Integrand size = 105, antiderivative size = 26 \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=5 \left (-6+3 x-\left (x-(3+x)^2\right )^2 \log (-25+x) \log (x)\right ) \]
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Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 1.80 (sec) , antiderivative size = 106, normalized size of antiderivative = 4.08, number of steps used = 134, number of rules used = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {1607, 6820, 12, 6874, 14, 2465, 2436, 2332, 2441, 2352, 2442, 45, 712, 2464, 2341, 2417, 2458, 2393, 2354, 2438, 2423, 2439, 2353, 2481, 2422, 2421, 6724, 2388, 2338, 2372} \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=2868750 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )+2868750 \operatorname {PolyLog}\left (2,\frac {x}{25}\right )-5 x^4 \log (x-25) \log (x)-50 x^3 \log (x-25) \log (x)-215 x^2 \log (x-25) \log (x)+15 x-2880405 \log (25) \log (x-25)-11655 \log (x-25) \log \left (\frac {x}{25}\right )+2868750 \log (25-x) \log (x)+450 (25-x) \log (x-25) \log (x)-2868750 \log (25) \log (x) \]
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Rule 12
Rule 14
Rule 45
Rule 712
Rule 1607
Rule 2332
Rule 2338
Rule 2341
Rule 2352
Rule 2353
Rule 2354
Rule 2372
Rule 2388
Rule 2393
Rule 2417
Rule 2421
Rule 2422
Rule 2423
Rule 2436
Rule 2438
Rule 2439
Rule 2441
Rule 2442
Rule 2458
Rule 2464
Rule 2465
Rule 2481
Rule 6724
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{(-25+x) x} \, dx \\ & = \int \frac {5 \left (\left (-225-116 x-20 x^2+x^3\right ) \log (-25+x) \left (9+5 x+x^2+2 x (5+2 x) \log (x)\right )+x \left (75-3 x+\left (9+5 x+x^2\right )^2 \log (x)\right )\right )}{(25-x) x} \, dx \\ & = 5 \int \frac {\left (-225-116 x-20 x^2+x^3\right ) \log (-25+x) \left (9+5 x+x^2+2 x (5+2 x) \log (x)\right )+x \left (75-3 x+\left (9+5 x+x^2\right )^2 \log (x)\right )}{(25-x) x} \, dx \\ & = 5 \int \left (\frac {3 x-81 \log (-25+x)-90 x \log (-25+x)-43 x^2 \log (-25+x)-10 x^3 \log (-25+x)-x^4 \log (-25+x)}{x}-\frac {\left (9+5 x+x^2\right ) \left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x)}{-25+x}\right ) \, dx \\ & = 5 \int \frac {3 x-81 \log (-25+x)-90 x \log (-25+x)-43 x^2 \log (-25+x)-10 x^3 \log (-25+x)-x^4 \log (-25+x)}{x} \, dx-5 \int \frac {\left (9+5 x+x^2\right ) \left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x)}{-25+x} \, dx \\ & = 5 \int \left (3-\frac {\left (9+5 x+x^2\right )^2 \log (-25+x)}{x}\right ) \, dx-5 \int \left (30 \left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x)+\frac {759 \left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x)}{-25+x}+x \left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x)\right ) \, dx \\ & = 15 x-5 \int \frac {\left (9+5 x+x^2\right )^2 \log (-25+x)}{x} \, dx-5 \int x \left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x) \, dx-150 \int \left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x) \, dx-3795 \int \frac {\left (9+5 x+x^2-250 \log (-25+x)-90 x \log (-25+x)+4 x^2 \log (-25+x)\right ) \log (x)}{-25+x} \, dx \\ & = 15 x-5 \int \left (90 \log (-25+x)+\frac {81 \log (-25+x)}{x}+43 x \log (-25+x)+10 x^2 \log (-25+x)+x^3 \log (-25+x)\right ) \, dx-5 \int \left (9 x \log (x)+5 x^2 \log (x)+x^3 \log (x)-250 x \log (-25+x) \log (x)-90 x^2 \log (-25+x) \log (x)+4 x^3 \log (-25+x) \log (x)\right ) \, dx-150 \int \left (9 \log (x)+5 x \log (x)+x^2 \log (x)-250 \log (-25+x) \log (x)-90 x \log (-25+x) \log (x)+4 x^2 \log (-25+x) \log (x)\right ) \, dx-3795 \int \left (\frac {9 \log (x)}{-25+x}+\frac {5 x \log (x)}{-25+x}+\frac {x^2 \log (x)}{-25+x}-\frac {250 \log (-25+x) \log (x)}{-25+x}-\frac {90 x \log (-25+x) \log (x)}{-25+x}+\frac {4 x^2 \log (-25+x) \log (x)}{-25+x}\right ) \, dx \\ & = 15 x-5 \int x^3 \log (-25+x) \, dx-5 \int x^3 \log (x) \, dx-20 \int x^3 \log (-25+x) \log (x) \, dx-25 \int x^2 \log (x) \, dx-45 \int x \log (x) \, dx-50 \int x^2 \log (-25+x) \, dx-150 \int x^2 \log (x) \, dx-215 \int x \log (-25+x) \, dx-405 \int \frac {\log (-25+x)}{x} \, dx-450 \int \log (-25+x) \, dx+450 \int x^2 \log (-25+x) \log (x) \, dx-600 \int x^2 \log (-25+x) \log (x) \, dx-750 \int x \log (x) \, dx+1250 \int x \log (-25+x) \log (x) \, dx-1350 \int \log (x) \, dx-3795 \int \frac {x^2 \log (x)}{-25+x} \, dx+13500 \int x \log (-25+x) \log (x) \, dx-15180 \int \frac {x^2 \log (-25+x) \log (x)}{-25+x} \, dx-18975 \int \frac {x \log (x)}{-25+x} \, dx-34155 \int \frac {\log (x)}{-25+x} \, dx+37500 \int \log (-25+x) \log (x) \, dx+341550 \int \frac {x \log (-25+x) \log (x)}{-25+x} \, dx+948750 \int \frac {\log (-25+x) \log (x)}{-25+x} \, dx \\ & = 1365 x+\frac {795 x^2}{4}+\frac {175 x^3}{9}+\frac {5 x^4}{16}-\frac {215}{2} x^2 \log (-25+x)-\frac {50}{3} x^3 \log (-25+x)-\frac {5}{4} x^4 \log (-25+x)-34155 \log (25) \log (-25+x)-405 \log (-25+x) \log \left (\frac {x}{25}\right )-113850 x \log (x)-\frac {3795}{2} x^2 \log (x)-1875000 \log (25-x) \log (x)-37500 (25-x) \log (-25+x) \log (x)+7375 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+\frac {5}{4} \int \frac {x^4}{-25+x} \, dx+\frac {50}{3} \int \frac {x^3}{-25+x} \, dx+20 \int \left (-\frac {15625}{4}-\frac {625 x}{8}-\frac {25 x^2}{12}-\frac {x^3}{16}-\frac {390625 \log (25-x)}{4 x}+\frac {1}{4} x^3 \log (-25+x)\right ) \, dx+\frac {215}{2} \int \frac {x^2}{-25+x} \, dx+405 \int \frac {\log \left (\frac {x}{25}\right )}{-25+x} \, dx-450 \int \left (-\frac {625}{3}-\frac {25 x}{6}-\frac {x^2}{9}-\frac {15625 \log (25-x)}{3 x}+\frac {1}{3} x^2 \log (-25+x)\right ) \, dx-450 \text {Subst}(\int \log (x) \, dx,x,-25+x)+600 \int \left (-\frac {625}{3}-\frac {25 x}{6}-\frac {x^2}{9}-\frac {15625 \log (25-x)}{3 x}+\frac {1}{3} x^2 \log (-25+x)\right ) \, dx-1250 \int \left (-\frac {25}{2}-\frac {x}{4}-\frac {625 \log (25-x)}{2 x}+\frac {1}{2} x \log (-25+x)\right ) \, dx-3795 \int \left (25 \log (x)+\frac {625 \log (x)}{-25+x}+x \log (x)\right ) \, dx-13500 \int \left (-\frac {25}{2}-\frac {x}{4}-\frac {625 \log (25-x)}{2 x}+\frac {1}{2} x \log (-25+x)\right ) \, dx-15180 \int \left (25 \log (-25+x) \log (x)+\frac {625 \log (-25+x) \log (x)}{-25+x}+x \log (-25+x) \log (x)\right ) \, dx-18975 \int \left (\log (x)+\frac {25 \log (x)}{-25+x}\right ) \, dx-34155 \int \frac {\log \left (\frac {x}{25}\right )}{-25+x} \, dx-37500 \int \left (-1-\frac {(25-x) \log (-25+x)}{x}\right ) \, dx+341550 \int \left (\log (-25+x) \log (x)+\frac {25 \log (-25+x) \log (x)}{-25+x}\right ) \, dx+948750 \text {Subst}\left (\int \frac {\log (x) \log (25+x)}{x} \, dx,x,-25+x\right ) \\ & = 114315 x+\frac {3795 x^2}{4}+450 (25-x) \log (-25+x)-\frac {215}{2} x^2 \log (-25+x)-\frac {50}{3} x^3 \log (-25+x)-\frac {5}{4} x^4 \log (-25+x)-34155 \log (25) \log (-25+x)-405 \log (-25+x) \log \left (\frac {x}{25}\right )-113850 x \log (x)-\frac {3795}{2} x^2 \log (x)-1875000 \log (25-x) \log (x)-37500 (25-x) \log (-25+x) \log (x)+7375 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+474375 \log ^2(-25+x) \log (x)+33750 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )+\frac {5}{4} \int \left (15625+\frac {390625}{-25+x}+625 x+25 x^2+x^3\right ) \, dx+5 \int x^3 \log (-25+x) \, dx+\frac {50}{3} \int \left (625+\frac {15625}{-25+x}+25 x+x^2\right ) \, dx+\frac {215}{2} \int \left (25+\frac {625}{-25+x}+x\right ) \, dx-150 \int x^2 \log (-25+x) \, dx+200 \int x^2 \log (-25+x) \, dx-625 \int x \log (-25+x) \, dx-3795 \int x \log (x) \, dx-6750 \int x \log (-25+x) \, dx-15180 \int x \log (-25+x) \log (x) \, dx-18975 \int \log (x) \, dx+37500 \int \frac {(25-x) \log (-25+x)}{x} \, dx-94875 \int \log (x) \, dx+341550 \int \log (-25+x) \log (x) \, dx-379500 \int \log (-25+x) \log (x) \, dx+390625 \int \frac {\log (25-x)}{x} \, dx-474375 \int \frac {\log (x)}{-25+x} \, dx-474375 \text {Subst}\left (\int \frac {\log ^2(x)}{25+x} \, dx,x,-25+x\right )-1953125 \int \frac {\log (25-x)}{x} \, dx+2343750 \int \frac {\log (25-x)}{x} \, dx-2371875 \int \frac {\log (x)}{-25+x} \, dx-3125000 \int \frac {\log (25-x)}{x} \, dx+4218750 \int \frac {\log (25-x)}{x} \, dx+8538750 \int \frac {\log (-25+x) \log (x)}{-25+x} \, dx-9487500 \int \frac {\log (-25+x) \log (x)}{-25+x} \, dx \\ & = \frac {3129605 x}{12}+\frac {61205 x^2}{24}+\frac {575 x^3}{36}+\frac {5 x^4}{16}+\frac {9790625}{12} \log (25-x)+450 (25-x) \log (-25+x)-3795 x^2 \log (-25+x)-2880405 \log (25) \log (-25+x)-405 \log (-25+x) \log \left (\frac {x}{25}\right )-474375 \log ^2(-25+x) \log \left (\frac {x}{25}\right )+1875000 \log (25) \log (x)+2868750 \log (25-x) \log (x)+450 (25-x) \log (-25+x) \log (x)-215 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+474375 \log ^2(-25+x) \log (x)+33750 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )-\frac {5}{4} \int \frac {x^4}{-25+x} \, dx+50 \int \frac {x^3}{-25+x} \, dx-\frac {200}{3} \int \frac {x^3}{-25+x} \, dx+\frac {625}{2} \int \frac {x^2}{-25+x} \, dx+3375 \int \frac {x^2}{-25+x} \, dx+15180 \int \left (-\frac {25}{2}-\frac {x}{4}-\frac {625 \log (25-x)}{2 x}+\frac {1}{2} x \log (-25+x)\right ) \, dx-37500 \text {Subst}\left (\int \frac {x \log (x)}{25+x} \, dx,x,-25+x\right )-341550 \int \left (-1-\frac {(25-x) \log (-25+x)}{x}\right ) \, dx+379500 \int \left (-1-\frac {(25-x) \log (-25+x)}{x}\right ) \, dx+390625 \int \frac {\log \left (1-\frac {x}{25}\right )}{x} \, dx-474375 \int \frac {\log \left (\frac {x}{25}\right )}{-25+x} \, dx+948750 \text {Subst}\left (\int \frac {\log \left (1+\frac {x}{25}\right ) \log (x)}{x} \, dx,x,-25+x\right )-1953125 \int \frac {\log \left (1-\frac {x}{25}\right )}{x} \, dx+2343750 \int \frac {\log \left (1-\frac {x}{25}\right )}{x} \, dx-2371875 \int \frac {\log \left (\frac {x}{25}\right )}{-25+x} \, dx-3125000 \int \frac {\log \left (1-\frac {x}{25}\right )}{x} \, dx+4218750 \int \frac {\log \left (1-\frac {x}{25}\right )}{x} \, dx+8538750 \text {Subst}\left (\int \frac {\log (x) \log (25+x)}{x} \, dx,x,-25+x\right )-9487500 \text {Subst}\left (\int \frac {\log (x) \log (25+x)}{x} \, dx,x,-25+x\right ) \\ & = \frac {397205 x}{12}+\frac {15665 x^2}{24}+\frac {575 x^3}{36}+\frac {5 x^4}{16}+\frac {9790625}{12} \log (25-x)+450 (25-x) \log (-25+x)-3795 x^2 \log (-25+x)-2880405 \log (25) \log (-25+x)-405 \log (-25+x) \log \left (\frac {x}{25}\right )-474375 \log ^2(-25+x) \log \left (\frac {x}{25}\right )+1875000 \log (25) \log (x)+2868750 \log (25-x) \log (x)+450 (25-x) \log (-25+x) \log (x)-215 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+2880000 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )-948750 \log (-25+x) \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )-1875000 \operatorname {PolyLog}\left (2,\frac {x}{25}\right )-\frac {5}{4} \int \left (15625+\frac {390625}{-25+x}+625 x+25 x^2+x^3\right ) \, dx+50 \int \left (625+\frac {15625}{-25+x}+25 x+x^2\right ) \, dx-\frac {200}{3} \int \left (625+\frac {15625}{-25+x}+25 x+x^2\right ) \, dx+\frac {625}{2} \int \left (25+\frac {625}{-25+x}+x\right ) \, dx+3375 \int \left (25+\frac {625}{-25+x}+x\right ) \, dx+7590 \int x \log (-25+x) \, dx-37500 \text {Subst}\left (\int \left (\log (x)-\frac {25 \log (x)}{25+x}\right ) \, dx,x,-25+x\right )+341550 \int \frac {(25-x) \log (-25+x)}{x} \, dx-379500 \int \frac {(25-x) \log (-25+x)}{x} \, dx+948750 \text {Subst}\left (\int \frac {\operatorname {PolyLog}\left (2,-\frac {x}{25}\right )}{x} \, dx,x,-25+x\right )-4269375 \text {Subst}\left (\int \frac {\log ^2(x)}{25+x} \, dx,x,-25+x\right )-4743750 \int \frac {\log (25-x)}{x} \, dx+4743750 \text {Subst}\left (\int \frac {\log ^2(x)}{25+x} \, dx,x,-25+x\right ) \\ & = 95340 x+\frac {3795 x^2}{2}+2371875 \log (25-x)+450 (25-x) \log (-25+x)-2880405 \log (25) \log (-25+x)-405 \log (-25+x) \log \left (\frac {x}{25}\right )-2868750 \log (25) \log (x)+2868750 \log (25-x) \log (x)+450 (25-x) \log (-25+x) \log (x)-215 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+2880000 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )-948750 \log (-25+x) \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )-1875000 \operatorname {PolyLog}\left (2,\frac {x}{25}\right )+948750 \operatorname {PolyLog}\left (3,1-\frac {x}{25}\right )-3795 \int \frac {x^2}{-25+x} \, dx-37500 \text {Subst}(\int \log (x) \, dx,x,-25+x)-341550 \text {Subst}\left (\int \frac {x \log (x)}{25+x} \, dx,x,-25+x\right )+379500 \text {Subst}\left (\int \frac {x \log (x)}{25+x} \, dx,x,-25+x\right )+937500 \text {Subst}\left (\int \frac {\log (x)}{25+x} \, dx,x,-25+x\right )-4743750 \int \frac {\log \left (1-\frac {x}{25}\right )}{x} \, dx+8538750 \text {Subst}\left (\int \frac {\log \left (1+\frac {x}{25}\right ) \log (x)}{x} \, dx,x,-25+x\right )-9487500 \text {Subst}\left (\int \frac {\log \left (1+\frac {x}{25}\right ) \log (x)}{x} \, dx,x,-25+x\right ) \\ & = 132840 x+\frac {3795 x^2}{2}+2371875 \log (25-x)+37950 (25-x) \log (-25+x)-2880405 \log (25) \log (-25+x)+937095 \log (-25+x) \log \left (\frac {x}{25}\right )-2868750 \log (25) \log (x)+2868750 \log (25-x) \log (x)+450 (25-x) \log (-25+x) \log (x)-215 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+2880000 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )+2868750 \operatorname {PolyLog}\left (2,\frac {x}{25}\right )+948750 \operatorname {PolyLog}\left (3,1-\frac {x}{25}\right )-3795 \int \left (25+\frac {625}{-25+x}+x\right ) \, dx-341550 \text {Subst}\left (\int \left (\log (x)-\frac {25 \log (x)}{25+x}\right ) \, dx,x,-25+x\right )+379500 \text {Subst}\left (\int \left (\log (x)-\frac {25 \log (x)}{25+x}\right ) \, dx,x,-25+x\right )-937500 \text {Subst}\left (\int \frac {\log \left (1+\frac {x}{25}\right )}{x} \, dx,x,-25+x\right )+8538750 \text {Subst}\left (\int \frac {\operatorname {PolyLog}\left (2,-\frac {x}{25}\right )}{x} \, dx,x,-25+x\right )-9487500 \text {Subst}\left (\int \frac {\operatorname {PolyLog}\left (2,-\frac {x}{25}\right )}{x} \, dx,x,-25+x\right ) \\ & = 37965 x+37950 (25-x) \log (-25+x)-2880405 \log (25) \log (-25+x)+937095 \log (-25+x) \log \left (\frac {x}{25}\right )-2868750 \log (25) \log (x)+2868750 \log (25-x) \log (x)+450 (25-x) \log (-25+x) \log (x)-215 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+3817500 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )+2868750 \operatorname {PolyLog}\left (2,\frac {x}{25}\right )-341550 \text {Subst}(\int \log (x) \, dx,x,-25+x)+379500 \text {Subst}(\int \log (x) \, dx,x,-25+x)+8538750 \text {Subst}\left (\int \frac {\log (x)}{25+x} \, dx,x,-25+x\right )-9487500 \text {Subst}\left (\int \frac {\log (x)}{25+x} \, dx,x,-25+x\right ) \\ & = 15 x-2880405 \log (25) \log (-25+x)-11655 \log (-25+x) \log \left (\frac {x}{25}\right )-2868750 \log (25) \log (x)+2868750 \log (25-x) \log (x)+450 (25-x) \log (-25+x) \log (x)-215 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+3817500 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )+2868750 \operatorname {PolyLog}\left (2,\frac {x}{25}\right )-8538750 \text {Subst}\left (\int \frac {\log \left (1+\frac {x}{25}\right )}{x} \, dx,x,-25+x\right )+9487500 \text {Subst}\left (\int \frac {\log \left (1+\frac {x}{25}\right )}{x} \, dx,x,-25+x\right ) \\ & = 15 x-2880405 \log (25) \log (-25+x)-11655 \log (-25+x) \log \left (\frac {x}{25}\right )-2868750 \log (25) \log (x)+2868750 \log (25-x) \log (x)+450 (25-x) \log (-25+x) \log (x)-215 x^2 \log (-25+x) \log (x)-50 x^3 \log (-25+x) \log (x)-5 x^4 \log (-25+x) \log (x)+2868750 \operatorname {PolyLog}\left (2,1-\frac {x}{25}\right )+2868750 \operatorname {PolyLog}\left (2,\frac {x}{25}\right ) \\ \end{align*}
Time = 0.71 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88 \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=-5 \left (-3 x+\left (9+5 x+x^2\right )^2 \log (-25+x) \log (x)\right ) \]
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Time = 0.34 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88
method | result | size |
risch | \(-5 \left (x^{2}+5 x +9\right )^{2} \ln \left (x \right ) \ln \left (x -25\right )+15 x\) | \(23\) |
parallelrisch | \(-5 \ln \left (x \right ) \ln \left (x -25\right ) x^{4}-50 \ln \left (x \right ) \ln \left (x -25\right ) x^{3}-215 \ln \left (x \right ) \ln \left (x -25\right ) x^{2}-450 \ln \left (x \right ) \ln \left (x -25\right ) x -405 \ln \left (x \right ) \ln \left (x -25\right )+15 x +\frac {375}{2}\) | \(56\) |
default | \(15 x -5 \left (\left (-\frac {1}{4}+\ln \left (x \right )\right ) x^{4}+\left (-\frac {10}{3}+10 \ln \left (x \right )\right ) x^{3}+\left (-\frac {43}{2}+43 \ln \left (x \right )\right ) x^{2}+\left (-90+90 \ln \left (x \right )\right ) x \right ) \ln \left (x -25\right )-405 \left (\ln \left (x \right )-\ln \left (\frac {x}{25}\right )\right ) \ln \left (-\frac {x}{25}+1\right )-\frac {9925625 \ln \left (x -25\right )}{12}-\frac {5 \left (x -25\right )^{4} \ln \left (x -25\right )}{4}-\frac {231366875}{144}-\frac {425 \left (x -25\right )^{3} \ln \left (x -25\right )}{3}-6045 \left (x -25\right )^{2} \ln \left (x -25\right )-115200 \left (x -25\right ) \ln \left (x -25\right )-405 \ln \left (x -25\right ) \ln \left (\frac {x}{25}\right )\) | \(124\) |
parts | \(15 x -5 \left (\left (-\frac {1}{4}+\ln \left (x \right )\right ) x^{4}+\left (-\frac {10}{3}+10 \ln \left (x \right )\right ) x^{3}+\left (-\frac {43}{2}+43 \ln \left (x \right )\right ) x^{2}+\left (-90+90 \ln \left (x \right )\right ) x \right ) \ln \left (x -25\right )-405 \left (\ln \left (x \right )-\ln \left (\frac {x}{25}\right )\right ) \ln \left (-\frac {x}{25}+1\right )-\frac {9925625 \ln \left (x -25\right )}{12}-\frac {5 \left (x -25\right )^{4} \ln \left (x -25\right )}{4}-\frac {231366875}{144}-\frac {425 \left (x -25\right )^{3} \ln \left (x -25\right )}{3}-6045 \left (x -25\right )^{2} \ln \left (x -25\right )-115200 \left (x -25\right ) \ln \left (x -25\right )-405 \ln \left (x -25\right ) \ln \left (\frac {x}{25}\right )\) | \(124\) |
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Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=-5 \, {\left (x^{4} + 10 \, x^{3} + 43 \, x^{2} + 90 \, x + 81\right )} \log \left (x - 25\right ) \log \left (x\right ) + 15 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (22) = 44\).
Time = 0.20 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.77 \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=15 x + \left (- 5 x^{4} \log {\left (x \right )} - 50 x^{3} \log {\left (x \right )} - 215 x^{2} \log {\left (x \right )} - 450 x \log {\left (x \right )} - 405 \log {\left (x \right )}\right ) \log {\left (x - 25 \right )} \]
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Time = 0.23 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=-5 \, {\left (x^{4} + 10 \, x^{3} + 43 \, x^{2} + 90 \, x + 81\right )} \log \left (x - 25\right ) \log \left (x\right ) + 15 \, x \]
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Time = 0.27 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35 \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=-5 \, {\left ({\left (x^{4} + 10 \, x^{3} + 43 \, x^{2} + 90 \, x\right )} \log \left (x\right ) + 81 \, \log \left (x\right )\right )} \log \left (x - 25\right ) + 15 \, x \]
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Time = 12.92 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {-375 x+15 x^2+\left (10125+10845 x+4925 x^2+1035 x^3+75 x^4-5 x^5\right ) \log (-25+x)+\left (-405 x-450 x^2-215 x^3-50 x^4-5 x^5+\left (11250 x+10300 x^2+3320 x^3+350 x^4-20 x^5\right ) \log (-25+x)\right ) \log (x)}{-25 x+x^2} \, dx=15\,x-\ln \left (x-25\right )\,\ln \left (x\right )\,\left (5\,x^4+50\,x^3+215\,x^2+450\,x+405\right ) \]
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