Integrand size = 182, antiderivative size = 31 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (-5-x^2+3 x (5+x) \left (3+2 x+e^{-x} x^2\right )\right )^2} \]
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\[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=\int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (1350 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^5+180 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^6-108 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^7-18 \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^8-6 \exp \left (-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^2 \left (75-905 x-955 x^2-173 x^3+26 x^4+6 x^5\right )+2 \exp \left (e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) \left (-225+1645 x+5040 x^2+3968 x^3+1140 x^4+108 x^5\right )\right ) \, dx \\ & = 2 \int \exp \left (e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) \left (-225+1645 x+5040 x^2+3968 x^3+1140 x^4+108 x^5\right ) \, dx-6 \int \exp \left (-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^2 \left (75-905 x-955 x^2-173 x^3+26 x^4+6 x^5\right ) \, dx-18 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^8 \, dx-108 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^7 \, dx+180 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^6 \, dx+1350 \int \exp \left (-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )\right ) x^5 \, dx \\ & = 2 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} \left (-225+1645 x+5040 x^2+3968 x^3+1140 x^4+108 x^5\right ) \, dx-6 \int \left (75 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^2-905 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^3-955 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^4-173 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5+26 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6+6 e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7\right ) \, dx-18 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^8 \, dx-108 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx+180 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+1350 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx \\ & = 2 \int \left (-225 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2}+1645 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x+5040 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^2+3968 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^3+1140 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^4+108 e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^5\right ) \, dx-18 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^8 \, dx-36 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-108 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-156 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+180 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx-450 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^2 \, dx+1038 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+1350 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+5430 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^3 \, dx+5730 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^4 \, dx \\ & = -\left (18 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^8 \, dx\right )-36 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-108 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^7 \, dx-156 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+180 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^6 \, dx+216 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^5 \, dx-450 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} \, dx-450 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^2 \, dx+1038 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+1350 \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^5 \, dx+2280 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^4 \, dx+3290 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x \, dx+5430 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^3 \, dx+5730 \int e^{-x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} x^4 \, dx+7936 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^3 \, dx+10080 \int e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} x^2 \, dx \\ \end{align*}
Time = 0.22 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.23 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{e^{-2 x} \left (3 x^3 (5+x)+e^x \left (-5+45 x+38 x^2+6 x^3\right )\right )^2} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(86\) vs. \(2(29)=58\).
Time = 2.07 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.81
method | result | size |
parallelrisch | \({\mathrm e}^{\left (\left (36 x^{6}+456 x^{5}+1984 x^{4}+3360 x^{3}+1645 x^{2}-450 x +25\right ) {\mathrm e}^{2 x}+\left (36 x^{7}+408 x^{6}+1410 x^{5}+1320 x^{4}-150 x^{3}\right ) {\mathrm e}^{x}+9 x^{8}+90 x^{7}+225 x^{6}\right ) {\mathrm e}^{-2 x}}\) | \(87\) |
risch | \({\mathrm e}^{\left (36 x^{7} {\mathrm e}^{x}+9 x^{8}+408 x^{6} {\mathrm e}^{x}+36 \,{\mathrm e}^{2 x} x^{6}+90 x^{7}+1410 x^{5} {\mathrm e}^{x}+456 x^{5} {\mathrm e}^{2 x}+225 x^{6}+1320 \,{\mathrm e}^{x} x^{4}+1984 \,{\mathrm e}^{2 x} x^{4}-150 \,{\mathrm e}^{x} x^{3}+3360 \,{\mathrm e}^{2 x} x^{3}+1645 \,{\mathrm e}^{2 x} x^{2}-450 x \,{\mathrm e}^{2 x}+25 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}}\) | \(116\) |
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Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 91, normalized size of antiderivative = 2.94 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left ({\left (9 \, x^{8} + 90 \, x^{7} + 225 \, x^{6} + {\left (36 \, x^{6} + 456 \, x^{5} + 1984 \, x^{4} + 3360 \, x^{3} + 1645 \, x^{2} - 452 \, x + 25\right )} e^{\left (2 \, x\right )} + 6 \, {\left (6 \, x^{7} + 68 \, x^{6} + 235 \, x^{5} + 220 \, x^{4} - 25 \, x^{3}\right )} e^{x}\right )} e^{\left (-2 \, x\right )} + 2 \, x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (26) = 52\).
Time = 0.35 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.74 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (9 x^{8} + 90 x^{7} + 225 x^{6} + \left (36 x^{7} + 408 x^{6} + 1410 x^{5} + 1320 x^{4} - 150 x^{3}\right ) e^{x} + \left (36 x^{6} + 456 x^{5} + 1984 x^{4} + 3360 x^{3} + 1645 x^{2} - 450 x + 25\right ) e^{2 x}\right ) e^{- 2 x}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (29) = 58\).
Time = 1.26 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=e^{\left (9 \, x^{8} e^{\left (-2 \, x\right )} + 36 \, x^{7} e^{\left (-x\right )} + 90 \, x^{7} e^{\left (-2 \, x\right )} + 408 \, x^{6} e^{\left (-x\right )} + 225 \, x^{6} e^{\left (-2 \, x\right )} + 36 \, x^{6} + 1410 \, x^{5} e^{\left (-x\right )} + 456 \, x^{5} + 1320 \, x^{4} e^{\left (-x\right )} + 1984 \, x^{4} - 150 \, x^{3} e^{\left (-x\right )} + 3360 \, x^{3} + 1645 \, x^{2} - 450 \, x + 25\right )} \]
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\[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx=\int { -2 \, {\left (9 \, x^{8} + 54 \, x^{7} - 90 \, x^{6} - 675 \, x^{5} - {\left (108 \, x^{5} + 1140 \, x^{4} + 3968 \, x^{3} + 5040 \, x^{2} + 1645 \, x - 225\right )} e^{\left (2 \, x\right )} + 3 \, {\left (6 \, x^{7} + 26 \, x^{6} - 173 \, x^{5} - 955 \, x^{4} - 905 \, x^{3} + 75 \, x^{2}\right )} e^{x}\right )} e^{\left ({\left (9 \, x^{8} + 90 \, x^{7} + 225 \, x^{6} + {\left (36 \, x^{6} + 456 \, x^{5} + 1984 \, x^{4} + 3360 \, x^{3} + 1645 \, x^{2} - 450 \, x + 25\right )} e^{\left (2 \, x\right )} + 6 \, {\left (6 \, x^{7} + 68 \, x^{6} + 235 \, x^{5} + 220 \, x^{4} - 25 \, x^{3}\right )} e^{x}\right )} e^{\left (-2 \, x\right )} - 2 \, x\right )} \,d x } \]
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Time = 9.70 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.77 \[ \int e^{-2 x+e^{-2 x} \left (225 x^6+90 x^7+9 x^8+e^{2 x} \left (25-450 x+1645 x^2+3360 x^3+1984 x^4+456 x^5+36 x^6\right )+e^x \left (-150 x^3+1320 x^4+1410 x^5+408 x^6+36 x^7\right )\right )} \left (1350 x^5+180 x^6-108 x^7-18 x^8+e^{2 x} \left (-450+3290 x+10080 x^2+7936 x^3+2280 x^4+216 x^5\right )+e^x \left (-450 x^2+5430 x^3+5730 x^4+1038 x^5-156 x^6-36 x^7\right )\right ) \, dx={\mathrm {e}}^{-450\,x}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{36\,x^6}\,{\mathrm {e}}^{456\,x^5}\,{\mathrm {e}}^{1645\,x^2}\,{\mathrm {e}}^{1984\,x^4}\,{\mathrm {e}}^{3360\,x^3}\,{\mathrm {e}}^{9\,x^8\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{36\,x^7\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{90\,x^7\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{-150\,x^3\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{225\,x^6\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{408\,x^6\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{1320\,x^4\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{1410\,x^5\,{\mathrm {e}}^{-x}} \]
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