} - 3\right )} e^{\left (e^{\left ({\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )} e^{4} + 4 \, {\left (x^{2} + 6 \, x + 9\right )} e^{2} + 4\right )}\right )}}{x^{4}} \,d x } \]
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Time = 12.55 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.43 \[ \int \frac {-3 x^2+e^{e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )}} \left (-75+e^{4+e^2 \left (36+24 x+4 x^2\right )+e^4 \left (81+108 x+54 x^2+12 x^3+x^4\right )} \left (e^2 \left (600 x+200 x^2\right )+e^4 \left (2700 x+2700 x^2+900 x^3+100 x^4\right )\right )\right )}{x^4} \, dx=\frac {25\,{\mathrm {e}}^{{\mathrm {e}}^{x^4\,{\mathrm {e}}^4}\,{\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{12\,x^3\,{\mathrm {e}}^4}\,{\mathrm {e}}^{54\,x^2\,{\mathrm {e}}^4}\,{\mathrm {e}}^{36\,{\mathrm {e}}^2}\,{\mathrm {e}}^{81\,{\mathrm {e}}^4}\,{\mathrm {e}}^4\,{\mathrm {e}}^{24\,x\,{\mathrm {e}}^2}\,{\mathrm {e}}^{108\,x\,{\mathrm {e}}^4}}}{x^3}+\frac {3}{x} \]
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