Integrand size = 282, antiderivative size = 30 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=\frac {\left (-1+e^5-x\right )^4 \left (-1-x+\left (-1+5 x^2 \log (x)\right )^2\right )}{x} \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(470\) vs. \(2(30)=60\).
Time = 0.29 (sec) , antiderivative size = 470, normalized size of antiderivative = 15.67, number of steps used = 25, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {2403, 2332, 2341, 6, 2342} \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=25 x^7 \log ^2(x)+100 \left (1-e^5\right ) x^6 \log ^2(x)-2 \left (5-12 e^5+6 e^{10}\right ) x^5+12 \left (1-e^5\right )^2 x^5-2 x^5+150 \left (1-e^5\right )^2 x^5 \log ^2(x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)-60 \left (1-e^5\right )^2 x^5 \log (x)-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4+\frac {25}{2} \left (1-e^5\right )^3 x^4+10 e^5 x^4-11 x^4+100 \left (1-e^5\right )^3 x^4 \log ^2(x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)-50 \left (1-e^5\right )^3 x^4 \log (x)+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3+\frac {50}{9} \left (1-e^5\right )^4 x^3-20 e^{10} x^3+44 e^5 x^3-24 x^3+25 \left (1-e^5\right )^4 x^3 \log ^2(x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)-\frac {50}{3} \left (1-e^5\right )^4 x^3 \log (x)+20 \left (1-e^5\right )^3 x^2-66 e^{10} x^2+72 e^5 x^2-26 x^2-40 \left (1-e^5\right )^3 x^2 \log (x)-2 \left (7+5 e^{20}\right ) x+10 \left (1-e^5\right )^4 x-72 e^{10} x+52 e^5 x+\frac {1}{5} e^{15} (10 x+11)^2-10 \left (1-e^5\right )^4 x \log (x) \]
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Rule 6
Rule 2332
Rule 2341
Rule 2342
Rule 2403
Rubi steps \begin{align*} \text {integral}& = -2 \left (7+5 e^{20}\right ) x-26 x^2-24 x^3-11 x^4-2 x^5+\frac {1}{5} e^{15} (11+10 x)^2+e^5 \int \left (52+144 x+132 x^2+40 x^3\right ) \, dx+e^{10} \int \left (-72-132 x-60 x^2\right ) \, dx+\int \left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x) \, dx+\int \left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x) \, dx \\ & = 52 e^5 x-72 e^{10} x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3-11 x^4+10 e^5 x^4-2 x^5+\frac {1}{5} e^{15} (11+10 x)^2+\int \left (\left (75+75 e^{20}\right ) x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x) \, dx+\int \left (-10 \left (-1+e^5\right )^4 \log (x)+80 \left (-1+e^5\right )^3 x \log (x)+10 \left (-1+e^5\right )^2 \left (-13-10 e^5+5 e^{10}\right ) x^2 \log (x)-40 \left (-1+11 e^5-15 e^{10}+5 e^{15}\right ) x^3 \log (x)+50 \left (5-12 e^5+6 e^{10}\right ) x^4 \log (x)-200 \left (-1+e^5\right ) x^5 \log (x)+50 x^6 \log (x)\right ) \, dx \\ & = 52 e^5 x-72 e^{10} x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3-11 x^4+10 e^5 x^4-2 x^5+\frac {1}{5} e^{15} (11+10 x)^2+50 \int x^6 \log (x) \, dx+\left (200 \left (1-e^5\right )\right ) \int x^5 \log (x) \, dx-\left (80 \left (1-e^5\right )^3\right ) \int x \log (x) \, dx-\left (10 \left (1-e^5\right )^4\right ) \int \log (x) \, dx-\left (10 \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right )\right ) \int x^2 \log (x) \, dx+\left (50 \left (5-12 e^5+6 e^{10}\right )\right ) \int x^4 \log (x) \, dx+\left (40 \left (1-11 e^5+15 e^{10}-5 e^{15}\right )\right ) \int x^3 \log (x) \, dx+\int \left (75 \left (-1+e^5\right )^4 x^2 \log ^2(x)-400 \left (-1+e^5\right )^3 x^3 \log ^2(x)+750 \left (-1+e^5\right )^2 x^4 \log ^2(x)-600 \left (-1+e^5\right ) x^5 \log ^2(x)+175 x^6 \log ^2(x)\right ) \, dx \\ & = 52 e^5 x-72 e^{10} x+10 \left (1-e^5\right )^4 x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2+20 \left (1-e^5\right )^3 x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3-11 x^4+10 e^5 x^4-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4-2 x^5-2 \left (5-12 e^5+6 e^{10}\right ) x^5-\frac {50}{9} \left (1-e^5\right ) x^6-\frac {50 x^7}{49}+\frac {1}{5} e^{15} (11+10 x)^2-10 \left (1-e^5\right )^4 x \log (x)-40 \left (1-e^5\right )^3 x^2 \log (x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)+\frac {100}{3} \left (1-e^5\right ) x^6 \log (x)+\frac {50}{7} x^7 \log (x)+175 \int x^6 \log ^2(x) \, dx+\left (600 \left (1-e^5\right )\right ) \int x^5 \log ^2(x) \, dx+\left (750 \left (1-e^5\right )^2\right ) \int x^4 \log ^2(x) \, dx+\left (400 \left (1-e^5\right )^3\right ) \int x^3 \log ^2(x) \, dx+\left (75 \left (1-e^5\right )^4\right ) \int x^2 \log ^2(x) \, dx \\ & = 52 e^5 x-72 e^{10} x+10 \left (1-e^5\right )^4 x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2+20 \left (1-e^5\right )^3 x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3-11 x^4+10 e^5 x^4-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4-2 x^5-2 \left (5-12 e^5+6 e^{10}\right ) x^5-\frac {50}{9} \left (1-e^5\right ) x^6-\frac {50 x^7}{49}+\frac {1}{5} e^{15} (11+10 x)^2-10 \left (1-e^5\right )^4 x \log (x)-40 \left (1-e^5\right )^3 x^2 \log (x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)+\frac {100}{3} \left (1-e^5\right ) x^6 \log (x)+\frac {50}{7} x^7 \log (x)+25 \left (1-e^5\right )^4 x^3 \log ^2(x)+100 \left (1-e^5\right )^3 x^4 \log ^2(x)+150 \left (1-e^5\right )^2 x^5 \log ^2(x)+100 \left (1-e^5\right ) x^6 \log ^2(x)+25 x^7 \log ^2(x)-50 \int x^6 \log (x) \, dx-\left (200 \left (1-e^5\right )\right ) \int x^5 \log (x) \, dx-\left (300 \left (1-e^5\right )^2\right ) \int x^4 \log (x) \, dx-\left (200 \left (1-e^5\right )^3\right ) \int x^3 \log (x) \, dx-\left (50 \left (1-e^5\right )^4\right ) \int x^2 \log (x) \, dx \\ & = 52 e^5 x-72 e^{10} x+10 \left (1-e^5\right )^4 x-2 \left (7+5 e^{20}\right ) x-26 x^2+72 e^5 x^2-66 e^{10} x^2+20 \left (1-e^5\right )^3 x^2-24 x^3+44 e^5 x^3-20 e^{10} x^3+\frac {50}{9} \left (1-e^5\right )^4 x^3+\frac {10}{9} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3-11 x^4+10 e^5 x^4+\frac {25}{2} \left (1-e^5\right )^3 x^4-\frac {5}{2} \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4-2 x^5+12 \left (1-e^5\right )^2 x^5-2 \left (5-12 e^5+6 e^{10}\right ) x^5+\frac {1}{5} e^{15} (11+10 x)^2-10 \left (1-e^5\right )^4 x \log (x)-40 \left (1-e^5\right )^3 x^2 \log (x)-\frac {50}{3} \left (1-e^5\right )^4 x^3 \log (x)-\frac {10}{3} \left (1-e^5\right )^2 \left (13+10 e^5-5 e^{10}\right ) x^3 \log (x)-50 \left (1-e^5\right )^3 x^4 \log (x)+10 \left (1-11 e^5+15 e^{10}-5 e^{15}\right ) x^4 \log (x)-60 \left (1-e^5\right )^2 x^5 \log (x)+10 \left (5-12 e^5+6 e^{10}\right ) x^5 \log (x)+25 \left (1-e^5\right )^4 x^3 \log ^2(x)+100 \left (1-e^5\right )^3 x^4 \log ^2(x)+150 \left (1-e^5\right )^2 x^5 \log ^2(x)+100 \left (1-e^5\right ) x^6 \log ^2(x)+25 x^7 \log ^2(x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(76\) vs. \(2(30)=60\).
Time = 0.43 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.53 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=x \left (-4+4 e^{15}-6 x-4 x^2-x^3-6 e^{10} (2+x)+4 e^5 \left (3+3 x+x^2\right )-10 \left (1-e^5+x\right )^4 \log (x)+25 x^2 \left (1-e^5+x\right )^4 \log ^2(x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(242\) vs. \(2(29)=58\).
Time = 0.25 (sec) , antiderivative size = 243, normalized size of antiderivative = 8.10
method | result | size |
norman | \(\left (-4+4 \,{\mathrm e}^{5}\right ) x^{3}+\left (-6-6 \,{\mathrm e}^{10}+12 \,{\mathrm e}^{5}\right ) x^{2}+\left (-4+4 \,{\mathrm e}^{15}-12 \,{\mathrm e}^{10}+12 \,{\mathrm e}^{5}\right ) x +\left (-100 \,{\mathrm e}^{5}+100\right ) x^{6} \ln \left (x \right )^{2}+\left (40 \,{\mathrm e}^{5}-40\right ) x^{4} \ln \left (x \right )+\left (-60 \,{\mathrm e}^{10}+120 \,{\mathrm e}^{5}-60\right ) x^{3} \ln \left (x \right )+\left (150 \,{\mathrm e}^{10}-300 \,{\mathrm e}^{5}+150\right ) x^{5} \ln \left (x \right )^{2}+\left (-100 \,{\mathrm e}^{15}+300 \,{\mathrm e}^{10}-300 \,{\mathrm e}^{5}+100\right ) x^{4} \ln \left (x \right )^{2}+\left (40 \,{\mathrm e}^{15}-120 \,{\mathrm e}^{10}+120 \,{\mathrm e}^{5}-40\right ) x^{2} \ln \left (x \right )+\left (40 \,{\mathrm e}^{15}-60 \,{\mathrm e}^{10}-10 \,{\mathrm e}^{20}+40 \,{\mathrm e}^{5}-10\right ) x \ln \left (x \right )+\left (25 \,{\mathrm e}^{20}-100 \,{\mathrm e}^{15}+150 \,{\mathrm e}^{10}-100 \,{\mathrm e}^{5}+25\right ) x^{3} \ln \left (x \right )^{2}-x^{4}-10 x^{5} \ln \left (x \right )+25 x^{7} \ln \left (x \right )^{2}\) | \(243\) |
risch | \(25 \,{\mathrm e}^{20} \ln \left (x \right )^{2} x^{3}-100 \,{\mathrm e}^{15} \ln \left (x \right )^{2} x^{4}+150 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{5}-100 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{3}+40 \,{\mathrm e}^{15} \ln \left (x \right ) x^{2}+150 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{3}-10 \ln \left (x \right ) x \,{\mathrm e}^{20}-100 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{6}-60 x^{3} {\mathrm e}^{10} \ln \left (x \right )-60 \,{\mathrm e}^{10} \ln \left (x \right ) x -100 \,{\mathrm e}^{15} \ln \left (x \right )^{2} x^{3}+300 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{4}-6 x^{2} {\mathrm e}^{10}-4 x +120 x^{2} {\mathrm e}^{5} \ln \left (x \right )+4 x \,{\mathrm e}^{15}+25 x^{7} \ln \left (x \right )^{2}-12 x \,{\mathrm e}^{10}+100 x^{6} \ln \left (x \right )^{2}-10 x^{5} \ln \left (x \right )+100 x^{4} \ln \left (x \right )^{2}+12 x^{2} {\mathrm e}^{5}-40 x^{4} \ln \left (x \right )-10 x \ln \left (x \right )+4 x^{3} {\mathrm e}^{5}+150 x^{5} \ln \left (x \right )^{2}+25 x^{3} \ln \left (x \right )^{2}+12 x \,{\mathrm e}^{5}-120 x^{2} {\mathrm e}^{10} \ln \left (x \right )+40 x \,{\mathrm e}^{5} \ln \left (x \right )+120 x^{3} {\mathrm e}^{5} \ln \left (x \right )-x^{4}-4 x^{3}-6 x^{2}-60 x^{3} \ln \left (x \right )-40 x^{2} \ln \left (x \right )+40 \,{\mathrm e}^{15} \ln \left (x \right ) x -300 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{5}-300 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{4}+40 \,{\mathrm e}^{5} \ln \left (x \right ) x^{4}\) | \(356\) |
parallelrisch | \(25 \,{\mathrm e}^{20} \ln \left (x \right )^{2} x^{3}-100 \,{\mathrm e}^{15} \ln \left (x \right )^{2} x^{4}+150 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{5}-100 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{3}+40 \,{\mathrm e}^{15} \ln \left (x \right ) x^{2}+150 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{3}-10 \ln \left (x \right ) x \,{\mathrm e}^{20}-100 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{6}-60 x^{3} {\mathrm e}^{10} \ln \left (x \right )-60 \,{\mathrm e}^{10} \ln \left (x \right ) x -100 \,{\mathrm e}^{15} \ln \left (x \right )^{2} x^{3}+300 \,{\mathrm e}^{10} \ln \left (x \right )^{2} x^{4}-6 x^{2} {\mathrm e}^{10}+10 x +120 x^{2} {\mathrm e}^{5} \ln \left (x \right )+4 x \,{\mathrm e}^{15}+25 x^{7} \ln \left (x \right )^{2}-12 x \,{\mathrm e}^{10}+100 x^{6} \ln \left (x \right )^{2}-10 x^{5} \ln \left (x \right )+100 x^{4} \ln \left (x \right )^{2}+12 x^{2} {\mathrm e}^{5}-40 x^{4} \ln \left (x \right )-10 x \ln \left (x \right )+4 x^{3} {\mathrm e}^{5}+10 x \,{\mathrm e}^{20}+150 x^{5} \ln \left (x \right )^{2}+25 x^{3} \ln \left (x \right )^{2}+12 x \,{\mathrm e}^{5}-120 x^{2} {\mathrm e}^{10} \ln \left (x \right )+40 x \,{\mathrm e}^{5} \ln \left (x \right )+120 x^{3} {\mathrm e}^{5} \ln \left (x \right )-x^{4}-4 x^{3}-6 x^{2}-60 x^{3} \ln \left (x \right )-40 x^{2} \ln \left (x \right )+40 \,{\mathrm e}^{15} \ln \left (x \right ) x -300 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{5}-300 \,{\mathrm e}^{5} \ln \left (x \right )^{2} x^{4}+40 \,{\mathrm e}^{5} \ln \left (x \right ) x^{4}+\left (-14-10 \,{\mathrm e}^{20}\right ) x\) | \(373\) |
default | \(\text {Expression too large to display}\) | \(726\) |
parts | \(\text {Expression too large to display}\) | \(735\) |
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[Out]
Leaf count of result is larger than twice the leaf count of optimal. 203 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 203, normalized size of antiderivative = 6.77 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=-x^{4} - 4 \, x^{3} + 25 \, {\left (x^{7} + 4 \, x^{6} + 6 \, x^{5} + 4 \, x^{4} + x^{3} e^{20} + x^{3} - 4 \, {\left (x^{4} + x^{3}\right )} e^{15} + 6 \, {\left (x^{5} + 2 \, x^{4} + x^{3}\right )} e^{10} - 4 \, {\left (x^{6} + 3 \, x^{5} + 3 \, x^{4} + x^{3}\right )} e^{5}\right )} \log \left (x\right )^{2} - 6 \, x^{2} + 4 \, x e^{15} - 6 \, {\left (x^{2} + 2 \, x\right )} e^{10} + 4 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x\right )} e^{5} - 10 \, {\left (x^{5} + 4 \, x^{4} + 6 \, x^{3} + 4 \, x^{2} + x e^{20} - 4 \, {\left (x^{2} + x\right )} e^{15} + 6 \, {\left (x^{3} + 2 \, x^{2} + x\right )} e^{10} - 4 \, {\left (x^{4} + 3 \, x^{3} + 3 \, x^{2} + x\right )} e^{5} + x\right )} \log \left (x\right ) - 4 \, x \]
[In]
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Leaf count of result is larger than twice the leaf count of optimal. 267 vs. \(2 (24) = 48\).
Time = 0.24 (sec) , antiderivative size = 267, normalized size of antiderivative = 8.90 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=- x^{4} + x^{3} \left (-4 + 4 e^{5}\right ) + x^{2} \left (- 6 e^{10} - 6 + 12 e^{5}\right ) + x \left (- 12 e^{10} - 4 + 12 e^{5} + 4 e^{15}\right ) + \left (- 10 x^{5} - 40 x^{4} + 40 x^{4} e^{5} - 60 x^{3} e^{10} - 60 x^{3} + 120 x^{3} e^{5} - 120 x^{2} e^{10} - 40 x^{2} + 120 x^{2} e^{5} + 40 x^{2} e^{15} - 10 x e^{20} - 60 x e^{10} - 10 x + 40 x e^{5} + 40 x e^{15}\right ) \log {\left (x \right )} + \left (25 x^{7} - 100 x^{6} e^{5} + 100 x^{6} - 300 x^{5} e^{5} + 150 x^{5} + 150 x^{5} e^{10} - 100 x^{4} e^{15} - 300 x^{4} e^{5} + 100 x^{4} + 300 x^{4} e^{10} - 100 x^{3} e^{15} - 100 x^{3} e^{5} + 25 x^{3} + 150 x^{3} e^{10} + 25 x^{3} e^{20}\right ) \log {\left (x \right )}^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 526 vs. \(2 (29) = 58\).
Time = 0.21 (sec) , antiderivative size = 526, normalized size of antiderivative = 17.53 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=\frac {25}{49} \, {\left (49 \, \log \left (x\right )^{2} - 14 \, \log \left (x\right ) + 2\right )} x^{7} - \frac {50}{9} \, {\left (18 \, {\left (e^{5} - 1\right )} \log \left (x\right )^{2} - 6 \, {\left (e^{5} - 1\right )} \log \left (x\right ) + e^{5} - 1\right )} x^{6} - \frac {50}{49} \, x^{7} + \frac {50}{9} \, x^{6} {\left (e^{5} - 1\right )} + 6 \, {\left (25 \, {\left (e^{10} - 2 \, e^{5} + 1\right )} \log \left (x\right )^{2} - 10 \, {\left (e^{10} - 2 \, e^{5} + 1\right )} \log \left (x\right ) + 2 \, e^{10} - 4 \, e^{5} + 2\right )} x^{5} - 2 \, x^{5} {\left (6 \, e^{10} - 12 \, e^{5} + 5\right )} - \frac {25}{2} \, {\left (8 \, {\left (e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} \log \left (x\right )^{2} - 4 \, {\left (e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} \log \left (x\right ) + e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} x^{4} - 2 \, x^{5} + \frac {5}{2} \, x^{4} {\left (5 \, e^{15} - 15 \, e^{10} + 11 \, e^{5} - 1\right )} + \frac {25}{9} \, {\left (9 \, {\left (e^{20} - 4 \, e^{15} + 6 \, e^{10} - 4 \, e^{5} + 1\right )} \log \left (x\right )^{2} - 6 \, {\left (e^{20} - 4 \, e^{15} + 6 \, e^{10} - 4 \, e^{5} + 1\right )} \log \left (x\right ) + 2 \, e^{20} - 8 \, e^{15} + 12 \, e^{10} - 8 \, e^{5} + 2\right )} x^{3} - 11 \, x^{4} - \frac {10}{9} \, x^{3} {\left (5 \, e^{20} - 20 \, e^{15} + 12 \, e^{10} + 16 \, e^{5} - 13\right )} - 24 \, x^{3} - 20 \, x^{2} {\left (e^{15} - 3 \, e^{10} + 3 \, e^{5} - 1\right )} - 26 \, x^{2} + 10 \, x {\left (e^{20} - 4 \, e^{15} + 6 \, e^{10} - 4 \, e^{5} + 1\right )} - 10 \, x e^{20} + 4 \, {\left (5 \, x^{2} + 11 \, x\right )} e^{15} - 2 \, {\left (10 \, x^{3} + 33 \, x^{2} + 36 \, x\right )} e^{10} + 2 \, {\left (5 \, x^{4} + 22 \, x^{3} + 36 \, x^{2} + 26 \, x\right )} e^{5} + \frac {10}{21} \, {\left (15 \, x^{7} + 70 \, x^{6} + 105 \, x^{5} + 21 \, x^{4} - 91 \, x^{3} - 84 \, x^{2} + 7 \, {\left (5 \, x^{3} - 3 \, x\right )} e^{20} - 7 \, {\left (15 \, x^{4} + 20 \, x^{3} - 12 \, x^{2} - 12 \, x\right )} e^{15} + 21 \, {\left (6 \, x^{5} + 15 \, x^{4} + 4 \, x^{3} - 12 \, x^{2} - 6 \, x\right )} e^{10} - 7 \, {\left (10 \, x^{6} + 36 \, x^{5} + 33 \, x^{4} - 16 \, x^{3} - 36 \, x^{2} - 12 \, x\right )} e^{5} - 21 \, x\right )} \log \left (x\right ) - 14 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 400 vs. \(2 (29) = 58\).
Time = 0.30 (sec) , antiderivative size = 400, normalized size of antiderivative = 13.33 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=25 \, x^{7} \log \left (x\right )^{2} - 100 \, x^{6} e^{5} \log \left (x\right )^{2} + 100 \, x^{6} \log \left (x\right )^{2} + 150 \, x^{5} e^{10} \log \left (x\right )^{2} - 300 \, x^{5} e^{5} \log \left (x\right )^{2} + 150 \, x^{5} \log \left (x\right )^{2} - 100 \, x^{4} e^{15} \log \left (x\right )^{2} + 300 \, x^{4} e^{10} \log \left (x\right )^{2} - 300 \, x^{4} e^{5} \log \left (x\right )^{2} - 10 \, x^{5} \log \left (x\right ) + 40 \, x^{4} e^{5} \log \left (x\right ) + 100 \, x^{4} \log \left (x\right )^{2} + 25 \, x^{3} e^{20} \log \left (x\right )^{2} - 100 \, x^{3} e^{15} \log \left (x\right )^{2} + 150 \, x^{3} e^{10} \log \left (x\right )^{2} - 100 \, x^{3} e^{5} \log \left (x\right )^{2} - 10 \, x^{4} e^{5} - 40 \, x^{4} \log \left (x\right ) - 60 \, x^{3} e^{10} \log \left (x\right ) + 120 \, x^{3} e^{5} \log \left (x\right ) + 25 \, x^{3} \log \left (x\right )^{2} - x^{4} + 20 \, x^{3} e^{10} - 40 \, x^{3} e^{5} - 60 \, x^{3} \log \left (x\right ) + 40 \, x^{2} e^{15} \log \left (x\right ) - 120 \, x^{2} e^{10} \log \left (x\right ) + 120 \, x^{2} e^{5} \log \left (x\right ) - 4 \, x^{3} - 20 \, x^{2} e^{15} + 60 \, x^{2} e^{10} - 60 \, x^{2} e^{5} - 40 \, x^{2} \log \left (x\right ) - 10 \, x e^{20} \log \left (x\right ) + 40 \, x e^{15} \log \left (x\right ) - 60 \, x e^{10} \log \left (x\right ) + 40 \, x e^{5} \log \left (x\right ) - 6 \, x^{2} + 4 \, {\left (5 \, x^{2} + 11 \, x\right )} e^{15} - 40 \, x e^{15} - 2 \, {\left (10 \, x^{3} + 33 \, x^{2} + 36 \, x\right )} e^{10} + 60 \, x e^{10} + 2 \, {\left (5 \, x^{4} + 22 \, x^{3} + 36 \, x^{2} + 26 \, x\right )} e^{5} - 40 \, x e^{5} - 10 \, x \log \left (x\right ) - 4 \, x \]
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Time = 14.75 (sec) , antiderivative size = 153, normalized size of antiderivative = 5.10 \[ \int \left (-14-10 e^{20}-52 x-72 x^2-44 x^3-10 x^4+e^{15} (44+40 x)+e^{10} \left (-72-132 x-60 x^2\right )+e^5 \left (52+144 x+132 x^2+40 x^3\right )+\left (-10-80 x-130 x^2+40 x^3+250 x^4+200 x^5+50 x^6+e^{20} \left (-10+50 x^2\right )+e^{15} \left (40+80 x-200 x^2-200 x^3\right )+e^{10} \left (-60-240 x+120 x^2+600 x^3+300 x^4\right )+e^5 \left (40+240 x+160 x^2-440 x^3-600 x^4-200 x^5\right )\right ) \log (x)+\left (75 x^2+75 e^{20} x^2+400 x^3+750 x^4+600 x^5+175 x^6+e^{15} \left (-300 x^2-400 x^3\right )+e^{10} \left (450 x^2+1200 x^3+750 x^4\right )+e^5 \left (-300 x^2-1200 x^3-1500 x^4-600 x^5\right )\right ) \log ^2(x)\right ) \, dx=x\,\left (4\,{\left ({\mathrm {e}}^5-1\right )}^3-10\,\ln \left (x\right )\,{\left ({\mathrm {e}}^5-1\right )}^4\right )+25\,x^7\,{\ln \left (x\right )}^2-x^2\,\left (6\,{\left ({\mathrm {e}}^5-1\right )}^2-40\,\ln \left (x\right )\,{\left ({\mathrm {e}}^5-1\right )}^3\right )+x^3\,\left (25\,{\left ({\mathrm {e}}^5-1\right )}^4\,{\ln \left (x\right )}^2-60\,{\left ({\mathrm {e}}^5-1\right )}^2\,\ln \left (x\right )+4\,{\mathrm {e}}^5-4\right )-x^5\,\left (10\,\ln \left (x\right )-150\,{\ln \left (x\right )}^2\,{\left ({\mathrm {e}}^5-1\right )}^2\right )-x^4\,\left (100\,{\left ({\mathrm {e}}^5-1\right )}^3\,{\ln \left (x\right )}^2+\left (40-40\,{\mathrm {e}}^5\right )\,\ln \left (x\right )+1\right )-x^6\,{\ln \left (x\right )}^2\,\left (100\,{\mathrm {e}}^5-100\right ) \]
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