Integrand size = 237, antiderivative size = 32 \[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=\left (-x+\frac {x}{25-x}-\log \left (-e^2+\frac {e}{x}-2 x\right )\right )^2 \]
[Out]
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 3.81 (sec) , antiderivative size = 791, normalized size of antiderivative = 24.72, number of steps used = 62, number of rules used = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.101, Rules used = {6820, 12, 6860, 1642, 648, 632, 212, 642, 2608, 2603, 1671, 2605, 2604, 2404, 2338, 2353, 2352, 2354, 2438, 2465, 2441, 2437, 2440, 2439} \[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=-\frac {50 \sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {4 x+e^2}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}+\sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {4 x+e^2}{\sqrt {e \left (8+e^3\right )}}\right )-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {4 x+e^2}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-2 \operatorname {PolyLog}\left (2,-\frac {4 x-\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right )-2 \operatorname {PolyLog}\left (2,\frac {4 x+\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right )+x^2-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (-2 x^2-e^2 x+e\right )}{2 \left (1250-e+25 e^2\right )}+\frac {25 \left (100+e^2\right ) \log \left (-2 x^2-e^2 x+e\right )}{1250-e+25 e^2}+\frac {1}{2} e^2 \log \left (-2 x^2-e^2 x+e\right )+2 x-\frac {1300}{25-x}+\frac {625}{(25-x)^2}-\log ^2(x)-\log ^2\left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )-\log ^2\left (4 x+\sqrt {e \left (8+e^3\right )}+e^2\right )+2 x \log \left (-2 x+\frac {e}{x}-e^2\right )-\frac {50 \log \left (-2 x+\frac {e}{x}-e^2\right )}{25-x}-2 \log \left (-2 x+\frac {e}{x}-e^2\right ) \log (x)+2 \log \left (e^2+\sqrt {e \left (8+e^3\right )}\right ) \log (x)-2 \log (x)+2 \log \left (-2 x+\frac {e}{x}-e^2\right ) \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )+2 \log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right ) \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )+2 \log \left (\frac {1}{4} \left (\sqrt {e \left (8+e^3\right )}-e^2\right )\right ) \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right )+2 \log \left (-2 x+\frac {e}{x}-e^2\right ) \log \left (4 x+\sqrt {e \left (8+e^3\right )}+e^2\right )-2 \log \left (-\frac {4 x-\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right ) \log \left (4 x+\sqrt {e \left (8+e^3\right )}+e^2\right )-2 \log \left (4 x-\sqrt {e \left (8+e^3\right )}+e^2\right ) \log \left (\frac {4 x+\sqrt {e \left (8+e^3\right )}+e^2}{2 \sqrt {e \left (8+e^3\right )}}\right )+2 \log (x) \log \left (\frac {4 x}{e^2+\sqrt {e \left (8+e^3\right )}}+1\right ) \]
[In]
[Out]
Rule 12
Rule 212
Rule 632
Rule 642
Rule 648
Rule 1642
Rule 1671
Rule 2338
Rule 2352
Rule 2353
Rule 2354
Rule 2404
Rule 2437
Rule 2438
Rule 2439
Rule 2440
Rule 2441
Rule 2465
Rule 2603
Rule 2604
Rule 2605
Rule 2608
Rule 6820
Rule 6860
Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (e^2 x^2 \left (600-50 x+x^2\right )-e \left (-625+650 x-51 x^2+x^3\right )+2 x^2 \left (625+550 x-49 x^2+x^3\right )\right ) \left ((-24+x) x+(-25+x) \log \left (-e^2+\frac {e}{x}-2 x\right )\right )}{(25-x)^3 x \left (e-e^2 x-2 x^2\right )} \, dx \\ & = 2 \int \frac {\left (e^2 x^2 \left (600-50 x+x^2\right )-e \left (-625+650 x-51 x^2+x^3\right )+2 x^2 \left (625+550 x-49 x^2+x^3\right )\right ) \left ((-24+x) x+(-25+x) \log \left (-e^2+\frac {e}{x}-2 x\right )\right )}{(25-x)^3 x \left (e-e^2 x-2 x^2\right )} \, dx \\ & = 2 \int \left (\frac {(24-x) \left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right )}{(25-x)^3 \left (e-e^2 x-2 x^2\right )}+\frac {\left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{(25-x)^2 x \left (e-e^2 x-2 x^2\right )}\right ) \, dx \\ & = 2 \int \frac {(24-x) \left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right )}{(25-x)^3 \left (e-e^2 x-2 x^2\right )} \, dx+2 \int \frac {\left (-625 e+650 e x-1250 \left (1+\frac {3 e (17+200 e)}{1250}\right ) x^2-1100 \left (1-\frac {e (1+50 e)}{1100}\right ) x^3+98 \left (1-\frac {e^2}{98}\right ) x^4-2 x^5\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{(25-x)^2 x \left (e-e^2 x-2 x^2\right )} \, dx \\ & = 2 \int \left (2-\frac {625}{(-25+x)^3}-\frac {650}{(-25+x)^2}+\frac {1250+e}{\left (1250-e+25 e^2\right ) (-25+x)}+x+\frac {e \left (-2400+2 e-49 e^2+\left (4+1200 e-e^2+25 e^3\right ) x\right )}{\left (1250-e+25 e^2\right ) \left (e-e^2 x-2 x^2\right )}\right ) \, dx+2 \int \left (\log \left (-e^2+\frac {e}{x}-2 x\right )-\frac {25 \log \left (-e^2+\frac {e}{x}-2 x\right )}{(-25+x)^2}-\frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{x}+\frac {\left (e^2+4 x\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{-e+e^2 x+2 x^2}\right ) \, dx \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+4 x+x^2+\frac {2 (1250+e) \log (25-x)}{1250-e+25 e^2}+2 \int \log \left (-e^2+\frac {e}{x}-2 x\right ) \, dx-2 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{x} \, dx+2 \int \frac {\left (e^2+4 x\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{-e+e^2 x+2 x^2} \, dx-50 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{(-25+x)^2} \, dx+\frac {(2 e) \int \frac {-2400+2 e-49 e^2+\left (4+1200 e-e^2+25 e^3\right ) x}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2} \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+4 x+x^2-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )+\frac {2 (1250+e) \log (25-x)}{1250-e+25 e^2}-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-2 \int \frac {-e-2 x^2}{e-e^2 x-2 x^2} \, dx+2 \int \left (\frac {4 \log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x}+\frac {4 \log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x}\right ) \, dx+2 \int \frac {\left (-2-\frac {e}{x^2}\right ) \log (x)}{-e^2+\frac {e}{x}-2 x} \, dx-50 \int \frac {e+2 x^2}{(25-x) x \left (e-e^2 x-2 x^2\right )} \, dx-\frac {\left (e (2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right )\right ) \int \frac {1}{e-e^2 x-2 x^2} \, dx}{2 \left (1250-e+25 e^2\right )}-\frac {\left (e \left (4+1200 e-e^2+25 e^3\right )\right ) \int \frac {-e^2-4 x}{e-e^2 x-2 x^2} \, dx}{2 \left (1250-e+25 e^2\right )} \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+4 x+x^2-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )+\frac {2 (1250+e) \log (25-x)}{1250-e+25 e^2}-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}-2 \int \left (1-\frac {2 e-e^2 x}{e-e^2 x-2 x^2}\right ) \, dx+2 \int \left (-\frac {\log (x)}{x}+\frac {\left (e^2+4 x\right ) \log (x)}{-e+e^2 x+2 x^2}\right ) \, dx+8 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx+8 \int \frac {\log \left (-e^2+\frac {e}{x}-2 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x} \, dx-50 \int \left (\frac {1250+e}{25 \left (1250-e+25 e^2\right ) (-25+x)}+\frac {1}{25 x}+\frac {e \left (4+50 e+e^3\right )+2 \left (100+e^2\right ) x}{\left (1250-e+25 e^2\right ) \left (e-e^2 x-2 x^2\right )}\right ) \, dx+\frac {\left (e (2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right )\right ) \text {Subst}\left (\int \frac {1}{e \left (8+e^3\right )-x^2} \, dx,x,-e^2-4 x\right )}{1250-e+25 e^2} \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}+2 \int \frac {2 e-e^2 x}{e-e^2 x-2 x^2} \, dx-2 \int \frac {\log (x)}{x} \, dx+2 \int \frac {\left (e^2+4 x\right ) \log (x)}{-e+e^2 x+2 x^2} \, dx-2 \int \frac {\left (-2-\frac {e}{x^2}\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e^2+\frac {e}{x}-2 x} \, dx-2 \int \frac {\left (-2-\frac {e}{x^2}\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e^2+\frac {e}{x}-2 x} \, dx-\frac {50 \int \frac {e \left (4+50 e+e^3\right )+2 \left (100+e^2\right ) x}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2} \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}+2 \int \left (\frac {4 \log (x)}{e^2-\sqrt {e \left (8+e^3\right )}+4 x}+\frac {4 \log (x)}{e^2+\sqrt {e \left (8+e^3\right )}+4 x}\right ) \, dx-2 \int \left (-\frac {\log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{x}+\frac {\left (e^2+4 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2}\right ) \, dx-2 \int \left (-\frac {\log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{x}+\frac {\left (e^2+4 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2}\right ) \, dx+\frac {1}{2} e^2 \int \frac {-e^2-4 x}{e-e^2 x-2 x^2} \, dx+\frac {\left (25 \left (100+e^2\right )\right ) \int \frac {-e^2-4 x}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2}+\frac {1}{2} \left (e \left (8+e^3\right )\right ) \int \frac {1}{e-e^2 x-2 x^2} \, dx-\frac {\left (25 e \left (8+e^3\right )\right ) \int \frac {1}{e-e^2 x-2 x^2} \, dx}{1250-e+25 e^2} \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )+\frac {1}{2} e^2 \log \left (e-e^2 x-2 x^2\right )+\frac {25 \left (100+e^2\right ) \log \left (e-e^2 x-2 x^2\right )}{1250-e+25 e^2}-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}+2 \int \frac {\log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{x} \, dx-2 \int \frac {\left (e^2+4 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2} \, dx+2 \int \frac {\log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{x} \, dx-2 \int \frac {\left (e^2+4 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{-e+e^2 x+2 x^2} \, dx+8 \int \frac {\log (x)}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx+8 \int \frac {\log (x)}{e^2+\sqrt {e \left (8+e^3\right )}+4 x} \, dx-\left (e \left (8+e^3\right )\right ) \text {Subst}\left (\int \frac {1}{e \left (8+e^3\right )-x^2} \, dx,x,-e^2-4 x\right )+\frac {\left (50 e \left (8+e^3\right )\right ) \text {Subst}\left (\int \frac {1}{e \left (8+e^3\right )-x^2} \, dx,x,-e^2-4 x\right )}{1250-e+25 e^2} \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}+\sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )-\frac {50 \sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)+2 \log \left (e^2+\sqrt {e \left (8+e^3\right )}\right ) \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (\frac {1}{4} \left (-e^2+\sqrt {e \left (8+e^3\right )}\right )\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log (x) \log \left (1+\frac {4 x}{e^2+\sqrt {e \left (8+e^3\right )}}\right )+\frac {1}{2} e^2 \log \left (e-e^2 x-2 x^2\right )+\frac {25 \left (100+e^2\right ) \log \left (e-e^2 x-2 x^2\right )}{1250-e+25 e^2}-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}-2 \int \left (\frac {4 \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x}+\frac {4 \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x}\right ) \, dx-2 \int \left (\frac {4 \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x}+\frac {4 \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x}\right ) \, dx+8 \int \frac {\log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx-8 \int \frac {\log \left (\frac {4 x}{-e^2+\sqrt {e \left (8+e^3\right )}}\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}+\sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )-\frac {50 \sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)+2 \log \left (e^2+\sqrt {e \left (8+e^3\right )}\right ) \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (\frac {1}{4} \left (-e^2+\sqrt {e \left (8+e^3\right )}\right )\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log (x) \log \left (1+\frac {4 x}{e^2+\sqrt {e \left (8+e^3\right )}}\right )+\frac {1}{2} e^2 \log \left (e-e^2 x-2 x^2\right )+\frac {25 \left (100+e^2\right ) \log \left (e-e^2 x-2 x^2\right )}{1250-e+25 e^2}-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}-8 \int \frac {\log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx-8 \int \frac {\log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x} \, dx-8 \int \frac {\log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx-8 \int \frac {\log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x} \, dx \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}+\sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )-\frac {50 \sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)+2 \log \left (e^2+\sqrt {e \left (8+e^3\right )}\right ) \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (\frac {1}{4} \left (-e^2+\sqrt {e \left (8+e^3\right )}\right )\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-2 \log \left (-\frac {e^2-\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-2 \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right ) \log \left (\frac {e^2+\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right )+2 \log (x) \log \left (1+\frac {4 x}{e^2+\sqrt {e \left (8+e^3\right )}}\right )+\frac {1}{2} e^2 \log \left (e-e^2 x-2 x^2\right )+\frac {25 \left (100+e^2\right ) \log \left (e-e^2 x-2 x^2\right )}{1250-e+25 e^2}-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}-2 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )-2 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )+8 \int \frac {\log \left (\frac {4 \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )}{4 \left (e^2-\sqrt {e \left (8+e^3\right )}\right )-4 \left (e^2+\sqrt {e \left (8+e^3\right )}\right )}\right )}{e^2+\sqrt {e \left (8+e^3\right )}+4 x} \, dx+8 \int \frac {\log \left (\frac {4 \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )}{-4 \left (e^2-\sqrt {e \left (8+e^3\right )}\right )+4 \left (e^2+\sqrt {e \left (8+e^3\right )}\right )}\right )}{e^2-\sqrt {e \left (8+e^3\right )}+4 x} \, dx \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}+\sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )-\frac {50 \sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)+2 \log \left (e^2+\sqrt {e \left (8+e^3\right )}\right ) \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (\frac {1}{4} \left (-e^2+\sqrt {e \left (8+e^3\right )}\right )\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )-\log ^2\left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-2 \log \left (-\frac {e^2-\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-\log ^2\left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-2 \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right ) \log \left (\frac {e^2+\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right )+2 \log (x) \log \left (1+\frac {4 x}{e^2+\sqrt {e \left (8+e^3\right )}}\right )+\frac {1}{2} e^2 \log \left (e-e^2 x-2 x^2\right )+\frac {25 \left (100+e^2\right ) \log \left (e-e^2 x-2 x^2\right )}{1250-e+25 e^2}-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}+2 \text {Subst}\left (\int \frac {\log \left (1+\frac {4 x}{4 \left (e^2-\sqrt {e \left (8+e^3\right )}\right )-4 \left (e^2+\sqrt {e \left (8+e^3\right )}\right )}\right )}{x} \, dx,x,e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \text {Subst}\left (\int \frac {\log \left (1+\frac {4 x}{-4 \left (e^2-\sqrt {e \left (8+e^3\right )}\right )+4 \left (e^2+\sqrt {e \left (8+e^3\right )}\right )}\right )}{x} \, dx,x,e^2-\sqrt {e \left (8+e^3\right )}+4 x\right ) \\ & = \frac {625}{(25-x)^2}-\frac {1300}{25-x}+2 x+x^2-\frac {(2+e) \left (4-2 e+e^2\right ) \left (1200-e+25 e^2\right ) \sqrt {\frac {e}{8+e^3}} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}+\sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )-\frac {50 \sqrt {e \left (8+e^3\right )} \text {arctanh}\left (\frac {e^2+4 x}{\sqrt {e \left (8+e^3\right )}}\right )}{1250-e+25 e^2}-\frac {50 \log \left (-e^2+\frac {e}{x}-2 x\right )}{25-x}+2 x \log \left (-e^2+\frac {e}{x}-2 x\right )-2 \log (x)+2 \log \left (e^2+\sqrt {e \left (8+e^3\right )}\right ) \log (x)-2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log (x)-\log ^2(x)+2 \log \left (\frac {1}{4} \left (-e^2+\sqrt {e \left (8+e^3\right )}\right )\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-\frac {4 x}{e^2-\sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )-\log ^2\left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right )+2 \log \left (-e^2+\frac {e}{x}-2 x\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-2 \log \left (-\frac {e^2-\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right ) \log \left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-\log ^2\left (e^2+\sqrt {e \left (8+e^3\right )}+4 x\right )-2 \log \left (e^2-\sqrt {e \left (8+e^3\right )}+4 x\right ) \log \left (\frac {e^2+\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right )+2 \log (x) \log \left (1+\frac {4 x}{e^2+\sqrt {e \left (8+e^3\right )}}\right )+\frac {1}{2} e^2 \log \left (e-e^2 x-2 x^2\right )+\frac {25 \left (100+e^2\right ) \log \left (e-e^2 x-2 x^2\right )}{1250-e+25 e^2}-\frac {e \left (4+1200 e-e^2+25 e^3\right ) \log \left (e-e^2 x-2 x^2\right )}{2 \left (1250-e+25 e^2\right )}-2 \operatorname {PolyLog}\left (2,-\frac {e^2-\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right )-2 \operatorname {PolyLog}\left (2,\frac {e^2+\sqrt {e \left (8+e^3\right )}+4 x}{2 \sqrt {e \left (8+e^3\right )}}\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(96\) vs. \(2(32)=64\).
Time = 0.15 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.00 \[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=2 \left (\frac {625}{2 (-25+x)^2}+\frac {650}{-25+x}+x+\frac {x^2}{2}+\frac {\left (25-25 x+x^2\right ) \log \left (-e^2+\frac {e}{x}-2 x\right )}{-25+x}+\frac {1}{2} \log ^2\left (-e^2+\frac {e}{x}-2 x\right )-\log (x)+\log \left (-e+e^2 x+2 x^2\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(155\) vs. \(2(32)=64\).
Time = 3.45 (sec) , antiderivative size = 156, normalized size of antiderivative = 4.88
method | result | size |
norman | \(\frac {x^{4}+x^{2} \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )^{2}+28800 x -98 \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right ) x^{2}+1200 x \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )-48 x^{3}+625 \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )^{2}-50 x \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right )^{2}-360000+2 \ln \left (\frac {-{\mathrm e}^{2} x +{\mathrm e}-2 x^{2}}{x}\right ) x^{3}}{\left (x -25\right )^{2}}\) | \(156\) |
parallelrisch | \(-\frac {\left (-625 x^{4} {\mathrm e}^{2}-1250 \,{\mathrm e}^{2} \ln \left (-\frac {{\mathrm e}^{2} x +2 x^{2}-{\mathrm e}}{x}\right ) x^{3}-625 \,{\mathrm e}^{2} x^{2} \ln \left (-\frac {{\mathrm e}^{2} x +2 x^{2}-{\mathrm e}}{x}\right )^{2}+30000 x^{3} {\mathrm e}^{2}+61250 \,{\mathrm e}^{2} \ln \left (-\frac {{\mathrm e}^{2} x +2 x^{2}-{\mathrm e}}{x}\right ) x^{2}+31250 \,{\mathrm e}^{2} x \ln \left (-\frac {{\mathrm e}^{2} x +2 x^{2}-{\mathrm e}}{x}\right )^{2}-360000 x^{2} {\mathrm e}^{2}-750000 \,{\mathrm e}^{2} \ln \left (-\frac {{\mathrm e}^{2} x +2 x^{2}-{\mathrm e}}{x}\right ) x -390625 \,{\mathrm e}^{2} \ln \left (-\frac {{\mathrm e}^{2} x +2 x^{2}-{\mathrm e}}{x}\right )^{2}\right ) {\mathrm e}^{-2}}{625 \left (x^{2}-50 x +625\right )}\) | \(218\) |
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Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 94, normalized size of antiderivative = 2.94 \[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=\frac {x^{4} - 48 \, x^{3} + {\left (x^{2} - 50 \, x + 625\right )} \log \left (-\frac {2 \, x^{2} + x e^{2} - e}{x}\right )^{2} + 525 \, x^{2} + 2 \, {\left (x^{3} - 49 \, x^{2} + 600 \, x\right )} \log \left (-\frac {2 \, x^{2} + x e^{2} - e}{x}\right ) + 2550 \, x - 31875}{x^{2} - 50 \, x + 625} \]
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Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (20) = 40\).
Time = 2.97 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.88 \[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=x^{2} + 2 x + \frac {1300 x - 31875}{x^{2} - 50 x + 625} - 2 \log {\left (x \right )} + \log {\left (\frac {- 2 x^{2} - x e^{2} + e}{x} \right )}^{2} + 2 \log {\left (x^{2} + \frac {x e^{2}}{2} - \frac {e}{2} \right )} + \frac {\left (2 x^{2} - 50 x + 50\right ) \log {\left (\frac {- 2 x^{2} - x e^{2} + e}{x} \right )}}{x - 25} \]
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Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (26) = 52\).
Time = 0.48 (sec) , antiderivative size = 123, normalized size of antiderivative = 3.84 \[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=\frac {x^{4} - 48 \, x^{3} + {\left (x^{2} - 50 \, x + 625\right )} \log \left (-2 \, x^{2} - x e^{2} + e\right )^{2} + {\left (x^{2} - 50 \, x + 625\right )} \log \left (x\right )^{2} + 525 \, x^{2} + 2 \, {\left (x^{3} - 49 \, x^{2} - {\left (x^{2} - 50 \, x + 625\right )} \log \left (x\right ) + 600 \, x\right )} \log \left (-2 \, x^{2} - x e^{2} + e\right ) - 2 \, {\left (x^{3} - 49 \, x^{2} + 600 \, x\right )} \log \left (x\right ) + 2550 \, x - 31875}{x^{2} - 50 \, x + 625} \]
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\[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=\int { \frac {2 \, {\left (2 \, x^{7} - 146 \, x^{6} + 3452 \, x^{5} - 25150 \, x^{4} - 30000 \, x^{3} + {\left (x^{6} - 74 \, x^{5} + 1800 \, x^{4} - 14400 \, x^{3}\right )} e^{2} - {\left (x^{5} - 75 \, x^{4} + 1874 \, x^{3} - 16225 \, x^{2} + 15000 \, x\right )} e + {\left (2 \, x^{6} - 148 \, x^{5} + 3550 \, x^{4} - 26250 \, x^{3} - 31250 \, x^{2} + {\left (x^{5} - 75 \, x^{4} + 1850 \, x^{3} - 15000 \, x^{2}\right )} e^{2} - {\left (x^{4} - 76 \, x^{3} + 1925 \, x^{2} - 16875 \, x + 15625\right )} e\right )} \log \left (-\frac {2 \, x^{2} + x e^{2} - e}{x}\right )\right )}}{2 \, x^{6} - 150 \, x^{5} + 3750 \, x^{4} - 31250 \, x^{3} + {\left (x^{5} - 75 \, x^{4} + 1875 \, x^{3} - 15625 \, x^{2}\right )} e^{2} - {\left (x^{4} - 75 \, x^{3} + 1875 \, x^{2} - 15625 \, x\right )} e} \,d x } \]
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Time = 14.27 (sec) , antiderivative size = 98, normalized size of antiderivative = 3.06 \[ \int \frac {-60000 x^3-50300 x^4+6904 x^5-292 x^6+4 x^7+e \left (-30000 x+32450 x^2-3748 x^3+150 x^4-2 x^5\right )+e^2 \left (-28800 x^3+3600 x^4-148 x^5+2 x^6\right )+\left (-62500 x^2-52500 x^3+7100 x^4-296 x^5+4 x^6+e \left (-31250+33750 x-3850 x^2+152 x^3-2 x^4\right )+e^2 \left (-30000 x^2+3700 x^3-150 x^4+2 x^5\right )\right ) \log \left (\frac {e-e^2 x-2 x^2}{x}\right )}{-31250 x^3+3750 x^4-150 x^5+2 x^6+e \left (15625 x-1875 x^2+75 x^3-x^4\right )+e^2 \left (-15625 x^2+1875 x^3-75 x^4+x^5\right )} \, dx=2\,x-48\,\ln \left (x^2+\frac {{\mathrm {e}}^2\,x}{2}-\frac {\mathrm {e}}{2}\right )+48\,\ln \left (x\right )+\frac {1300\,x-31875}{x^2-50\,x+625}+{\ln \left (-\frac {2\,x^2+{\mathrm {e}}^2\,x-\mathrm {e}}{x}\right )}^2+x^2+\frac {\ln \left (-\frac {2\,x^2+{\mathrm {e}}^2\,x-\mathrm {e}}{x}\right )\,\left (x^2-600\right )}{\frac {x}{2}-\frac {25}{2}} \]
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