Integrand size = 177, antiderivative size = 33 \[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=\left (e^{-x+5 x \left (4-\left (8+x \log \left (e^{-x} x\right )\right )^2\right )}-x\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(208\) vs. \(2(33)=66\).
Time = 1.69 (sec) , antiderivative size = 208, normalized size of antiderivative = 6.30, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6838, 2326} \[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=x^2+\left (e^{-x} x\right )^{-160 x^2} e^{-10 x^3 \log ^2\left (e^{-x} x\right )-602 x}-\frac {2 \left (e^{-x} x\right )^{-80 x^2} e^{-5 x^3 \log ^2\left (e^{-x} x\right )-301 x} \left (-80 x^3+15 x^3 \log ^2\left (e^{-x} x\right )+80 x^2+10 \left (-x^4+x^3+16 x^2\right ) \log \left (e^{-x} x\right )+301 x\right )}{15 x^2 \log ^2\left (e^{-x} x\right )+10 e^x \left (e^{-x}-e^{-x} x\right ) x^2 \log \left (e^{-x} x\right )+80 e^x \left (e^{-x}-e^{-x} x\right ) x+160 x \log \left (e^{-x} x\right )+301} \]
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Rule 2326
Rule 6838
Rubi steps \begin{align*} \text {integral}& = x^2+\int \exp \left (-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )\right ) \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right ) \, dx+\int \exp \left (-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )\right ) \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right ) \, dx \\ & = x^2+e^{-602 x-10 x^3 \log ^2\left (e^{-x} x\right )} \left (e^{-x} x\right )^{-160 x^2}-\frac {2 e^{-301 x-5 x^3 \log ^2\left (e^{-x} x\right )} \left (e^{-x} x\right )^{-80 x^2} \left (301 x+80 x^2-80 x^3+10 \left (16 x^2+x^3-x^4\right ) \log \left (e^{-x} x\right )+15 x^3 \log ^2\left (e^{-x} x\right )\right )}{301+80 e^x x \left (e^{-x}-e^{-x} x\right )+160 x \log \left (e^{-x} x\right )+10 e^x x^2 \left (e^{-x}-e^{-x} x\right ) \log \left (e^{-x} x\right )+15 x^2 \log ^2\left (e^{-x} x\right )} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(173\) vs. \(2(33)=66\).
Time = 0.42 (sec) , antiderivative size = 173, normalized size of antiderivative = 5.24 \[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=e^{-2 x \left (301+80 x^2+10 x^4+5 x^2 \log ^2\left (e^{-x} x\right )\right )} x^{20 x^4} \left (e^{-x} x\right )^{-20 x^2 \left (8+x^2\right )} \left (e^{10 x^3 \left (8+x \left (x-\log (x)+\log \left (e^{-x} x\right )\right )\right )}-e^{x \left (301+5 x^4+5 x^2 \log ^2(x)+80 x \left (x-\log (x)+\log \left (e^{-x} x\right )\right )+5 x^2 \left (x-\log (x)+\log \left (e^{-x} x\right )\right )^2\right )} x^{1+80 x^2+10 x^3 \left (-\log (x)+\log \left (e^{-x} x\right )\right )}\right )^2 \]
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Leaf count of result is larger than twice the leaf count of optimal. \(71\) vs. \(2(31)=62\).
Time = 0.39 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.18
method | result | size |
parallelrisch | \(x^{2}-2 \,{\mathrm e}^{-5 x^{3} \ln \left (x \,{\mathrm e}^{-x}\right )^{2}-80 \ln \left (x \,{\mathrm e}^{-x}\right ) x^{2}-301 x} x +{\mathrm e}^{-10 x^{3} \ln \left (x \,{\mathrm e}^{-x}\right )^{2}-160 \ln \left (x \,{\mathrm e}^{-x}\right ) x^{2}-602 x}\) | \(72\) |
risch | \(\text {Expression too large to display}\) | \(1157\) |
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Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (29) = 58\).
Time = 0.25 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.09 \[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=x^{2} - 2 \, x e^{\left (-5 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 301 \, x\right )} + e^{\left (-10 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 160 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 602 \, x\right )} \]
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Timed out. \[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (29) = 58\).
Time = 0.31 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.52 \[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=x^{2} - 2 \, x e^{\left (-5 \, x^{5} + 10 \, x^{4} \log \left (x\right ) - 5 \, x^{3} \log \left (x\right )^{2} + 80 \, x^{3} - 80 \, x^{2} \log \left (x\right ) - 301 \, x\right )} + e^{\left (-10 \, x^{5} + 20 \, x^{4} \log \left (x\right ) - 10 \, x^{3} \log \left (x\right )^{2} + 160 \, x^{3} - 160 \, x^{2} \log \left (x\right ) - 602 \, x\right )} \]
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\[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=\int { 2 \, {\left (15 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{3} + 80 \, x^{2} - 10 \, {\left (x^{4} - x^{3} - 16 \, x^{2}\right )} \log \left (x e^{\left (-x\right )}\right ) + 301 \, x - 1\right )} e^{\left (-5 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 301 \, x\right )} - 2 \, {\left (15 \, x^{2} \log \left (x e^{\left (-x\right )}\right )^{2} - 80 \, x^{2} - 10 \, {\left (x^{3} - x^{2} - 16 \, x\right )} \log \left (x e^{\left (-x\right )}\right ) + 80 \, x + 301\right )} e^{\left (-10 \, x^{3} \log \left (x e^{\left (-x\right )}\right )^{2} - 160 \, x^{2} \log \left (x e^{\left (-x\right )}\right ) - 602 \, x\right )} + 2 \, x \,d x } \]
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Time = 9.30 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.79 \[ \int \left (2 x+e^{-602 x-160 x^2 \log \left (e^{-x} x\right )-10 x^3 \log ^2\left (e^{-x} x\right )} \left (-602-160 x+160 x^2+\left (-320 x-20 x^2+20 x^3\right ) \log \left (e^{-x} x\right )-30 x^2 \log ^2\left (e^{-x} x\right )\right )+e^{-301 x-80 x^2 \log \left (e^{-x} x\right )-5 x^3 \log ^2\left (e^{-x} x\right )} \left (-2+602 x+160 x^2-160 x^3+\left (320 x^2+20 x^3-20 x^4\right ) \log \left (e^{-x} x\right )+30 x^3 \log ^2\left (e^{-x} x\right )\right )\right ) \, dx=x^2+\frac {x^{20\,x^4}\,{\mathrm {e}}^{-602\,x}\,{\mathrm {e}}^{-10\,x^5}\,{\mathrm {e}}^{160\,x^3}\,{\mathrm {e}}^{-10\,x^3\,{\ln \left (x\right )}^2}}{x^{160\,x^2}}-\frac {2\,x\,x^{10\,x^4}\,{\mathrm {e}}^{-301\,x}\,{\mathrm {e}}^{-5\,x^5}\,{\mathrm {e}}^{80\,x^3}\,{\mathrm {e}}^{-5\,x^3\,{\ln \left (x\right )}^2}}{x^{80\,x^2}} \]
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