Integrand size = 355, antiderivative size = 30 \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx=\left (2 x+x^2+\frac {3}{5 x \left (-7+\log ^2(5)-\log (4 x)\right )}\right )^2 \] Output:
(2*x+3/5/(ln(5)^2-7-ln(4*x))/x+x^2)^2
Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(30)=60\).
Time = 0.08 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.07 \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx=\frac {2}{25} \left (50 x^2+50 x^3+\frac {25 x^4}{2}+\frac {9}{2 x^2 \left (7-\log ^2(5)+\log (4 x)\right )^2}-\frac {15 (2+x)}{7-\log ^2(5)+\log (4 x)}\right ) \] Input:
Integrate[(-144 + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 + (18 - 60*x^2 + 390*x^3 - 29400*x^4 - 44100*x^5 - 14700*x^6)*Log[5]^2 + ( -30*x^3 + 4200*x^4 + 6300*x^5 + 2100*x^6)*Log[5]^4 + (-200*x^4 - 300*x^5 - 100*x^6)*Log[5]^6 + (-18 + 60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 147 00*x^6 + (60*x^3 - 8400*x^4 - 12600*x^5 - 4200*x^6)*Log[5]^2 + (600*x^4 + 900*x^5 + 300*x^6)*Log[5]^4)*Log[4*x] + (-30*x^3 + 4200*x^4 + 6300*x^5 + 2 100*x^6 + (-600*x^4 - 900*x^5 - 300*x^6)*Log[5]^2)*Log[4*x]^2 + (200*x^4 + 300*x^5 + 100*x^6)*Log[4*x]^3)/(8575*x^3 - 3675*x^3*Log[5]^2 + 525*x^3*Lo g[5]^4 - 25*x^3*Log[5]^6 + (3675*x^3 - 1050*x^3*Log[5]^2 + 75*x^3*Log[5]^4 )*Log[4*x] + (525*x^3 - 75*x^3*Log[5]^2)*Log[4*x]^2 + 25*x^3*Log[4*x]^3),x ]
Output:
(2*(50*x^2 + 50*x^3 + (25*x^4)/2 + 9/(2*x^2*(7 - Log[5]^2 + Log[4*x])^2) - (15*(2 + x))/(7 - Log[5]^2 + Log[4*x])))/25
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {34300 x^6+102900 x^5+68600 x^4-1260 x^3+420 x^2+\left (-100 x^6-300 x^5-200 x^4\right ) \log ^6(5)+\left (100 x^6+300 x^5+200 x^4\right ) \log ^3(4 x)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3\right ) \log ^4(5)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3+\left (-300 x^6-900 x^5-600 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (-14700 x^6-44100 x^5-29400 x^4+390 x^3-60 x^2+18\right ) \log ^2(5)+\left (14700 x^6+44100 x^5+29400 x^4-390 x^3+60 x^2+\left (300 x^6+900 x^5+600 x^4\right ) \log ^4(5)+\left (-4200 x^6-12600 x^5-8400 x^4+60 x^3\right ) \log ^2(5)-18\right ) \log (4 x)-144}{8575 x^3-25 x^3 \log ^6(5)+525 x^3 \log ^4(5)+25 x^3 \log ^3(4 x)-3675 x^3 \log ^2(5)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+\left (3675 x^3+75 x^3 \log ^4(5)-1050 x^3 \log ^2(5)\right ) \log (4 x)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {34300 x^6+102900 x^5+68600 x^4-1260 x^3+420 x^2+\left (-100 x^6-300 x^5-200 x^4\right ) \log ^6(5)+\left (100 x^6+300 x^5+200 x^4\right ) \log ^3(4 x)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3\right ) \log ^4(5)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3+\left (-300 x^6-900 x^5-600 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (-14700 x^6-44100 x^5-29400 x^4+390 x^3-60 x^2+18\right ) \log ^2(5)+\left (14700 x^6+44100 x^5+29400 x^4-390 x^3+60 x^2+\left (300 x^6+900 x^5+600 x^4\right ) \log ^4(5)+\left (-4200 x^6-12600 x^5-8400 x^4+60 x^3\right ) \log ^2(5)-18\right ) \log (4 x)-144}{-25 x^3 \log ^6(5)+525 x^3 \log ^4(5)+25 x^3 \log ^3(4 x)+x^3 \left (8575-3675 \log ^2(5)\right )+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+\left (3675 x^3+75 x^3 \log ^4(5)-1050 x^3 \log ^2(5)\right ) \log (4 x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {34300 x^6+102900 x^5+68600 x^4-1260 x^3+420 x^2+\left (-100 x^6-300 x^5-200 x^4\right ) \log ^6(5)+\left (100 x^6+300 x^5+200 x^4\right ) \log ^3(4 x)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3\right ) \log ^4(5)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3+\left (-300 x^6-900 x^5-600 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (-14700 x^6-44100 x^5-29400 x^4+390 x^3-60 x^2+18\right ) \log ^2(5)+\left (14700 x^6+44100 x^5+29400 x^4-390 x^3+60 x^2+\left (300 x^6+900 x^5+600 x^4\right ) \log ^4(5)+\left (-4200 x^6-12600 x^5-8400 x^4+60 x^3\right ) \log ^2(5)-18\right ) \log (4 x)-144}{25 x^3 \log ^3(4 x)+x^3 \left (8575-3675 \log ^2(5)\right )+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+x^3 \left (525 \log ^4(5)-25 \log ^6(5)\right )+\left (3675 x^3+75 x^3 \log ^4(5)-1050 x^3 \log ^2(5)\right ) \log (4 x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {34300 x^6+102900 x^5+68600 x^4-1260 x^3+420 x^2+\left (-100 x^6-300 x^5-200 x^4\right ) \log ^6(5)+\left (100 x^6+300 x^5+200 x^4\right ) \log ^3(4 x)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3\right ) \log ^4(5)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3+\left (-300 x^6-900 x^5-600 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (-14700 x^6-44100 x^5-29400 x^4+390 x^3-60 x^2+18\right ) \log ^2(5)+\left (14700 x^6+44100 x^5+29400 x^4-390 x^3+60 x^2+\left (300 x^6+900 x^5+600 x^4\right ) \log ^4(5)+\left (-4200 x^6-12600 x^5-8400 x^4+60 x^3\right ) \log ^2(5)-18\right ) \log (4 x)-144}{25 x^3 \log ^3(4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+\left (3675 x^3+75 x^3 \log ^4(5)-1050 x^3 \log ^2(5)\right ) \log (4 x)+x^3 \left (8575-25 \log ^6(5)+525 \log ^4(5)-3675 \log ^2(5)\right )}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {34300 x^6+102900 x^5+68600 x^4-1260 x^3+420 x^2+\left (-100 x^6-300 x^5-200 x^4\right ) \log ^6(5)+\left (100 x^6+300 x^5+200 x^4\right ) \log ^3(4 x)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3\right ) \log ^4(5)+\left (2100 x^6+6300 x^5+4200 x^4-30 x^3+\left (-300 x^6-900 x^5-600 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (-14700 x^6-44100 x^5-29400 x^4+390 x^3-60 x^2+18\right ) \log ^2(5)+\left (14700 x^6+44100 x^5+29400 x^4-390 x^3+60 x^2+\left (300 x^6+900 x^5+600 x^4\right ) \log ^4(5)+\left (-4200 x^6-12600 x^5-8400 x^4+60 x^3\right ) \log ^2(5)-18\right ) \log (4 x)-144}{25 x^3 \left (\log (4 x)+7 \left (1-\frac {\log ^2(5)}{7}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{25} \int -\frac {2 \left (-17150 x^6-51450 x^5-34300 x^4+630 x^3-210 x^2-50 \left (x^6+3 x^5+2 x^4\right ) \log ^3(4 x)+15 \left (-70 x^6-210 x^5-140 x^4+x^3+10 \left (x^6+3 x^5+2 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+3 \left (-2450 x^6-7350 x^5-4900 x^4+65 x^3-10 x^2-50 \left (x^6+3 x^5+2 x^4\right ) \log ^4(5)-10 \left (-70 x^6-210 x^5-140 x^4+x^3\right ) \log ^2(5)+3\right ) \log (4 x)+50 \left (x^6+3 x^5+2 x^4\right ) \log ^6(5)+15 \left (-70 x^6-210 x^5-140 x^4+x^3\right ) \log ^4(5)-3 \left (-2450 x^6-7350 x^5-4900 x^4+65 x^3-10 x^2+3\right ) \log ^2(5)+72\right )}{x^3 \left (\log (4 x)-\log ^2(5)+7\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {2}{25} \int \frac {-17150 x^6-51450 x^5-34300 x^4+630 x^3-210 x^2-50 \left (x^6+3 x^5+2 x^4\right ) \log ^3(4 x)+15 \left (-70 x^6-210 x^5-140 x^4+x^3+10 \left (x^6+3 x^5+2 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+3 \left (-2450 x^6-7350 x^5-4900 x^4+65 x^3-10 x^2-50 \left (x^6+3 x^5+2 x^4\right ) \log ^4(5)-10 \left (-70 x^6-210 x^5-140 x^4+x^3\right ) \log ^2(5)+3\right ) \log (4 x)+50 \left (x^6+3 x^5+2 x^4\right ) \log ^6(5)+15 \left (-70 x^6-210 x^5-140 x^4+x^3\right ) \log ^4(5)-3 \left (-2450 x^6-7350 x^5-4900 x^4+65 x^3-10 x^2+3\right ) \log ^2(5)+72}{x^3 \left (\log (4 x)-\log ^2(5)+7\right )^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -\frac {2}{25} \int \frac {-17150 x^6-51450 x^5-34300 x^4+630 x^3-210 x^2-50 \left (x^6+3 x^5+2 x^4\right ) \log ^3(4 x)+15 \left (-70 x^6-210 x^5-140 x^4+x^3+10 \left (x^6+3 x^5+2 x^4\right ) \log ^2(5)\right ) \log ^2(4 x)+3 \left (-2450 x^6-7350 x^5-4900 x^4+65 x^3-10 x^2-50 \left (x^6+3 x^5+2 x^4\right ) \log ^4(5)-10 \left (-70 x^6-210 x^5-140 x^4+x^3\right ) \log ^2(5)+3\right ) \log (4 x)+50 \left (x^6+3 x^5+2 x^4\right ) \log ^6(5)+15 \left (-70 x^6-210 x^5-140 x^4+x^3\right ) \log ^4(5)-3 \left (-2450 x^6-7350 x^5-4900 x^4+65 x^3-10 x^2+3\right ) \log ^2(5)+72}{x^3 \left (\log (4 x)+7 \left (1-\frac {\log ^2(5)}{7}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {2}{25} \int \left (-50 x \left (x^2+3 x+2\right )+\frac {15}{\log (4 x)+7 \left (1-\frac {\log ^2(5)}{7}\right )}+\frac {3 \left (-5 x^3-10 x^2+3\right )}{x^3 \left (\log (4 x)+7 \left (1-\frac {\log ^2(5)}{7}\right )\right )^2}+\frac {9}{x^3 \left (\log (4 x)+7 \left (1-\frac {\log ^2(5)}{7}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {2}{25} \left (3 \int \frac {-5 x^3-10 x^2+3}{x^3 \left (\log (4 x)+7 \left (1-\frac {\log ^2(5)}{7}\right )\right )^2}dx+288 e^{14-2 \log ^2(5)} \operatorname {ExpIntegralEi}\left (-2 \left (\log (4 x)-\log ^2(5)+7\right )\right )+\frac {15}{4} e^{\log ^2(5)-7} \operatorname {ExpIntegralEi}\left (\log (4 x)-\log ^2(5)+7\right )-\frac {25 x^4}{2}-50 x^3-50 x^2+\frac {9}{x^2 \left (\log (4 x)+7-\log ^2(5)\right )}-\frac {9}{2 x^2 \left (\log (4 x)+7-\log ^2(5)\right )^2}\right )\) |
Input:
Int[(-144 + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 + (18 - 60*x^2 + 390*x^3 - 29400*x^4 - 44100*x^5 - 14700*x^6)*Log[5]^2 + (-30*x^ 3 + 4200*x^4 + 6300*x^5 + 2100*x^6)*Log[5]^4 + (-200*x^4 - 300*x^5 - 100*x ^6)*Log[5]^6 + (-18 + 60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700*x^6 + (60*x^3 - 8400*x^4 - 12600*x^5 - 4200*x^6)*Log[5]^2 + (600*x^4 + 900*x^ 5 + 300*x^6)*Log[5]^4)*Log[4*x] + (-30*x^3 + 4200*x^4 + 6300*x^5 + 2100*x^ 6 + (-600*x^4 - 900*x^5 - 300*x^6)*Log[5]^2)*Log[4*x]^2 + (200*x^4 + 300*x ^5 + 100*x^6)*Log[4*x]^3)/(8575*x^3 - 3675*x^3*Log[5]^2 + 525*x^3*Log[5]^4 - 25*x^3*Log[5]^6 + (3675*x^3 - 1050*x^3*Log[5]^2 + 75*x^3*Log[5]^4)*Log[ 4*x] + (525*x^3 - 75*x^3*Log[5]^2)*Log[4*x]^2 + 25*x^3*Log[4*x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(28)=56\).
Time = 62.60 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.73
| method | result | size |
| risch | \(x^{4}+4 x^{3}+4 x^{2}+\frac {\frac {6 x^{3} \ln \left (5\right )^{2}}{5}+\frac {12 x^{2} \ln \left (5\right )^{2}}{5}-\frac {6 x^{3} \ln \left (4 x \right )}{5}-\frac {42 x^{3}}{5}-\frac {12 x^{2} \ln \left (4 x \right )}{5}-\frac {84 x^{2}}{5}+\frac {9}{25}}{x^{2} \left (\ln \left (5\right )^{2}-7-\ln \left (4 x \right )\right )^{2}}\) | \(82\) |
| parallelrisch | \(-\frac {-9+1400 x^{4} \ln \left (5\right )^{2}-30 x^{3} \ln \left (5\right )^{2}-60 x^{2} \ln \left (5\right )^{2}-1225 x^{6}+420 x^{2}+210 x^{3}-4900 x^{4}-4900 x^{5}-25 \ln \left (5\right )^{4} x^{6}-100 \ln \left (5\right )^{4} x^{5}-25 \ln \left (4 x \right )^{2} x^{6}+350 \ln \left (5\right )^{2} x^{6}-100 \ln \left (4 x \right )^{2} x^{5}-350 \ln \left (4 x \right ) x^{6}+1400 \ln \left (5\right )^{2} x^{5}-100 x^{4} \ln \left (4 x \right )^{2}-1400 \ln \left (4 x \right ) x^{5}-1400 \ln \left (4 x \right ) x^{4}+30 x^{3} \ln \left (4 x \right )+60 x^{2} \ln \left (4 x \right )+50 \ln \left (4 x \right ) \ln \left (5\right )^{2} x^{6}+200 \ln \left (4 x \right ) \ln \left (5\right )^{2} x^{5}+200 \ln \left (4 x \right ) \ln \left (5\right )^{2} x^{4}-100 \ln \left (5\right )^{4} x^{4}}{25 x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}\) | \(258\) |
| derivativedivides | \(-\frac {12}{5 \left (-\ln \left (5\right )^{2}+\ln \left (4 x \right )+7\right )}-\frac {6 x}{5 \left (-\ln \left (5\right )^{2}+\ln \left (4 x \right )+7\right )}+\frac {18 \ln \left (5\right )^{2} \ln \left (4 x \right )}{25 x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}+x^{4}+4 x^{3}+4 x^{2}+\frac {\frac {144 \ln \left (5\right )^{2}}{25}-\frac {144 \ln \left (4 x \right )}{25}-\frac {936}{25}}{x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}+\frac {\frac {18 \ln \left (5\right )^{4}}{25}-\frac {18 \ln \left (4 x \right ) \ln \left (5\right )^{2}}{25}-\frac {261 \ln \left (5\right )^{2}}{25}+\frac {144 \ln \left (4 x \right )}{25}+\frac {189}{5}}{x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}-\frac {18 \ln \left (5\right )^{4}}{25 x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}+\frac {117 \ln \left (5\right )^{2}}{25 x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}\) | \(313\) |
| default | \(-\frac {12}{5 \left (-\ln \left (5\right )^{2}+\ln \left (4 x \right )+7\right )}-\frac {6 x}{5 \left (-\ln \left (5\right )^{2}+\ln \left (4 x \right )+7\right )}+\frac {18 \ln \left (5\right )^{2} \ln \left (4 x \right )}{25 x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}+x^{4}+4 x^{3}+4 x^{2}+\frac {\frac {144 \ln \left (5\right )^{2}}{25}-\frac {144 \ln \left (4 x \right )}{25}-\frac {936}{25}}{x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}+\frac {\frac {18 \ln \left (5\right )^{4}}{25}-\frac {18 \ln \left (4 x \right ) \ln \left (5\right )^{2}}{25}-\frac {261 \ln \left (5\right )^{2}}{25}+\frac {144 \ln \left (4 x \right )}{25}+\frac {189}{5}}{x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}-\frac {18 \ln \left (5\right )^{4}}{25 x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}+\frac {117 \ln \left (5\right )^{2}}{25 x^{2} \left (\ln \left (5\right )^{4}-2 \ln \left (4 x \right ) \ln \left (5\right )^{2}+\ln \left (4 x \right )^{2}-14 \ln \left (5\right )^{2}+14 \ln \left (4 x \right )+49\right )}\) | \(313\) |
Input:
int(((100*x^6+300*x^5+200*x^4)*ln(4*x)^3+((-300*x^6-900*x^5-600*x^4)*ln(5) ^2+2100*x^6+6300*x^5+4200*x^4-30*x^3)*ln(4*x)^2+((300*x^6+900*x^5+600*x^4) *ln(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*ln(5)^2+14700*x^6+44100*x^5 +29400*x^4-390*x^3+60*x^2-18)*ln(4*x)+(-100*x^6-300*x^5-200*x^4)*ln(5)^6+( 2100*x^6+6300*x^5+4200*x^4-30*x^3)*ln(5)^4+(-14700*x^6-44100*x^5-29400*x^4 +390*x^3-60*x^2+18)*ln(5)^2+34300*x^6+102900*x^5+68600*x^4-1260*x^3+420*x^ 2-144)/(25*x^3*ln(4*x)^3+(-75*x^3*ln(5)^2+525*x^3)*ln(4*x)^2+(75*x^3*ln(5) ^4-1050*x^3*ln(5)^2+3675*x^3)*ln(4*x)-25*x^3*ln(5)^6+525*x^3*ln(5)^4-3675* x^3*ln(5)^2+8575*x^3),x,method=_RETURNVERBOSE)
Output:
x^4+4*x^3+4*x^2+3/25*(10*x^3*ln(5)^2+20*x^2*ln(5)^2-10*x^3*ln(4*x)-70*x^3- 20*x^2*ln(4*x)-140*x^2+3)/x^2/(ln(5)^2-7-ln(4*x))^2
Leaf count of result is larger than twice the leaf count of optimal. 210 vs. \(2 (32) = 64\).
Time = 0.11 (sec) , antiderivative size = 210, normalized size of antiderivative = 7.00 \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx=\frac {1225 \, x^{6} + 4900 \, x^{5} + 25 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (5\right )^{4} + 4900 \, x^{4} - 210 \, x^{3} - 10 \, {\left (35 \, x^{6} + 140 \, x^{5} + 140 \, x^{4} - 3 \, x^{3} - 6 \, x^{2}\right )} \log \left (5\right )^{2} + 25 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (4 \, x\right )^{2} - 420 \, x^{2} + 10 \, {\left (35 \, x^{6} + 140 \, x^{5} + 140 \, x^{4} - 3 \, x^{3} - 5 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (5\right )^{2} - 6 \, x^{2}\right )} \log \left (4 \, x\right ) + 9}{25 \, {\left (x^{2} \log \left (5\right )^{4} - 14 \, x^{2} \log \left (5\right )^{2} + x^{2} \log \left (4 \, x\right )^{2} + 49 \, x^{2} - 2 \, {\left (x^{2} \log \left (5\right )^{2} - 7 \, x^{2}\right )} \log \left (4 \, x\right )\right )}} \] Input:
integrate(((100*x^6+300*x^5+200*x^4)*log(4*x)^3+((-300*x^6-900*x^5-600*x^4 )*log(5)^2+2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(4*x)^2+((300*x^6+900*x^5 +600*x^4)*log(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*log(5)^2+14700*x^ 6+44100*x^5+29400*x^4-390*x^3+60*x^2-18)*log(4*x)+(-100*x^6-300*x^5-200*x^ 4)*log(5)^6+(2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(5)^4+(-14700*x^6-44100 *x^5-29400*x^4+390*x^3-60*x^2+18)*log(5)^2+34300*x^6+102900*x^5+68600*x^4- 1260*x^3+420*x^2-144)/(25*x^3*log(4*x)^3+(-75*x^3*log(5)^2+525*x^3)*log(4* x)^2+(75*x^3*log(5)^4-1050*x^3*log(5)^2+3675*x^3)*log(4*x)-25*x^3*log(5)^6 +525*x^3*log(5)^4-3675*x^3*log(5)^2+8575*x^3),x, algorithm="fricas")
Output:
1/25*(1225*x^6 + 4900*x^5 + 25*(x^6 + 4*x^5 + 4*x^4)*log(5)^4 + 4900*x^4 - 210*x^3 - 10*(35*x^6 + 140*x^5 + 140*x^4 - 3*x^3 - 6*x^2)*log(5)^2 + 25*( x^6 + 4*x^5 + 4*x^4)*log(4*x)^2 - 420*x^2 + 10*(35*x^6 + 140*x^5 + 140*x^4 - 3*x^3 - 5*(x^6 + 4*x^5 + 4*x^4)*log(5)^2 - 6*x^2)*log(4*x) + 9)/(x^2*lo g(5)^4 - 14*x^2*log(5)^2 + x^2*log(4*x)^2 + 49*x^2 - 2*(x^2*log(5)^2 - 7*x ^2)*log(4*x))
Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (24) = 48\).
Time = 0.20 (sec) , antiderivative size = 119, normalized size of antiderivative = 3.97 \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx=x^{4} + 4 x^{3} + 4 x^{2} + \frac {- 210 x^{3} + 30 x^{3} \log {\left (5 \right )}^{2} - 420 x^{2} + 60 x^{2} \log {\left (5 \right )}^{2} + \left (- 30 x^{3} - 60 x^{2}\right ) \log {\left (4 x \right )} + 9}{25 x^{2} \log {\left (4 x \right )}^{2} - 350 x^{2} \log {\left (5 \right )}^{2} + 25 x^{2} \log {\left (5 \right )}^{4} + 1225 x^{2} + \left (- 50 x^{2} \log {\left (5 \right )}^{2} + 350 x^{2}\right ) \log {\left (4 x \right )}} \] Input:
integrate(((100*x**6+300*x**5+200*x**4)*ln(4*x)**3+((-300*x**6-900*x**5-60 0*x**4)*ln(5)**2+2100*x**6+6300*x**5+4200*x**4-30*x**3)*ln(4*x)**2+((300*x **6+900*x**5+600*x**4)*ln(5)**4+(-4200*x**6-12600*x**5-8400*x**4+60*x**3)* ln(5)**2+14700*x**6+44100*x**5+29400*x**4-390*x**3+60*x**2-18)*ln(4*x)+(-1 00*x**6-300*x**5-200*x**4)*ln(5)**6+(2100*x**6+6300*x**5+4200*x**4-30*x**3 )*ln(5)**4+(-14700*x**6-44100*x**5-29400*x**4+390*x**3-60*x**2+18)*ln(5)** 2+34300*x**6+102900*x**5+68600*x**4-1260*x**3+420*x**2-144)/(25*x**3*ln(4* x)**3+(-75*x**3*ln(5)**2+525*x**3)*ln(4*x)**2+(75*x**3*ln(5)**4-1050*x**3* ln(5)**2+3675*x**3)*ln(4*x)-25*x**3*ln(5)**6+525*x**3*ln(5)**4-3675*x**3*l n(5)**2+8575*x**3),x)
Output:
x**4 + 4*x**3 + 4*x**2 + (-210*x**3 + 30*x**3*log(5)**2 - 420*x**2 + 60*x* *2*log(5)**2 + (-30*x**3 - 60*x**2)*log(4*x) + 9)/(25*x**2*log(4*x)**2 - 3 50*x**2*log(5)**2 + 25*x**2*log(5)**4 + 1225*x**2 + (-50*x**2*log(5)**2 + 350*x**2)*log(4*x))
Leaf count of result is larger than twice the leaf count of optimal. 275 vs. \(2 (32) = 64\).
Time = 0.16 (sec) , antiderivative size = 275, normalized size of antiderivative = 9.17 \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx=-\frac {25 \, {\left (\log \left (5\right )^{4} - 14 \, \log \left (5\right )^{2} - 4 \, {\left (\log \left (5\right )^{2} - 7\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} + 49\right )} x^{6} + 100 \, {\left (\log \left (5\right )^{4} - 14 \, \log \left (5\right )^{2} - 4 \, {\left (\log \left (5\right )^{2} - 7\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} + 49\right )} x^{5} + 100 \, {\left (\log \left (5\right )^{4} - 14 \, \log \left (5\right )^{2} - 4 \, {\left (\log \left (5\right )^{2} - 7\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} + 49\right )} x^{4} + 30 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (2\right ) - 7\right )} x^{3} + 60 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (2\right ) - 7\right )} x^{2} + 25 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (x\right )^{2} - 10 \, {\left (5 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (2\right ) - 7\right )} x^{6} + 20 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (2\right ) - 7\right )} x^{5} + 20 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (2\right ) - 7\right )} x^{4} + 3 \, x^{3} + 6 \, x^{2}\right )} \log \left (x\right ) + 9}{25 \, {\left (2 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (2\right ) - 7\right )} x^{2} \log \left (x\right ) - x^{2} \log \left (x\right )^{2} - {\left (\log \left (5\right )^{4} - 14 \, \log \left (5\right )^{2} - 4 \, {\left (\log \left (5\right )^{2} - 7\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} + 49\right )} x^{2}\right )}} \] Input:
integrate(((100*x^6+300*x^5+200*x^4)*log(4*x)^3+((-300*x^6-900*x^5-600*x^4 )*log(5)^2+2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(4*x)^2+((300*x^6+900*x^5 +600*x^4)*log(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*log(5)^2+14700*x^ 6+44100*x^5+29400*x^4-390*x^3+60*x^2-18)*log(4*x)+(-100*x^6-300*x^5-200*x^ 4)*log(5)^6+(2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(5)^4+(-14700*x^6-44100 *x^5-29400*x^4+390*x^3-60*x^2+18)*log(5)^2+34300*x^6+102900*x^5+68600*x^4- 1260*x^3+420*x^2-144)/(25*x^3*log(4*x)^3+(-75*x^3*log(5)^2+525*x^3)*log(4* x)^2+(75*x^3*log(5)^4-1050*x^3*log(5)^2+3675*x^3)*log(4*x)-25*x^3*log(5)^6 +525*x^3*log(5)^4-3675*x^3*log(5)^2+8575*x^3),x, algorithm="maxima")
Output:
-1/25*(25*(log(5)^4 - 14*log(5)^2 - 4*(log(5)^2 - 7)*log(2) + 4*log(2)^2 + 49)*x^6 + 100*(log(5)^4 - 14*log(5)^2 - 4*(log(5)^2 - 7)*log(2) + 4*log(2 )^2 + 49)*x^5 + 100*(log(5)^4 - 14*log(5)^2 - 4*(log(5)^2 - 7)*log(2) + 4* log(2)^2 + 49)*x^4 + 30*(log(5)^2 - 2*log(2) - 7)*x^3 + 60*(log(5)^2 - 2*l og(2) - 7)*x^2 + 25*(x^6 + 4*x^5 + 4*x^4)*log(x)^2 - 10*(5*(log(5)^2 - 2*l og(2) - 7)*x^6 + 20*(log(5)^2 - 2*log(2) - 7)*x^5 + 20*(log(5)^2 - 2*log(2 ) - 7)*x^4 + 3*x^3 + 6*x^2)*log(x) + 9)/(2*(log(5)^2 - 2*log(2) - 7)*x^2*l og(x) - x^2*log(x)^2 - (log(5)^4 - 14*log(5)^2 - 4*(log(5)^2 - 7)*log(2) + 4*log(2)^2 + 49)*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 121 vs. \(2 (32) = 64\).
Time = 0.18 (sec) , antiderivative size = 121, normalized size of antiderivative = 4.03 \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx=x^{4} + 4 \, x^{3} + 4 \, x^{2} + \frac {3 \, {\left (10 \, x^{3} \log \left (5\right )^{2} + 20 \, x^{2} \log \left (5\right )^{2} - 10 \, x^{3} \log \left (4 \, x\right ) - 70 \, x^{3} - 20 \, x^{2} \log \left (4 \, x\right ) - 140 \, x^{2} + 3\right )}}{25 \, {\left (x^{2} \log \left (5\right )^{4} - 2 \, x^{2} \log \left (5\right )^{2} \log \left (4 \, x\right ) - 14 \, x^{2} \log \left (5\right )^{2} + x^{2} \log \left (4 \, x\right )^{2} + 14 \, x^{2} \log \left (4 \, x\right ) + 49 \, x^{2}\right )}} \] Input:
integrate(((100*x^6+300*x^5+200*x^4)*log(4*x)^3+((-300*x^6-900*x^5-600*x^4 )*log(5)^2+2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(4*x)^2+((300*x^6+900*x^5 +600*x^4)*log(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*log(5)^2+14700*x^ 6+44100*x^5+29400*x^4-390*x^3+60*x^2-18)*log(4*x)+(-100*x^6-300*x^5-200*x^ 4)*log(5)^6+(2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(5)^4+(-14700*x^6-44100 *x^5-29400*x^4+390*x^3-60*x^2+18)*log(5)^2+34300*x^6+102900*x^5+68600*x^4- 1260*x^3+420*x^2-144)/(25*x^3*log(4*x)^3+(-75*x^3*log(5)^2+525*x^3)*log(4* x)^2+(75*x^3*log(5)^4-1050*x^3*log(5)^2+3675*x^3)*log(4*x)-25*x^3*log(5)^6 +525*x^3*log(5)^4-3675*x^3*log(5)^2+8575*x^3),x, algorithm="giac")
Output:
x^4 + 4*x^3 + 4*x^2 + 3/25*(10*x^3*log(5)^2 + 20*x^2*log(5)^2 - 10*x^3*log (4*x) - 70*x^3 - 20*x^2*log(4*x) - 140*x^2 + 3)/(x^2*log(5)^4 - 2*x^2*log( 5)^2*log(4*x) - 14*x^2*log(5)^2 + x^2*log(4*x)^2 + 14*x^2*log(4*x) + 49*x^ 2)
Timed out. \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx=\int \frac {{\ln \left (4\,x\right )}^3\,\left (100\,x^6+300\,x^5+200\,x^4\right )-{\ln \left (5\right )}^6\,\left (100\,x^6+300\,x^5+200\,x^4\right )+{\ln \left (5\right )}^4\,\left (2100\,x^6+6300\,x^5+4200\,x^4-30\,x^3\right )+{\ln \left (4\,x\right )}^2\,\left (4200\,x^4-30\,x^3-{\ln \left (5\right )}^2\,\left (300\,x^6+900\,x^5+600\,x^4\right )+6300\,x^5+2100\,x^6\right )-{\ln \left (5\right )}^2\,\left (14700\,x^6+44100\,x^5+29400\,x^4-390\,x^3+60\,x^2-18\right )+\ln \left (4\,x\right )\,\left ({\ln \left (5\right )}^4\,\left (300\,x^6+900\,x^5+600\,x^4\right )-{\ln \left (5\right )}^2\,\left (4200\,x^6+12600\,x^5+8400\,x^4-60\,x^3\right )+60\,x^2-390\,x^3+29400\,x^4+44100\,x^5+14700\,x^6-18\right )+420\,x^2-1260\,x^3+68600\,x^4+102900\,x^5+34300\,x^6-144}{525\,x^3\,{\ln \left (5\right )}^4-3675\,x^3\,{\ln \left (5\right )}^2-25\,x^3\,{\ln \left (5\right )}^6+\ln \left (4\,x\right )\,\left (75\,x^3\,{\ln \left (5\right )}^4-1050\,x^3\,{\ln \left (5\right )}^2+3675\,x^3\right )-{\ln \left (4\,x\right )}^2\,\left (75\,x^3\,{\ln \left (5\right )}^2-525\,x^3\right )+8575\,x^3+25\,x^3\,{\ln \left (4\,x\right )}^3} \,d x \] Input:
int((log(4*x)^3*(200*x^4 + 300*x^5 + 100*x^6) - log(5)^6*(200*x^4 + 300*x^ 5 + 100*x^6) + log(5)^4*(4200*x^4 - 30*x^3 + 6300*x^5 + 2100*x^6) + log(4* x)^2*(4200*x^4 - 30*x^3 - log(5)^2*(600*x^4 + 900*x^5 + 300*x^6) + 6300*x^ 5 + 2100*x^6) - log(5)^2*(60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700 *x^6 - 18) + log(4*x)*(log(5)^4*(600*x^4 + 900*x^5 + 300*x^6) - log(5)^2*( 8400*x^4 - 60*x^3 + 12600*x^5 + 4200*x^6) + 60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700*x^6 - 18) + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 - 144)/(525*x^3*log(5)^4 - 3675*x^3*log(5)^2 - 25*x^3*log(5)^ 6 + log(4*x)*(75*x^3*log(5)^4 - 1050*x^3*log(5)^2 + 3675*x^3) - log(4*x)^2 *(75*x^3*log(5)^2 - 525*x^3) + 8575*x^3 + 25*x^3*log(4*x)^3),x)
Output:
int((log(4*x)^3*(200*x^4 + 300*x^5 + 100*x^6) - log(5)^6*(200*x^4 + 300*x^ 5 + 100*x^6) + log(5)^4*(4200*x^4 - 30*x^3 + 6300*x^5 + 2100*x^6) + log(4* x)^2*(4200*x^4 - 30*x^3 - log(5)^2*(600*x^4 + 900*x^5 + 300*x^6) + 6300*x^ 5 + 2100*x^6) - log(5)^2*(60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700 *x^6 - 18) + log(4*x)*(log(5)^4*(600*x^4 + 900*x^5 + 300*x^6) - log(5)^2*( 8400*x^4 - 60*x^3 + 12600*x^5 + 4200*x^6) + 60*x^2 - 390*x^3 + 29400*x^4 + 44100*x^5 + 14700*x^6 - 18) + 420*x^2 - 1260*x^3 + 68600*x^4 + 102900*x^5 + 34300*x^6 - 144)/(525*x^3*log(5)^4 - 3675*x^3*log(5)^2 - 25*x^3*log(5)^ 6 + log(4*x)*(75*x^3*log(5)^4 - 1050*x^3*log(5)^2 + 3675*x^3) - log(4*x)^2 *(75*x^3*log(5)^2 - 525*x^3) + 8575*x^3 + 25*x^3*log(4*x)^3), x)
Time = 0.16 (sec) , antiderivative size = 436, normalized size of antiderivative = 14.53 \[ \int \frac {-144+420 x^2-1260 x^3+68600 x^4+102900 x^5+34300 x^6+\left (18-60 x^2+390 x^3-29400 x^4-44100 x^5-14700 x^6\right ) \log ^2(5)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6\right ) \log ^4(5)+\left (-200 x^4-300 x^5-100 x^6\right ) \log ^6(5)+\left (-18+60 x^2-390 x^3+29400 x^4+44100 x^5+14700 x^6+\left (60 x^3-8400 x^4-12600 x^5-4200 x^6\right ) \log ^2(5)+\left (600 x^4+900 x^5+300 x^6\right ) \log ^4(5)\right ) \log (4 x)+\left (-30 x^3+4200 x^4+6300 x^5+2100 x^6+\left (-600 x^4-900 x^5-300 x^6\right ) \log ^2(5)\right ) \log ^2(4 x)+\left (200 x^4+300 x^5+100 x^6\right ) \log ^3(4 x)}{8575 x^3-3675 x^3 \log ^2(5)+525 x^3 \log ^4(5)-25 x^3 \log ^6(5)+\left (3675 x^3-1050 x^3 \log ^2(5)+75 x^3 \log ^4(5)\right ) \log (4 x)+\left (525 x^3-75 x^3 \log ^2(5)\right ) \log ^2(4 x)+25 x^3 \log ^3(4 x)} \, dx =\text {Too large to display} \] Input:
int(((100*x^6+300*x^5+200*x^4)*log(4*x)^3+((-300*x^6-900*x^5-600*x^4)*log( 5)^2+2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(4*x)^2+((300*x^6+900*x^5+600*x ^4)*log(5)^4+(-4200*x^6-12600*x^5-8400*x^4+60*x^3)*log(5)^2+14700*x^6+4410 0*x^5+29400*x^4-390*x^3+60*x^2-18)*log(4*x)+(-100*x^6-300*x^5-200*x^4)*log (5)^6+(2100*x^6+6300*x^5+4200*x^4-30*x^3)*log(5)^4+(-14700*x^6-44100*x^5-2 9400*x^4+390*x^3-60*x^2+18)*log(5)^2+34300*x^6+102900*x^5+68600*x^4-1260*x ^3+420*x^2-144)/(25*x^3*log(4*x)^3+(-75*x^3*log(5)^2+525*x^3)*log(4*x)^2+( 75*x^3*log(5)^4-1050*x^3*log(5)^2+3675*x^3)*log(4*x)-25*x^3*log(5)^6+525*x ^3*log(5)^4-3675*x^3*log(5)^2+8575*x^3),x)
Output:
(25*log(4*x)**2*log(5)**2*x**6 + 100*log(4*x)**2*log(5)**2*x**5 + 100*log( 4*x)**2*log(5)**2*x**4 - 175*log(4*x)**2*x**6 - 700*log(4*x)**2*x**5 - 700 *log(4*x)**2*x**4 - 30*log(4*x)**2*x**2 - 50*log(4*x)*log(5)**4*x**6 - 200 *log(4*x)*log(5)**4*x**5 - 200*log(4*x)*log(5)**4*x**4 + 700*log(4*x)*log( 5)**2*x**6 + 2800*log(4*x)*log(5)**2*x**5 + 2800*log(4*x)*log(5)**2*x**4 - 30*log(4*x)*log(5)**2*x**3 - 2450*log(4*x)*x**6 - 9800*log(4*x)*x**5 - 98 00*log(4*x)*x**4 + 210*log(4*x)*x**3 + 25*log(5)**6*x**6 + 100*log(5)**6*x **5 + 100*log(5)**6*x**4 - 525*log(5)**4*x**6 - 2100*log(5)**4*x**5 - 2100 *log(5)**4*x**4 + 30*log(5)**4*x**3 + 30*log(5)**4*x**2 + 3675*log(5)**2*x **6 + 14700*log(5)**2*x**5 + 14700*log(5)**2*x**4 - 420*log(5)**2*x**3 - 4 20*log(5)**2*x**2 + 9*log(5)**2 - 8575*x**6 - 34300*x**5 - 34300*x**4 + 14 70*x**3 + 1470*x**2 - 63)/(25*x**2*(log(4*x)**2*log(5)**2 - 7*log(4*x)**2 - 2*log(4*x)*log(5)**4 + 28*log(4*x)*log(5)**2 - 98*log(4*x) + log(5)**6 - 21*log(5)**4 + 147*log(5)**2 - 343))