Integrand size = 673, antiderivative size = 25 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=\left (x-\frac {4 x}{\log ^2\left (3+x+x^4\right ) (5-\log (\log (x)))^2}\right )^2 \] Output:
(x-4/(5-ln(ln(x)))^2*x/ln(x^4+x+3)^2)^2
Time = 0.15 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.68 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=x^2 \left (1+\frac {16}{\log ^4\left (3+x+x^4\right ) (-5+\log (\log (x)))^4}-\frac {8}{\log ^2\left (3+x+x^4\right ) (-5+\log (\log (x)))^2}\right ) \] Input:
Integrate[((320*x^2 + 1280*x^5)*Log[x] + (-192*x - 64*x^2 - 64*x^5 + (-480 *x - 160*x^2 - 160*x^5)*Log[x])*Log[3 + x + x^4] + (-2000*x^2 - 8000*x^5)* Log[x]*Log[3 + x + x^4]^2 + (1200*x + 400*x^2 + 400*x^5 + (6000*x + 2000*x ^2 + 2000*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-18750*x - 6250*x^2 - 6250*x^ 5)*Log[x]*Log[3 + x + x^4]^5 + ((-64*x^2 - 256*x^5)*Log[x] + (96*x + 32*x^ 2 + 32*x^5)*Log[x]*Log[3 + x + x^4] + (1200*x^2 + 4800*x^5)*Log[x]*Log[3 + x + x^4]^2 + (-480*x - 160*x^2 - 160*x^5 + (-3600*x - 1200*x^2 - 1200*x^5 )*Log[x])*Log[3 + x + x^4]^3 + (18750*x + 6250*x^2 + 6250*x^5)*Log[x]*Log[ 3 + x + x^4]^5)*Log[Log[x]] + ((-240*x^2 - 960*x^5)*Log[x]*Log[3 + x + x^4 ]^2 + (48*x + 16*x^2 + 16*x^5 + (720*x + 240*x^2 + 240*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-7500*x - 2500*x^2 - 2500*x^5)*Log[x]*Log[3 + x + x^4]^5)* Log[Log[x]]^2 + ((16*x^2 + 64*x^5)*Log[x]*Log[3 + x + x^4]^2 + (-48*x - 16 *x^2 - 16*x^5)*Log[x]*Log[3 + x + x^4]^3 + (1500*x + 500*x^2 + 500*x^5)*Lo g[x]*Log[3 + x + x^4]^5)*Log[Log[x]]^3 + (-150*x - 50*x^2 - 50*x^5)*Log[x] *Log[3 + x + x^4]^5*Log[Log[x]]^4 + (6*x + 2*x^2 + 2*x^5)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^5)/((-9375 - 3125*x - 3125*x^4)*Log[x]*Log[3 + x + x ^4]^5 + (9375 + 3125*x + 3125*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]] + (-3750 - 1250*x - 1250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^2 + (75 0 + 250*x + 250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^3 + (-75 - 25*x - 25*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^4 + (3 + x + x^4)*Log[x]* Log[3 + x + x^4]^5*Log[Log[x]]^5),x]
Output:
x^2*(1 + 16/(Log[3 + x + x^4]^4*(-5 + Log[Log[x]])^4) - 8/(Log[3 + x + x^4 ]^2*(-5 + Log[Log[x]])^2))
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 {\left (1280 x^5+320 x^2\right ) \log (x)+\left (2 x^5+2 x^2+6 x\right ) \log (x) \log ^5(\log (x)) \log ^5\left (x^4+x+3\right )+\left (-6250 x^5-6250 x^2-18750 x\right ) \log (x) \log ^5\left (x^4+x+3\right )+\left (400 x^5+400 x^2+\left (2000 x^5+2000 x^2+6000 x\right ) \log (x)+1200 x\right ) \log ^3\left (x^4+x+3\right )+\left (-8000 x^5-2000 x^2\right ) \log (x) \log ^2\left (x^4+x+3\right )+\left (-50 x^5-50 x^2-150 x\right ) \log (x) \log ^4(\log (x)) \log ^5\left (x^4+x+3\right )+\left (\left (500 x^5+500 x^2+1500 x\right ) \log (x) \log ^5\left (x^4+x+3\right )+\left (-16 x^5-16 x^2-48 x\right ) \log (x) \log ^3\left (x^4+x+3\right )+\left (64 x^5+16 x^2\right ) \log (x) \log ^2\left (x^4+x+3\right )\right ) \log ^3(\log (x))+\left (\left (-2500 x^5-2500 x^2-7500 x\right ) \log (x) \log ^5\left (x^4+x+3\right )+\left (16 x^5+16 x^2+\left (240 x^5+240 x^2+720 x\right ) \log (x)+48 x\right ) \log ^3\left (x^4+x+3\right )+\left (-960 x^5-240 x^2\right ) \log (x) \log ^2\left (x^4+x+3\right )\right ) \log ^2(\log (x))+\left (\left (-256 x^5-64 x^2\right ) \log (x)+\left (6250 x^5+6250 x^2+18750 x\right ) \log (x) \log ^5\left (x^4+x+3\right )+\left (-160 x^5-160 x^2+\left (-1200 x^5-1200 x^2-3600 x\right ) \log (x)-480 x\right ) \log ^3\left (x^4+x+3\right )+\left (4800 x^5+1200 x^2\right ) \log (x) \log ^2\left (x^4+x+3\right )+\left (32 x^5+32 x^2+96 x\right ) \log (x) \log \left (x^4+x+3\right )\right ) \log (\log (x))+\left (-64 x^5-64 x^2+\left (-160 x^5-160 x^2-480 x\right ) \log (x)-192 x\right ) \log \left (x^4+x+3\right )}{\left (x^4+x+3\right ) \log (x) \log ^5(\log (x)) \log ^5\left (x^4+x+3\right )+\left (-3125 x^4-3125 x-9375\right ) \log (x) \log ^5\left (x^4+x+3\right )+\left (3125 x^4+3125 x+9375\right ) \log (x) \log (\log (x)) \log ^5\left (x^4+x+3\right )+\left (-25 x^4-25 x-75\right ) \log (x) \log ^4(\log (x)) \log ^5\left (x^4+x+3\right )+\left (250 x^4+250 x+750\right ) \log (x) \log ^3(\log (x)) \log ^5\left (x^4+x+3\right )+\left (-1250 x^4-1250 x-3750\right ) \log (x) \log ^2(\log (x)) \log ^5\left (x^4+x+3\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (\log (x) \left (8 \left (4 x^4+x\right )+\left (x^4+x+3\right ) (\log (\log (x))-5)^2 \log ^3\left (x^4+x+3\right )-4 \left (x^4+x+3\right ) \log \left (x^4+x+3\right )\right ) (\log (\log (x))-5)+8 \left (x^4+x+3\right ) \log \left (x^4+x+3\right )\right ) \left (4-\log ^2\left (x^4+x+3\right ) (\log (\log (x))-5)^2\right )}{\left (x^4+x+3\right ) \log (x) \log ^5\left (x^4+x+3\right ) (5-\log (\log (x)))^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {x \left (8 \left (x^4+x+3\right ) \log \left (x^4+x+3\right )-\log (x) \left (\left (x^4+x+3\right ) (5-\log (\log (x)))^2 \log ^3\left (x^4+x+3\right )-4 \left (x^4+x+3\right ) \log \left (x^4+x+3\right )+8 \left (4 x^4+x\right )\right ) (5-\log (\log (x)))\right ) \left (4-\log ^2\left (x^4+x+3\right ) (5-\log (\log (x)))^2\right )}{\left (x^4+x+3\right ) \log (x) \log ^5\left (x^4+x+3\right ) (5-\log (\log (x)))^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {8 \left (\log \left (x^4+x+3\right ) x^4-4 x^4+\log \left (x^4+x+3\right ) x-x+3 \log \left (x^4+x+3\right )\right ) x}{\left (x^4+x+3\right ) \log ^3\left (x^4+x+3\right ) (\log (\log (x))-5)^2}+\frac {8 x}{\log (x) \log ^2\left (x^4+x+3\right ) (\log (\log (x))-5)^3}+\frac {16 \left (\log \left (x^4+x+3\right ) x^4-8 x^4+\log \left (x^4+x+3\right ) x-2 x+3 \log \left (x^4+x+3\right )\right ) x}{\left (x^4+x+3\right ) \log ^5\left (x^4+x+3\right ) (\log (\log (x))-5)^4}-\frac {32 x}{\log (x) \log ^4\left (x^4+x+3\right ) (\log (\log (x))-5)^5}+x\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \left (-128 \int \frac {x}{\log ^5\left (x^4+x+3\right ) (\log (\log (x))-5)^4}dx+384 \int \frac {x}{\left (x^4+x+3\right ) \log ^5\left (x^4+x+3\right ) (\log (\log (x))-5)^4}dx-32 \int \frac {x}{\log (x) \log ^4\left (x^4+x+3\right ) (\log (\log (x))-5)^5}dx+16 \int \frac {x}{\log ^4\left (x^4+x+3\right ) (\log (\log (x))-5)^4}dx+32 \int \frac {x}{\log ^3\left (x^4+x+3\right ) (\log (\log (x))-5)^2}dx-96 \int \frac {x}{\left (x^4+x+3\right ) \log ^3\left (x^4+x+3\right ) (\log (\log (x))-5)^2}dx+8 \int \frac {x}{\log (x) \log ^2\left (x^4+x+3\right ) (\log (\log (x))-5)^3}dx-8 \int \frac {x}{\log ^2\left (x^4+x+3\right ) (\log (\log (x))-5)^2}dx+96 \int \frac {x^2}{\left (x^4+x+3\right ) \log ^5\left (x^4+x+3\right ) (\log (\log (x))-5)^4}dx-24 \int \frac {x^2}{\left (x^4+x+3\right ) \log ^3\left (x^4+x+3\right ) (\log (\log (x))-5)^2}dx+\frac {x^2}{2}\right )\) |
Input:
Int[((320*x^2 + 1280*x^5)*Log[x] + (-192*x - 64*x^2 - 64*x^5 + (-480*x - 1 60*x^2 - 160*x^5)*Log[x])*Log[3 + x + x^4] + (-2000*x^2 - 8000*x^5)*Log[x] *Log[3 + x + x^4]^2 + (1200*x + 400*x^2 + 400*x^5 + (6000*x + 2000*x^2 + 2 000*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-18750*x - 6250*x^2 - 6250*x^5)*Log [x]*Log[3 + x + x^4]^5 + ((-64*x^2 - 256*x^5)*Log[x] + (96*x + 32*x^2 + 32 *x^5)*Log[x]*Log[3 + x + x^4] + (1200*x^2 + 4800*x^5)*Log[x]*Log[3 + x + x ^4]^2 + (-480*x - 160*x^2 - 160*x^5 + (-3600*x - 1200*x^2 - 1200*x^5)*Log[ x])*Log[3 + x + x^4]^3 + (18750*x + 6250*x^2 + 6250*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log[Log[x]] + ((-240*x^2 - 960*x^5)*Log[x]*Log[3 + x + x^4]^2 + (48*x + 16*x^2 + 16*x^5 + (720*x + 240*x^2 + 240*x^5)*Log[x])*Log[3 + x + x^4]^3 + (-7500*x - 2500*x^2 - 2500*x^5)*Log[x]*Log[3 + x + x^4]^5)*Log[Lo g[x]]^2 + ((16*x^2 + 64*x^5)*Log[x]*Log[3 + x + x^4]^2 + (-48*x - 16*x^2 - 16*x^5)*Log[x]*Log[3 + x + x^4]^3 + (1500*x + 500*x^2 + 500*x^5)*Log[x]*L og[3 + x + x^4]^5)*Log[Log[x]]^3 + (-150*x - 50*x^2 - 50*x^5)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^4 + (6*x + 2*x^2 + 2*x^5)*Log[x]*Log[3 + x + x^4 ]^5*Log[Log[x]]^5)/((-9375 - 3125*x - 3125*x^4)*Log[x]*Log[3 + x + x^4]^5 + (9375 + 3125*x + 3125*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]] + (-375 0 - 1250*x - 1250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^2 + (750 + 25 0*x + 250*x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^3 + (-75 - 25*x - 25* x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^4 + (3 + x + x^4)*Log[x]*Log[3 + x + x^4]^5*Log[Log[x]]^5),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(25)=50\).
Time = 0.33 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72
\[x^{2}-\frac {8 x^{2} \left (\ln \left (\ln \left (x \right )\right )^{2} \ln \left (x^{4}+x +3\right )^{2}-10 \ln \left (x^{4}+x +3\right )^{2} \ln \left (\ln \left (x \right )\right )+25 \ln \left (x^{4}+x +3\right )^{2}-2\right )}{\ln \left (x^{4}+x +3\right )^{4} \left (\ln \left (\ln \left (x \right )\right )-5\right )^{4}}\]
Input:
int(((2*x^5+2*x^2+6*x)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^5+(-50*x^5-50*x^2-150 *x)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^4+((500*x^5+500*x^2+1500*x)*ln(x)*ln(x^4 +x+3)^5+(-16*x^5-16*x^2-48*x)*ln(x)*ln(x^4+x+3)^3+(64*x^5+16*x^2)*ln(x)*ln (x^4+x+3)^2)*ln(ln(x))^3+((-2500*x^5-2500*x^2-7500*x)*ln(x)*ln(x^4+x+3)^5+ ((240*x^5+240*x^2+720*x)*ln(x)+16*x^5+16*x^2+48*x)*ln(x^4+x+3)^3+(-960*x^5 -240*x^2)*ln(x)*ln(x^4+x+3)^2)*ln(ln(x))^2+((6250*x^5+6250*x^2+18750*x)*ln (x)*ln(x^4+x+3)^5+((-1200*x^5-1200*x^2-3600*x)*ln(x)-160*x^5-160*x^2-480*x )*ln(x^4+x+3)^3+(4800*x^5+1200*x^2)*ln(x)*ln(x^4+x+3)^2+(32*x^5+32*x^2+96* x)*ln(x)*ln(x^4+x+3)+(-256*x^5-64*x^2)*ln(x))*ln(ln(x))+(-6250*x^5-6250*x^ 2-18750*x)*ln(x)*ln(x^4+x+3)^5+((2000*x^5+2000*x^2+6000*x)*ln(x)+400*x^5+4 00*x^2+1200*x)*ln(x^4+x+3)^3+(-8000*x^5-2000*x^2)*ln(x)*ln(x^4+x+3)^2+((-1 60*x^5-160*x^2-480*x)*ln(x)-64*x^5-64*x^2-192*x)*ln(x^4+x+3)+(1280*x^5+320 *x^2)*ln(x))/((x^4+x+3)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^5+(-25*x^4-25*x-75)* ln(x)*ln(x^4+x+3)^5*ln(ln(x))^4+(250*x^4+250*x+750)*ln(x)*ln(x^4+x+3)^5*ln (ln(x))^3+(-1250*x^4-1250*x-3750)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))^2+(3125*x^ 4+3125*x+9375)*ln(x)*ln(x^4+x+3)^5*ln(ln(x))+(-3125*x^4-3125*x-9375)*ln(x) *ln(x^4+x+3)^5),x)
Output:
x^2-8*x^2*(ln(ln(x))^2*ln(x^4+x+3)^2-10*ln(x^4+x+3)^2*ln(ln(x))+25*ln(x^4+ x+3)^2-2)/ln(x^4+x+3)^4/(ln(ln(x))-5)^4
Leaf count of result is larger than twice the leaf count of optimal. 217 vs. \(2 (23) = 46\).
Time = 0.09 (sec) , antiderivative size = 217, normalized size of antiderivative = 8.68 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=\frac {x^{2} \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \left (x\right )\right )^{4} - 20 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \left (x\right )\right )^{3} + 625 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} - 200 \, x^{2} \log \left (x^{4} + x + 3\right )^{2} + 2 \, {\left (75 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} - 4 \, x^{2} \log \left (x^{4} + x + 3\right )^{2}\right )} \log \left (\log \left (x\right )\right )^{2} + 16 \, x^{2} - 20 \, {\left (25 \, x^{2} \log \left (x^{4} + x + 3\right )^{4} - 4 \, x^{2} \log \left (x^{4} + x + 3\right )^{2}\right )} \log \left (\log \left (x\right )\right )}{\log \left (x^{4} + x + 3\right )^{4} \log \left (\log \left (x\right )\right )^{4} - 20 \, \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \left (x\right )\right )^{3} + 150 \, \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \left (x\right )\right )^{2} - 500 \, \log \left (x^{4} + x + 3\right )^{4} \log \left (\log \left (x\right )\right ) + 625 \, \log \left (x^{4} + x + 3\right )^{4}} \] Input:
integrate(((2*x^5+2*x^2+6*x)*log(x)*log(x^4+x+3)^5*log(log(x))^5+(-50*x^5- 50*x^2-150*x)*log(x)*log(x^4+x+3)^5*log(log(x))^4+((500*x^5+500*x^2+1500*x )*log(x)*log(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*log(x)*log(x^4+x+3)^3+(64*x^ 5+16*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^3+((-2500*x^5-2500*x^2-7500*x )*log(x)*log(x^4+x+3)^5+((240*x^5+240*x^2+720*x)*log(x)+16*x^5+16*x^2+48*x )*log(x^4+x+3)^3+(-960*x^5-240*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^2+( (6250*x^5+6250*x^2+18750*x)*log(x)*log(x^4+x+3)^5+((-1200*x^5-1200*x^2-360 0*x)*log(x)-160*x^5-160*x^2-480*x)*log(x^4+x+3)^3+(4800*x^5+1200*x^2)*log( x)*log(x^4+x+3)^2+(32*x^5+32*x^2+96*x)*log(x)*log(x^4+x+3)+(-256*x^5-64*x^ 2)*log(x))*log(log(x))+(-6250*x^5-6250*x^2-18750*x)*log(x)*log(x^4+x+3)^5+ ((2000*x^5+2000*x^2+6000*x)*log(x)+400*x^5+400*x^2+1200*x)*log(x^4+x+3)^3+ (-8000*x^5-2000*x^2)*log(x)*log(x^4+x+3)^2+((-160*x^5-160*x^2-480*x)*log(x )-64*x^5-64*x^2-192*x)*log(x^4+x+3)+(1280*x^5+320*x^2)*log(x))/((x^4+x+3)* log(x)*log(x^4+x+3)^5*log(log(x))^5+(-25*x^4-25*x-75)*log(x)*log(x^4+x+3)^ 5*log(log(x))^4+(250*x^4+250*x+750)*log(x)*log(x^4+x+3)^5*log(log(x))^3+(- 1250*x^4-1250*x-3750)*log(x)*log(x^4+x+3)^5*log(log(x))^2+(3125*x^4+3125*x +9375)*log(x)*log(x^4+x+3)^5*log(log(x))+(-3125*x^4-3125*x-9375)*log(x)*lo g(x^4+x+3)^5),x, algorithm="fricas")
Output:
(x^2*log(x^4 + x + 3)^4*log(log(x))^4 - 20*x^2*log(x^4 + x + 3)^4*log(log( x))^3 + 625*x^2*log(x^4 + x + 3)^4 - 200*x^2*log(x^4 + x + 3)^2 + 2*(75*x^ 2*log(x^4 + x + 3)^4 - 4*x^2*log(x^4 + x + 3)^2)*log(log(x))^2 + 16*x^2 - 20*(25*x^2*log(x^4 + x + 3)^4 - 4*x^2*log(x^4 + x + 3)^2)*log(log(x)))/(lo g(x^4 + x + 3)^4*log(log(x))^4 - 20*log(x^4 + x + 3)^4*log(log(x))^3 + 150 *log(x^4 + x + 3)^4*log(log(x))^2 - 500*log(x^4 + x + 3)^4*log(log(x)) + 6 25*log(x^4 + x + 3)^4)
Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (24) = 48\).
Time = 0.56 (sec) , antiderivative size = 148, normalized size of antiderivative = 5.92 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=x^{2} + \frac {- 8 x^{2} \log {\left (x^{4} + x + 3 \right )}^{2} \log {\left (\log {\left (x \right )} \right )}^{2} + 80 x^{2} \log {\left (x^{4} + x + 3 \right )}^{2} \log {\left (\log {\left (x \right )} \right )} - 200 x^{2} \log {\left (x^{4} + x + 3 \right )}^{2} + 16 x^{2}}{\log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\left (x \right )} \right )}^{4} - 20 \log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\left (x \right )} \right )}^{3} + 150 \log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\left (x \right )} \right )}^{2} - 500 \log {\left (x^{4} + x + 3 \right )}^{4} \log {\left (\log {\left (x \right )} \right )} + 625 \log {\left (x^{4} + x + 3 \right )}^{4}} \] Input:
integrate(((2*x**5+2*x**2+6*x)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**5+(-50*x** 5-50*x**2-150*x)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**4+((500*x**5+500*x**2+15 00*x)*ln(x)*ln(x**4+x+3)**5+(-16*x**5-16*x**2-48*x)*ln(x)*ln(x**4+x+3)**3+ (64*x**5+16*x**2)*ln(x)*ln(x**4+x+3)**2)*ln(ln(x))**3+((-2500*x**5-2500*x* *2-7500*x)*ln(x)*ln(x**4+x+3)**5+((240*x**5+240*x**2+720*x)*ln(x)+16*x**5+ 16*x**2+48*x)*ln(x**4+x+3)**3+(-960*x**5-240*x**2)*ln(x)*ln(x**4+x+3)**2)* ln(ln(x))**2+((6250*x**5+6250*x**2+18750*x)*ln(x)*ln(x**4+x+3)**5+((-1200* x**5-1200*x**2-3600*x)*ln(x)-160*x**5-160*x**2-480*x)*ln(x**4+x+3)**3+(480 0*x**5+1200*x**2)*ln(x)*ln(x**4+x+3)**2+(32*x**5+32*x**2+96*x)*ln(x)*ln(x* *4+x+3)+(-256*x**5-64*x**2)*ln(x))*ln(ln(x))+(-6250*x**5-6250*x**2-18750*x )*ln(x)*ln(x**4+x+3)**5+((2000*x**5+2000*x**2+6000*x)*ln(x)+400*x**5+400*x **2+1200*x)*ln(x**4+x+3)**3+(-8000*x**5-2000*x**2)*ln(x)*ln(x**4+x+3)**2+( (-160*x**5-160*x**2-480*x)*ln(x)-64*x**5-64*x**2-192*x)*ln(x**4+x+3)+(1280 *x**5+320*x**2)*ln(x))/((x**4+x+3)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**5+(-25 *x**4-25*x-75)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))**4+(250*x**4+250*x+750)*ln( x)*ln(x**4+x+3)**5*ln(ln(x))**3+(-1250*x**4-1250*x-3750)*ln(x)*ln(x**4+x+3 )**5*ln(ln(x))**2+(3125*x**4+3125*x+9375)*ln(x)*ln(x**4+x+3)**5*ln(ln(x))+ (-3125*x**4-3125*x-9375)*ln(x)*ln(x**4+x+3)**5),x)
Output:
x**2 + (-8*x**2*log(x**4 + x + 3)**2*log(log(x))**2 + 80*x**2*log(x**4 + x + 3)**2*log(log(x)) - 200*x**2*log(x**4 + x + 3)**2 + 16*x**2)/(log(x**4 + x + 3)**4*log(log(x))**4 - 20*log(x**4 + x + 3)**4*log(log(x))**3 + 150* log(x**4 + x + 3)**4*log(log(x))**2 - 500*log(x**4 + x + 3)**4*log(log(x)) + 625*log(x**4 + x + 3)**4)
Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (23) = 46\).
Time = 0.76 (sec) , antiderivative size = 131, normalized size of antiderivative = 5.24 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=\frac {{\left (x^{2} \log \left (\log \left (x\right )\right )^{4} - 20 \, x^{2} \log \left (\log \left (x\right )\right )^{3} + 150 \, x^{2} \log \left (\log \left (x\right )\right )^{2} - 500 \, x^{2} \log \left (\log \left (x\right )\right ) + 625 \, x^{2}\right )} \log \left (x^{4} + x + 3\right )^{4} - 8 \, {\left (x^{2} \log \left (\log \left (x\right )\right )^{2} - 10 \, x^{2} \log \left (\log \left (x\right )\right ) + 25 \, x^{2}\right )} \log \left (x^{4} + x + 3\right )^{2} + 16 \, x^{2}}{{\left (\log \left (\log \left (x\right )\right )^{4} - 20 \, \log \left (\log \left (x\right )\right )^{3} + 150 \, \log \left (\log \left (x\right )\right )^{2} - 500 \, \log \left (\log \left (x\right )\right ) + 625\right )} \log \left (x^{4} + x + 3\right )^{4}} \] Input:
integrate(((2*x^5+2*x^2+6*x)*log(x)*log(x^4+x+3)^5*log(log(x))^5+(-50*x^5- 50*x^2-150*x)*log(x)*log(x^4+x+3)^5*log(log(x))^4+((500*x^5+500*x^2+1500*x )*log(x)*log(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*log(x)*log(x^4+x+3)^3+(64*x^ 5+16*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^3+((-2500*x^5-2500*x^2-7500*x )*log(x)*log(x^4+x+3)^5+((240*x^5+240*x^2+720*x)*log(x)+16*x^5+16*x^2+48*x )*log(x^4+x+3)^3+(-960*x^5-240*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^2+( (6250*x^5+6250*x^2+18750*x)*log(x)*log(x^4+x+3)^5+((-1200*x^5-1200*x^2-360 0*x)*log(x)-160*x^5-160*x^2-480*x)*log(x^4+x+3)^3+(4800*x^5+1200*x^2)*log( x)*log(x^4+x+3)^2+(32*x^5+32*x^2+96*x)*log(x)*log(x^4+x+3)+(-256*x^5-64*x^ 2)*log(x))*log(log(x))+(-6250*x^5-6250*x^2-18750*x)*log(x)*log(x^4+x+3)^5+ ((2000*x^5+2000*x^2+6000*x)*log(x)+400*x^5+400*x^2+1200*x)*log(x^4+x+3)^3+ (-8000*x^5-2000*x^2)*log(x)*log(x^4+x+3)^2+((-160*x^5-160*x^2-480*x)*log(x )-64*x^5-64*x^2-192*x)*log(x^4+x+3)+(1280*x^5+320*x^2)*log(x))/((x^4+x+3)* log(x)*log(x^4+x+3)^5*log(log(x))^5+(-25*x^4-25*x-75)*log(x)*log(x^4+x+3)^ 5*log(log(x))^4+(250*x^4+250*x+750)*log(x)*log(x^4+x+3)^5*log(log(x))^3+(- 1250*x^4-1250*x-3750)*log(x)*log(x^4+x+3)^5*log(log(x))^2+(3125*x^4+3125*x +9375)*log(x)*log(x^4+x+3)^5*log(log(x))+(-3125*x^4-3125*x-9375)*log(x)*lo g(x^4+x+3)^5),x, algorithm="maxima")
Output:
((x^2*log(log(x))^4 - 20*x^2*log(log(x))^3 + 150*x^2*log(log(x))^2 - 500*x ^2*log(log(x)) + 625*x^2)*log(x^4 + x + 3)^4 - 8*(x^2*log(log(x))^2 - 10*x ^2*log(log(x)) + 25*x^2)*log(x^4 + x + 3)^2 + 16*x^2)/((log(log(x))^4 - 20 *log(log(x))^3 + 150*log(log(x))^2 - 500*log(log(x)) + 625)*log(x^4 + x + 3)^4)
Leaf count of result is larger than twice the leaf count of optimal. 1110 vs. \(2 (23) = 46\).
Time = 66.62 (sec) , antiderivative size = 1110, normalized size of antiderivative = 44.40 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=\text {Too large to display} \] Input:
integrate(((2*x^5+2*x^2+6*x)*log(x)*log(x^4+x+3)^5*log(log(x))^5+(-50*x^5- 50*x^2-150*x)*log(x)*log(x^4+x+3)^5*log(log(x))^4+((500*x^5+500*x^2+1500*x )*log(x)*log(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*log(x)*log(x^4+x+3)^3+(64*x^ 5+16*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^3+((-2500*x^5-2500*x^2-7500*x )*log(x)*log(x^4+x+3)^5+((240*x^5+240*x^2+720*x)*log(x)+16*x^5+16*x^2+48*x )*log(x^4+x+3)^3+(-960*x^5-240*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^2+( (6250*x^5+6250*x^2+18750*x)*log(x)*log(x^4+x+3)^5+((-1200*x^5-1200*x^2-360 0*x)*log(x)-160*x^5-160*x^2-480*x)*log(x^4+x+3)^3+(4800*x^5+1200*x^2)*log( x)*log(x^4+x+3)^2+(32*x^5+32*x^2+96*x)*log(x)*log(x^4+x+3)+(-256*x^5-64*x^ 2)*log(x))*log(log(x))+(-6250*x^5-6250*x^2-18750*x)*log(x)*log(x^4+x+3)^5+ ((2000*x^5+2000*x^2+6000*x)*log(x)+400*x^5+400*x^2+1200*x)*log(x^4+x+3)^3+ (-8000*x^5-2000*x^2)*log(x)*log(x^4+x+3)^2+((-160*x^5-160*x^2-480*x)*log(x )-64*x^5-64*x^2-192*x)*log(x^4+x+3)+(1280*x^5+320*x^2)*log(x))/((x^4+x+3)* log(x)*log(x^4+x+3)^5*log(log(x))^5+(-25*x^4-25*x-75)*log(x)*log(x^4+x+3)^ 5*log(log(x))^4+(250*x^4+250*x+750)*log(x)*log(x^4+x+3)^5*log(log(x))^3+(- 1250*x^4-1250*x-3750)*log(x)*log(x^4+x+3)^5*log(log(x))^2+(3125*x^4+3125*x +9375)*log(x)*log(x^4+x+3)^5*log(log(x))+(-3125*x^4-3125*x-9375)*log(x)*lo g(x^4+x+3)^5),x, algorithm="giac")
Output:
x^2 - 8*(16*x^12*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 160*x^12*log(x^ 4 + x + 3)^2*log(x)*log(log(x)) + 400*x^12*log(x^4 + x + 3)^2*log(x) + 24* x^9*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 32*x^12*log(x) - 240*x^9*log (x^4 + x + 3)^2*log(x)*log(log(x)) + 48*x^8*log(x^4 + x + 3)^2*log(x)*log( log(x))^2 + 600*x^9*log(x^4 + x + 3)^2*log(x) - 480*x^8*log(x^4 + x + 3)^2 *log(x)*log(log(x)) + 1200*x^8*log(x^4 + x + 3)^2*log(x) + 9*x^6*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 48*x^9*log(x) - 90*x^6*log(x^4 + x + 3)^2 *log(x)*log(log(x)) + 24*x^5*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 96* x^8*log(x) + 225*x^6*log(x^4 + x + 3)^2*log(x) - 240*x^5*log(x^4 + x + 3)^ 2*log(x)*log(log(x)) + 600*x^5*log(x^4 + x + 3)^2*log(x) + x^3*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 18*x^6*log(x) - 10*x^3*log(x^4 + x + 3)^2*l og(x)*log(log(x)) + 3*x^2*log(x^4 + x + 3)^2*log(x)*log(log(x))^2 - 48*x^5 *log(x) + 25*x^3*log(x^4 + x + 3)^2*log(x) - 30*x^2*log(x^4 + x + 3)^2*log (x)*log(log(x)) + 75*x^2*log(x^4 + x + 3)^2*log(x) - 2*x^3*log(x) - 6*x^2* log(x))/(16*x^10*log(x^4 + x + 3)^4*log(x)*log(log(x))^4 - 320*x^10*log(x^ 4 + x + 3)^4*log(x)*log(log(x))^3 + 2400*x^10*log(x^4 + x + 3)^4*log(x)*lo g(log(x))^2 - 8000*x^10*log(x^4 + x + 3)^4*log(x)*log(log(x)) + 24*x^7*log (x^4 + x + 3)^4*log(x)*log(log(x))^4 + 10000*x^10*log(x^4 + x + 3)^4*log(x ) - 480*x^7*log(x^4 + x + 3)^4*log(x)*log(log(x))^3 + 48*x^6*log(x^4 + x + 3)^4*log(x)*log(log(x))^4 + 3600*x^7*log(x^4 + x + 3)^4*log(x)*log(log...
Time = 130.72 (sec) , antiderivative size = 324597, normalized size of antiderivative = 12983.88 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=\text {Too large to display} \] Input:
int((log(x + x^4 + 3)*(192*x + 64*x^2 + 64*x^5 + log(x)*(480*x + 160*x^2 + 160*x^5)) - log(x)*(320*x^2 + 1280*x^5) - log(x + x^4 + 3)^3*(1200*x + 40 0*x^2 + 400*x^5 + log(x)*(6000*x + 2000*x^2 + 2000*x^5)) - log(log(x))*(lo g(x + x^4 + 3)*log(x)*(96*x + 32*x^2 + 32*x^5) - log(x + x^4 + 3)^3*(480*x + 160*x^2 + 160*x^5 + log(x)*(3600*x + 1200*x^2 + 1200*x^5)) - log(x)*(64 *x^2 + 256*x^5) + log(x + x^4 + 3)^5*log(x)*(18750*x + 6250*x^2 + 6250*x^5 ) + log(x + x^4 + 3)^2*log(x)*(1200*x^2 + 4800*x^5)) - log(log(x))^3*(log( x + x^4 + 3)^5*log(x)*(1500*x + 500*x^2 + 500*x^5) - log(x + x^4 + 3)^3*lo g(x)*(48*x + 16*x^2 + 16*x^5) + log(x + x^4 + 3)^2*log(x)*(16*x^2 + 64*x^5 )) + log(log(x))^2*(log(x + x^4 + 3)^5*log(x)*(7500*x + 2500*x^2 + 2500*x^ 5) - log(x + x^4 + 3)^3*(48*x + 16*x^2 + 16*x^5 + log(x)*(720*x + 240*x^2 + 240*x^5)) + log(x + x^4 + 3)^2*log(x)*(240*x^2 + 960*x^5)) + log(x + x^4 + 3)^5*log(x)*(18750*x + 6250*x^2 + 6250*x^5) + log(x + x^4 + 3)^2*log(x) *(2000*x^2 + 8000*x^5) - log(x + x^4 + 3)^5*log(log(x))^5*log(x)*(6*x + 2* x^2 + 2*x^5) + log(x + x^4 + 3)^5*log(log(x))^4*log(x)*(150*x + 50*x^2 + 5 0*x^5))/(log(x + x^4 + 3)^5*log(x)*(3125*x + 3125*x^4 + 9375) - log(x + x^ 4 + 3)^5*log(log(x))^5*log(x)*(x + x^4 + 3) - log(x + x^4 + 3)^5*log(log(x ))*log(x)*(3125*x + 3125*x^4 + 9375) + log(x + x^4 + 3)^5*log(log(x))^4*lo g(x)*(25*x + 25*x^4 + 75) - log(x + x^4 + 3)^5*log(log(x))^3*log(x)*(250*x + 250*x^4 + 750) + log(x + x^4 + 3)^5*log(log(x))^2*log(x)*(1250*x + 1250 *x^4 + 3750)),x)
Output:
((log(log(x))^5*(1836*x - 4374*log(x) + 7020*x*log(x)^2 - 972*x^2*log(x) + 38025*x*log(x)^3 - 52488*x^3*log(x) - 78732*x^4*log(x) - 20898*x^5*log(x) - 524880*x^7*log(x) - 189054*x^8*log(x) + 2799360*x^9*log(x) - 1399680*x^ 10*log(x) - 946728*x^11*log(x) + 16796160*x^12*log(x) - 2954880*x^14*log(x ) + 40310784*x^15*log(x) + 6718464*x^16*log(x) - 6283008*x^17*log(x) + 358 31808*x^18*log(x) + 8957952*x^19*log(x) - 9580032*x^20*log(x) - 9455616*x^ 23*log(x) - 3981312*x^26*log(x) + 3240*log(x)^2 + 2160*x^2*log(x)^2 + 5794 4*x^2*log(x)^3 - 136080*x^3*log(x)^2 - 1648620*x^3*log(x)^3 + 28080*x^4*lo g(x)^2 - 2759400*x^4*log(x)^3 + 31860*x^5*log(x)^2 - 3553817*x^5*log(x)^3 - 2799360*x^6*log(x)^2 - 23796720*x^6*log(x)^3 - 790560*x^7*log(x)^2 + 120 94920*x^7*log(x)^3 + 167400*x^8*log(x)^2 + 25935992*x^8*log(x)^3 - 1886976 0*x^9*log(x)^2 - 67571280*x^9*log(x)^3 - 8225280*x^10*log(x)^2 - 117330480 *x^10*log(x)^3 + 373680*x^11*log(x)^2 - 19495004*x^11*log(x)^3 - 57231360* x^12*log(x)^2 + 90288000*x^12*log(x)^3 - 32071680*x^13*log(x)^2 - 17289504 0*x^13*log(x)^3 + 656640*x^14*log(x)^2 - 32945680*x^14*log(x)^3 - 74649600 *x^15*log(x)^2 + 953976960*x^15*log(x)^3 - 58060800*x^16*log(x)^2 + 338688 0*x^17*log(x)^2 + 5272216*x^17*log(x)^3 - 26542080*x^18*log(x)^2 + 1392353 280*x^18*log(x)^3 - 47554560*x^19*log(x)^2 + 290154240*x^19*log(x)^3 + 113 35680*x^20*log(x)^2 + 80633792*x^20*log(x)^3 - 17694720*x^22*log(x)^2 + 16 035840*x^23*log(x)^2 + 93535168*x^23*log(x)^3 + 8847360*x^26*log(x)^2 +...
Time = 0.29 (sec) , antiderivative size = 156, normalized size of antiderivative = 6.24 \[ \int \frac {\left (320 x^2+1280 x^5\right ) \log (x)+\left (-192 x-64 x^2-64 x^5+\left (-480 x-160 x^2-160 x^5\right ) \log (x)\right ) \log \left (3+x+x^4\right )+\left (-2000 x^2-8000 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (1200 x+400 x^2+400 x^5+\left (6000 x+2000 x^2+2000 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-18750 x-6250 x^2-6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (\left (-64 x^2-256 x^5\right ) \log (x)+\left (96 x+32 x^2+32 x^5\right ) \log (x) \log \left (3+x+x^4\right )+\left (1200 x^2+4800 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-480 x-160 x^2-160 x^5+\left (-3600 x-1200 x^2-1200 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (18750 x+6250 x^2+6250 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log (\log (x))+\left (\left (-240 x^2-960 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (48 x+16 x^2+16 x^5+\left (720 x+240 x^2+240 x^5\right ) \log (x)\right ) \log ^3\left (3+x+x^4\right )+\left (-7500 x-2500 x^2-2500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^2(\log (x))+\left (\left (16 x^2+64 x^5\right ) \log (x) \log ^2\left (3+x+x^4\right )+\left (-48 x-16 x^2-16 x^5\right ) \log (x) \log ^3\left (3+x+x^4\right )+\left (1500 x+500 x^2+500 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right )\right ) \log ^3(\log (x))+\left (-150 x-50 x^2-50 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (6 x+2 x^2+2 x^5\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))}{\left (-9375-3125 x-3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right )+\left (9375+3125 x+3125 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log (\log (x))+\left (-3750-1250 x-1250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^2(\log (x))+\left (750+250 x+250 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^3(\log (x))+\left (-75-25 x-25 x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^4(\log (x))+\left (3+x+x^4\right ) \log (x) \log ^5\left (3+x+x^4\right ) \log ^5(\log (x))} \, dx=\frac {x^{2} \left (\mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{4} \mathrm {log}\left (x^{4}+x +3\right )^{4}-20 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{3} \mathrm {log}\left (x^{4}+x +3\right )^{4}+150 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2} \mathrm {log}\left (x^{4}+x +3\right )^{4}-8 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2} \mathrm {log}\left (x^{4}+x +3\right )^{2}-500 \,\mathrm {log}\left (\mathrm {log}\left (x \right )\right ) \mathrm {log}\left (x^{4}+x +3\right )^{4}+80 \,\mathrm {log}\left (\mathrm {log}\left (x \right )\right ) \mathrm {log}\left (x^{4}+x +3\right )^{2}+625 \mathrm {log}\left (x^{4}+x +3\right )^{4}-200 \mathrm {log}\left (x^{4}+x +3\right )^{2}+16\right )}{\mathrm {log}\left (x^{4}+x +3\right )^{4} \left (\mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{4}-20 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{3}+150 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2}-500 \,\mathrm {log}\left (\mathrm {log}\left (x \right )\right )+625\right )} \] Input:
int(((2*x^5+2*x^2+6*x)*log(x)*log(x^4+x+3)^5*log(log(x))^5+(-50*x^5-50*x^2 -150*x)*log(x)*log(x^4+x+3)^5*log(log(x))^4+((500*x^5+500*x^2+1500*x)*log( x)*log(x^4+x+3)^5+(-16*x^5-16*x^2-48*x)*log(x)*log(x^4+x+3)^3+(64*x^5+16*x ^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^3+((-2500*x^5-2500*x^2-7500*x)*log( x)*log(x^4+x+3)^5+((240*x^5+240*x^2+720*x)*log(x)+16*x^5+16*x^2+48*x)*log( x^4+x+3)^3+(-960*x^5-240*x^2)*log(x)*log(x^4+x+3)^2)*log(log(x))^2+((6250* x^5+6250*x^2+18750*x)*log(x)*log(x^4+x+3)^5+((-1200*x^5-1200*x^2-3600*x)*l og(x)-160*x^5-160*x^2-480*x)*log(x^4+x+3)^3+(4800*x^5+1200*x^2)*log(x)*log (x^4+x+3)^2+(32*x^5+32*x^2+96*x)*log(x)*log(x^4+x+3)+(-256*x^5-64*x^2)*log (x))*log(log(x))+(-6250*x^5-6250*x^2-18750*x)*log(x)*log(x^4+x+3)^5+((2000 *x^5+2000*x^2+6000*x)*log(x)+400*x^5+400*x^2+1200*x)*log(x^4+x+3)^3+(-8000 *x^5-2000*x^2)*log(x)*log(x^4+x+3)^2+((-160*x^5-160*x^2-480*x)*log(x)-64*x ^5-64*x^2-192*x)*log(x^4+x+3)+(1280*x^5+320*x^2)*log(x))/((x^4+x+3)*log(x) *log(x^4+x+3)^5*log(log(x))^5+(-25*x^4-25*x-75)*log(x)*log(x^4+x+3)^5*log( log(x))^4+(250*x^4+250*x+750)*log(x)*log(x^4+x+3)^5*log(log(x))^3+(-1250*x ^4-1250*x-3750)*log(x)*log(x^4+x+3)^5*log(log(x))^2+(3125*x^4+3125*x+9375) *log(x)*log(x^4+x+3)^5*log(log(x))+(-3125*x^4-3125*x-9375)*log(x)*log(x^4+ x+3)^5),x)
Output:
(x**2*(log(log(x))**4*log(x**4 + x + 3)**4 - 20*log(log(x))**3*log(x**4 + x + 3)**4 + 150*log(log(x))**2*log(x**4 + x + 3)**4 - 8*log(log(x))**2*log (x**4 + x + 3)**2 - 500*log(log(x))*log(x**4 + x + 3)**4 + 80*log(log(x))* log(x**4 + x + 3)**2 + 625*log(x**4 + x + 3)**4 - 200*log(x**4 + x + 3)**2 + 16))/(log(x**4 + x + 3)**4*(log(log(x))**4 - 20*log(log(x))**3 + 150*lo g(log(x))**2 - 500*log(log(x)) + 625))