Integrand size = 254, antiderivative size = 16 \[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=\log \left (3-\log (x)+\frac {1}{\left (2+x^2+\log (x)\right )^4}\right ) \] Output:
ln(3+1/(2+x^2+ln(x))^4-ln(x))
Leaf count is larger than twice the leaf count of optimal. \(138\) vs. \(2(16)=32\).
Time = 0.15 (sec) , antiderivative size = 138, normalized size of antiderivative = 8.62 \[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=-4 \log \left (2+x^2+\log (x)\right )+\log \left (49+96 x^2+72 x^4+24 x^6+3 x^8+80 \log (x)+112 x^2 \log (x)+48 x^4 \log (x)+4 x^6 \log (x)-x^8 \log (x)+40 \log ^2(x)+24 x^2 \log ^2(x)-6 x^4 \log ^2(x)-4 x^6 \log ^2(x)-12 x^2 \log ^3(x)-6 x^4 \log ^3(x)-5 \log ^4(x)-4 x^2 \log ^4(x)-\log ^5(x)\right ) \] Input:
Integrate[(36 + 88*x^2 + 80*x^4 + 40*x^6 + 10*x^8 + x^10 + (80 + 160*x^2 + 120*x^4 + 40*x^6 + 5*x^8)*Log[x] + (80 + 120*x^2 + 60*x^4 + 10*x^6)*Log[x ]^2 + (40 + 40*x^2 + 10*x^4)*Log[x]^3 + (10 + 5*x^2)*Log[x]^4 + Log[x]^5)/ (-98*x - 241*x^3 - 240*x^5 - 120*x^7 - 30*x^9 - 3*x^11 + (-209*x - 400*x^3 - 280*x^5 - 80*x^7 - 5*x^9 + x^11)*Log[x] + (-160*x - 200*x^3 - 60*x^5 + 10*x^7 + 5*x^9)*Log[x]^2 + (-40*x + 30*x^5 + 10*x^7)*Log[x]^3 + (10*x + 25 *x^3 + 10*x^5)*Log[x]^4 + (7*x + 5*x^3)*Log[x]^5 + x*Log[x]^6),x]
Output:
-4*Log[2 + x^2 + Log[x]] + Log[49 + 96*x^2 + 72*x^4 + 24*x^6 + 3*x^8 + 80* Log[x] + 112*x^2*Log[x] + 48*x^4*Log[x] + 4*x^6*Log[x] - x^8*Log[x] + 40*L og[x]^2 + 24*x^2*Log[x]^2 - 6*x^4*Log[x]^2 - 4*x^6*Log[x]^2 - 12*x^2*Log[x ]^3 - 6*x^4*Log[x]^3 - 5*Log[x]^4 - 4*x^2*Log[x]^4 - Log[x]^5]
Leaf count is larger than twice the leaf count of optimal. \(138\) vs. \(2(16)=32\).
Time = 4.11 (sec) , antiderivative size = 138, normalized size of antiderivative = 8.62, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {7293, 2009}
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.
| \(\displaystyle \int \frac {x^{10}+10 x^8+40 x^6+80 x^4+88 x^2+\left (5 x^2+10\right ) \log ^4(x)+\left (10 x^4+40 x^2+40\right ) \log ^3(x)+\left (10 x^6+60 x^4+120 x^2+80\right ) \log ^2(x)+\left (5 x^8+40 x^6+120 x^4+160 x^2+80\right ) \log (x)+\log ^5(x)+36}{-3 x^{11}-30 x^9-120 x^7-240 x^5-241 x^3+\left (5 x^3+7 x\right ) \log ^5(x)+\left (10 x^7+30 x^5-40 x\right ) \log ^3(x)+\left (10 x^5+25 x^3+10 x\right ) \log ^4(x)+\left (5 x^9+10 x^7-60 x^5-200 x^3-160 x\right ) \log ^2(x)+\left (x^{11}-5 x^9-80 x^7-280 x^5-400 x^3-209 x\right ) \log (x)-98 x+x \log ^6(x)} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (x^2+\log (x)+2\right )^3 \left (-23 x^2+8 x^2 \log (x)+5 \log (x)-10\right )}{x \left (-3 x^8+x^8 \log (x)-24 x^6+4 x^6 \log ^2(x)-4 x^6 \log (x)-72 x^4+6 x^4 \log ^3(x)+6 x^4 \log ^2(x)-48 x^4 \log (x)-96 x^2+4 x^2 \log ^4(x)+12 x^2 \log ^3(x)-24 x^2 \log ^2(x)-112 x^2 \log (x)+\log ^5(x)+5 \log ^4(x)-40 \log ^2(x)-80 \log (x)-49\right )}-\frac {4 \left (2 x^2+1\right )}{x \left (x^2+\log (x)+2\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \log \left (3 x^8+x^8 (-\log (x))+24 x^6-4 x^6 \log ^2(x)+4 x^6 \log (x)+72 x^4-6 x^4 \log ^3(x)-6 x^4 \log ^2(x)+48 x^4 \log (x)+96 x^2-4 x^2 \log ^4(x)-12 x^2 \log ^3(x)+24 x^2 \log ^2(x)+112 x^2 \log (x)-\log ^5(x)-5 \log ^4(x)+40 \log ^2(x)+80 \log (x)+49\right )-4 \log \left (x^2+\log (x)+2\right )\) |
Input:
Int[(36 + 88*x^2 + 80*x^4 + 40*x^6 + 10*x^8 + x^10 + (80 + 160*x^2 + 120*x ^4 + 40*x^6 + 5*x^8)*Log[x] + (80 + 120*x^2 + 60*x^4 + 10*x^6)*Log[x]^2 + (40 + 40*x^2 + 10*x^4)*Log[x]^3 + (10 + 5*x^2)*Log[x]^4 + Log[x]^5)/(-98*x - 241*x^3 - 240*x^5 - 120*x^7 - 30*x^9 - 3*x^11 + (-209*x - 400*x^3 - 280 *x^5 - 80*x^7 - 5*x^9 + x^11)*Log[x] + (-160*x - 200*x^3 - 60*x^5 + 10*x^7 + 5*x^9)*Log[x]^2 + (-40*x + 30*x^5 + 10*x^7)*Log[x]^3 + (10*x + 25*x^3 + 10*x^5)*Log[x]^4 + (7*x + 5*x^3)*Log[x]^5 + x*Log[x]^6),x]
Output:
-4*Log[2 + x^2 + Log[x]] + Log[49 + 96*x^2 + 72*x^4 + 24*x^6 + 3*x^8 + 80* Log[x] + 112*x^2*Log[x] + 48*x^4*Log[x] + 4*x^6*Log[x] - x^8*Log[x] + 40*L og[x]^2 + 24*x^2*Log[x]^2 - 6*x^4*Log[x]^2 - 4*x^6*Log[x]^2 - 12*x^2*Log[x ]^3 - 6*x^4*Log[x]^3 - 5*Log[x]^4 - 4*x^2*Log[x]^4 - Log[x]^5]
Leaf count of result is larger than twice the leaf count of optimal. \(98\) vs. \(2(16)=32\).
Time = 11.20 (sec) , antiderivative size = 99, normalized size of antiderivative = 6.19
| method | result | size |
| default | \(\ln \left (\ln \left (x \right )-3\right )-4 \ln \left (2+x^{2}+\ln \left (x \right )\right )+\ln \left (x^{8}+\left (4 \ln \left (x \right )+8\right ) x^{6}+\left (6 \ln \left (x \right )^{2}+24 \ln \left (x \right )+24\right ) x^{4}+\left (4 \ln \left (x \right )^{3}+24 \ln \left (x \right )^{2}+48 \ln \left (x \right )+32\right ) x^{2}+\frac {\ln \left (x \right )^{5}+5 \ln \left (x \right )^{4}-40 \ln \left (x \right )^{2}-80 \ln \left (x \right )-49}{\ln \left (x \right )-3}\right )\) | \(99\) |
| risch | \(-4 \ln \left (2+x^{2}+\ln \left (x \right )\right )+\ln \left (\ln \left (x \right )^{5}+\left (4 x^{2}+5\right ) \ln \left (x \right )^{4}+\left (6 x^{4}+12 x^{2}\right ) \ln \left (x \right )^{3}+\left (4 x^{6}+6 x^{4}-24 x^{2}-40\right ) \ln \left (x \right )^{2}+\left (x^{8}-4 x^{6}-48 x^{4}-112 x^{2}-80\right ) \ln \left (x \right )-3 x^{8}-24 x^{6}-72 x^{4}-96 x^{2}-49\right )\) | \(112\) |
| parallelrisch | \(-4 \ln \left (2+x^{2}+\ln \left (x \right )\right )+\ln \left (x^{8} \ln \left (x \right )-3 x^{8}+4 x^{6} \ln \left (x \right )^{2}-4 x^{6} \ln \left (x \right )+6 x^{4} \ln \left (x \right )^{3}-24 x^{6}+6 x^{4} \ln \left (x \right )^{2}+4 x^{2} \ln \left (x \right )^{4}-48 x^{4} \ln \left (x \right )+12 x^{2} \ln \left (x \right )^{3}+\ln \left (x \right )^{5}-72 x^{4}-24 x^{2} \ln \left (x \right )^{2}+5 \ln \left (x \right )^{4}-112 x^{2} \ln \left (x \right )-96 x^{2}-40 \ln \left (x \right )^{2}-80 \ln \left (x \right )-49\right )\) | \(136\) |
Input:
int((ln(x)^5+(5*x^2+10)*ln(x)^4+(10*x^4+40*x^2+40)*ln(x)^3+(10*x^6+60*x^4+ 120*x^2+80)*ln(x)^2+(5*x^8+40*x^6+120*x^4+160*x^2+80)*ln(x)+x^10+10*x^8+40 *x^6+80*x^4+88*x^2+36)/(x*ln(x)^6+(5*x^3+7*x)*ln(x)^5+(10*x^5+25*x^3+10*x) *ln(x)^4+(10*x^7+30*x^5-40*x)*ln(x)^3+(5*x^9+10*x^7-60*x^5-200*x^3-160*x)* ln(x)^2+(x^11-5*x^9-80*x^7-280*x^5-400*x^3-209*x)*ln(x)-3*x^11-30*x^9-120* x^7-240*x^5-241*x^3-98*x),x,method=_RETURNVERBOSE)
Output:
ln(ln(x)-3)-4*ln(2+x^2+ln(x))+ln(x^8+(4*ln(x)+8)*x^6+(6*ln(x)^2+24*ln(x)+2 4)*x^4+(4*ln(x)^3+24*ln(x)^2+48*ln(x)+32)*x^2+(ln(x)^5+5*ln(x)^4-40*ln(x)^ 2-80*ln(x)-49)/(ln(x)-3))
Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (16) = 32\).
Time = 0.13 (sec) , antiderivative size = 111, normalized size of antiderivative = 6.94 \[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=\log \left (-3 \, x^{8} - 24 \, x^{6} + {\left (4 \, x^{2} + 5\right )} \log \left (x\right )^{4} + \log \left (x\right )^{5} - 72 \, x^{4} + 6 \, {\left (x^{4} + 2 \, x^{2}\right )} \log \left (x\right )^{3} + 2 \, {\left (2 \, x^{6} + 3 \, x^{4} - 12 \, x^{2} - 20\right )} \log \left (x\right )^{2} - 96 \, x^{2} + {\left (x^{8} - 4 \, x^{6} - 48 \, x^{4} - 112 \, x^{2} - 80\right )} \log \left (x\right ) - 49\right ) - 4 \, \log \left (x^{2} + \log \left (x\right ) + 2\right ) \] Input:
integrate((log(x)^5+(5*x^2+10)*log(x)^4+(10*x^4+40*x^2+40)*log(x)^3+(10*x^ 6+60*x^4+120*x^2+80)*log(x)^2+(5*x^8+40*x^6+120*x^4+160*x^2+80)*log(x)+x^1 0+10*x^8+40*x^6+80*x^4+88*x^2+36)/(x*log(x)^6+(5*x^3+7*x)*log(x)^5+(10*x^5 +25*x^3+10*x)*log(x)^4+(10*x^7+30*x^5-40*x)*log(x)^3+(5*x^9+10*x^7-60*x^5- 200*x^3-160*x)*log(x)^2+(x^11-5*x^9-80*x^7-280*x^5-400*x^3-209*x)*log(x)-3 *x^11-30*x^9-120*x^7-240*x^5-241*x^3-98*x),x, algorithm="fricas")
Output:
log(-3*x^8 - 24*x^6 + (4*x^2 + 5)*log(x)^4 + log(x)^5 - 72*x^4 + 6*(x^4 + 2*x^2)*log(x)^3 + 2*(2*x^6 + 3*x^4 - 12*x^2 - 20)*log(x)^2 - 96*x^2 + (x^8 - 4*x^6 - 48*x^4 - 112*x^2 - 80)*log(x) - 49) - 4*log(x^2 + log(x) + 2)
Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (17) = 34\).
Time = 0.84 (sec) , antiderivative size = 112, normalized size of antiderivative = 7.00 \[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=- 4 \log {\left (x^{2} + \log {\left (x \right )} + 2 \right )} + \log {\left (- 3 x^{8} - 24 x^{6} - 72 x^{4} - 96 x^{2} + \left (4 x^{2} + 5\right ) \log {\left (x \right )}^{4} + \left (6 x^{4} + 12 x^{2}\right ) \log {\left (x \right )}^{3} + \left (4 x^{6} + 6 x^{4} - 24 x^{2} - 40\right ) \log {\left (x \right )}^{2} + \left (x^{8} - 4 x^{6} - 48 x^{4} - 112 x^{2} - 80\right ) \log {\left (x \right )} + \log {\left (x \right )}^{5} - 49 \right )} \] Input:
integrate((ln(x)**5+(5*x**2+10)*ln(x)**4+(10*x**4+40*x**2+40)*ln(x)**3+(10 *x**6+60*x**4+120*x**2+80)*ln(x)**2+(5*x**8+40*x**6+120*x**4+160*x**2+80)* ln(x)+x**10+10*x**8+40*x**6+80*x**4+88*x**2+36)/(x*ln(x)**6+(5*x**3+7*x)*l n(x)**5+(10*x**5+25*x**3+10*x)*ln(x)**4+(10*x**7+30*x**5-40*x)*ln(x)**3+(5 *x**9+10*x**7-60*x**5-200*x**3-160*x)*ln(x)**2+(x**11-5*x**9-80*x**7-280*x **5-400*x**3-209*x)*ln(x)-3*x**11-30*x**9-120*x**7-240*x**5-241*x**3-98*x) ,x)
Output:
-4*log(x**2 + log(x) + 2) + log(-3*x**8 - 24*x**6 - 72*x**4 - 96*x**2 + (4 *x**2 + 5)*log(x)**4 + (6*x**4 + 12*x**2)*log(x)**3 + (4*x**6 + 6*x**4 - 2 4*x**2 - 40)*log(x)**2 + (x**8 - 4*x**6 - 48*x**4 - 112*x**2 - 80)*log(x) + log(x)**5 - 49)
Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (16) = 32\).
Time = 0.10 (sec) , antiderivative size = 111, normalized size of antiderivative = 6.94 \[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=\log \left (-3 \, x^{8} - 24 \, x^{6} + {\left (4 \, x^{2} + 5\right )} \log \left (x\right )^{4} + \log \left (x\right )^{5} - 72 \, x^{4} + 6 \, {\left (x^{4} + 2 \, x^{2}\right )} \log \left (x\right )^{3} + 2 \, {\left (2 \, x^{6} + 3 \, x^{4} - 12 \, x^{2} - 20\right )} \log \left (x\right )^{2} - 96 \, x^{2} + {\left (x^{8} - 4 \, x^{6} - 48 \, x^{4} - 112 \, x^{2} - 80\right )} \log \left (x\right ) - 49\right ) - 4 \, \log \left (x^{2} + \log \left (x\right ) + 2\right ) \] Input:
integrate((log(x)^5+(5*x^2+10)*log(x)^4+(10*x^4+40*x^2+40)*log(x)^3+(10*x^ 6+60*x^4+120*x^2+80)*log(x)^2+(5*x^8+40*x^6+120*x^4+160*x^2+80)*log(x)+x^1 0+10*x^8+40*x^6+80*x^4+88*x^2+36)/(x*log(x)^6+(5*x^3+7*x)*log(x)^5+(10*x^5 +25*x^3+10*x)*log(x)^4+(10*x^7+30*x^5-40*x)*log(x)^3+(5*x^9+10*x^7-60*x^5- 200*x^3-160*x)*log(x)^2+(x^11-5*x^9-80*x^7-280*x^5-400*x^3-209*x)*log(x)-3 *x^11-30*x^9-120*x^7-240*x^5-241*x^3-98*x),x, algorithm="maxima")
Output:
log(-3*x^8 - 24*x^6 + (4*x^2 + 5)*log(x)^4 + log(x)^5 - 72*x^4 + 6*(x^4 + 2*x^2)*log(x)^3 + 2*(2*x^6 + 3*x^4 - 12*x^2 - 20)*log(x)^2 - 96*x^2 + (x^8 - 4*x^6 - 48*x^4 - 112*x^2 - 80)*log(x) - 49) - 4*log(x^2 + log(x) + 2)
Leaf count of result is larger than twice the leaf count of optimal. 135 vs. \(2 (16) = 32\).
Time = 0.80 (sec) , antiderivative size = 135, normalized size of antiderivative = 8.44 \[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=\log \left (x^{8} \log \left (x\right ) - 3 \, x^{8} + 4 \, x^{6} \log \left (x\right )^{2} - 4 \, x^{6} \log \left (x\right ) + 6 \, x^{4} \log \left (x\right )^{3} - 24 \, x^{6} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{2} \log \left (x\right )^{4} - 48 \, x^{4} \log \left (x\right ) + 12 \, x^{2} \log \left (x\right )^{3} + \log \left (x\right )^{5} - 72 \, x^{4} - 24 \, x^{2} \log \left (x\right )^{2} + 5 \, \log \left (x\right )^{4} - 112 \, x^{2} \log \left (x\right ) - 96 \, x^{2} - 40 \, \log \left (x\right )^{2} - 80 \, \log \left (x\right ) - 49\right ) - 4 \, \log \left (x^{2} + \log \left (x\right ) + 2\right ) \] Input:
integrate((log(x)^5+(5*x^2+10)*log(x)^4+(10*x^4+40*x^2+40)*log(x)^3+(10*x^ 6+60*x^4+120*x^2+80)*log(x)^2+(5*x^8+40*x^6+120*x^4+160*x^2+80)*log(x)+x^1 0+10*x^8+40*x^6+80*x^4+88*x^2+36)/(x*log(x)^6+(5*x^3+7*x)*log(x)^5+(10*x^5 +25*x^3+10*x)*log(x)^4+(10*x^7+30*x^5-40*x)*log(x)^3+(5*x^9+10*x^7-60*x^5- 200*x^3-160*x)*log(x)^2+(x^11-5*x^9-80*x^7-280*x^5-400*x^3-209*x)*log(x)-3 *x^11-30*x^9-120*x^7-240*x^5-241*x^3-98*x),x, algorithm="giac")
Output:
log(x^8*log(x) - 3*x^8 + 4*x^6*log(x)^2 - 4*x^6*log(x) + 6*x^4*log(x)^3 - 24*x^6 + 6*x^4*log(x)^2 + 4*x^2*log(x)^4 - 48*x^4*log(x) + 12*x^2*log(x)^3 + log(x)^5 - 72*x^4 - 24*x^2*log(x)^2 + 5*log(x)^4 - 112*x^2*log(x) - 96* x^2 - 40*log(x)^2 - 80*log(x) - 49) - 4*log(x^2 + log(x) + 2)
Timed out. \[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=\int -\frac {{\ln \left (x\right )}^4\,\left (5\,x^2+10\right )+{\ln \left (x\right )}^5+{\ln \left (x\right )}^3\,\left (10\,x^4+40\,x^2+40\right )+\ln \left (x\right )\,\left (5\,x^8+40\,x^6+120\,x^4+160\,x^2+80\right )+{\ln \left (x\right )}^2\,\left (10\,x^6+60\,x^4+120\,x^2+80\right )+88\,x^2+80\,x^4+40\,x^6+10\,x^8+x^{10}+36}{98\,x-{\ln \left (x\right )}^5\,\left (5\,x^3+7\,x\right )-x\,{\ln \left (x\right )}^6-{\ln \left (x\right )}^4\,\left (10\,x^5+25\,x^3+10\,x\right )-{\ln \left (x\right )}^3\,\left (10\,x^7+30\,x^5-40\,x\right )+\ln \left (x\right )\,\left (-x^{11}+5\,x^9+80\,x^7+280\,x^5+400\,x^3+209\,x\right )+{\ln \left (x\right )}^2\,\left (-5\,x^9-10\,x^7+60\,x^5+200\,x^3+160\,x\right )+241\,x^3+240\,x^5+120\,x^7+30\,x^9+3\,x^{11}} \,d x \] Input:
int(-(log(x)^4*(5*x^2 + 10) + log(x)^5 + log(x)^3*(40*x^2 + 10*x^4 + 40) + log(x)*(160*x^2 + 120*x^4 + 40*x^6 + 5*x^8 + 80) + log(x)^2*(120*x^2 + 60 *x^4 + 10*x^6 + 80) + 88*x^2 + 80*x^4 + 40*x^6 + 10*x^8 + x^10 + 36)/(98*x - log(x)^5*(7*x + 5*x^3) - x*log(x)^6 - log(x)^4*(10*x + 25*x^3 + 10*x^5) - log(x)^3*(30*x^5 - 40*x + 10*x^7) + log(x)*(209*x + 400*x^3 + 280*x^5 + 80*x^7 + 5*x^9 - x^11) + log(x)^2*(160*x + 200*x^3 + 60*x^5 - 10*x^7 - 5* x^9) + 241*x^3 + 240*x^5 + 120*x^7 + 30*x^9 + 3*x^11),x)
Output:
int(-(log(x)^4*(5*x^2 + 10) + log(x)^5 + log(x)^3*(40*x^2 + 10*x^4 + 40) + log(x)*(160*x^2 + 120*x^4 + 40*x^6 + 5*x^8 + 80) + log(x)^2*(120*x^2 + 60 *x^4 + 10*x^6 + 80) + 88*x^2 + 80*x^4 + 40*x^6 + 10*x^8 + x^10 + 36)/(98*x - log(x)^5*(7*x + 5*x^3) - x*log(x)^6 - log(x)^4*(10*x + 25*x^3 + 10*x^5) - log(x)^3*(30*x^5 - 40*x + 10*x^7) + log(x)*(209*x + 400*x^3 + 280*x^5 + 80*x^7 + 5*x^9 - x^11) + log(x)^2*(160*x + 200*x^3 + 60*x^5 - 10*x^7 - 5* x^9) + 241*x^3 + 240*x^5 + 120*x^7 + 30*x^9 + 3*x^11), x)
\[ \int \frac {36+88 x^2+80 x^4+40 x^6+10 x^8+x^{10}+\left (80+160 x^2+120 x^4+40 x^6+5 x^8\right ) \log (x)+\left (80+120 x^2+60 x^4+10 x^6\right ) \log ^2(x)+\left (40+40 x^2+10 x^4\right ) \log ^3(x)+\left (10+5 x^2\right ) \log ^4(x)+\log ^5(x)}{-98 x-241 x^3-240 x^5-120 x^7-30 x^9-3 x^{11}+\left (-209 x-400 x^3-280 x^5-80 x^7-5 x^9+x^{11}\right ) \log (x)+\left (-160 x-200 x^3-60 x^5+10 x^7+5 x^9\right ) \log ^2(x)+\left (-40 x+30 x^5+10 x^7\right ) \log ^3(x)+\left (10 x+25 x^3+10 x^5\right ) \log ^4(x)+\left (7 x+5 x^3\right ) \log ^5(x)+x \log ^6(x)} \, dx=\text {too large to display} \] Input:
int((log(x)^5+(5*x^2+10)*log(x)^4+(10*x^4+40*x^2+40)*log(x)^3+(10*x^6+60*x ^4+120*x^2+80)*log(x)^2+(5*x^8+40*x^6+120*x^4+160*x^2+80)*log(x)+x^10+10*x ^8+40*x^6+80*x^4+88*x^2+36)/(x*log(x)^6+(5*x^3+7*x)*log(x)^5+(10*x^5+25*x^ 3+10*x)*log(x)^4+(10*x^7+30*x^5-40*x)*log(x)^3+(5*x^9+10*x^7-60*x^5-200*x^ 3-160*x)*log(x)^2+(x^11-5*x^9-80*x^7-280*x^5-400*x^3-209*x)*log(x)-3*x^11- 30*x^9-120*x^7-240*x^5-241*x^3-98*x),x)
Output:
int(log(x)**5/(log(x)**6*x + 5*log(x)**5*x**3 + 7*log(x)**5*x + 10*log(x)* *4*x**5 + 25*log(x)**4*x**3 + 10*log(x)**4*x + 10*log(x)**3*x**7 + 30*log( x)**3*x**5 - 40*log(x)**3*x + 5*log(x)**2*x**9 + 10*log(x)**2*x**7 - 60*lo g(x)**2*x**5 - 200*log(x)**2*x**3 - 160*log(x)**2*x + log(x)*x**11 - 5*log (x)*x**9 - 80*log(x)*x**7 - 280*log(x)*x**5 - 400*log(x)*x**3 - 209*log(x) *x - 3*x**11 - 30*x**9 - 120*x**7 - 240*x**5 - 241*x**3 - 98*x),x) + 10*in t(log(x)**4/(log(x)**6*x + 5*log(x)**5*x**3 + 7*log(x)**5*x + 10*log(x)**4 *x**5 + 25*log(x)**4*x**3 + 10*log(x)**4*x + 10*log(x)**3*x**7 + 30*log(x) **3*x**5 - 40*log(x)**3*x + 5*log(x)**2*x**9 + 10*log(x)**2*x**7 - 60*log( x)**2*x**5 - 200*log(x)**2*x**3 - 160*log(x)**2*x + log(x)*x**11 - 5*log(x )*x**9 - 80*log(x)*x**7 - 280*log(x)*x**5 - 400*log(x)*x**3 - 209*log(x)*x - 3*x**11 - 30*x**9 - 120*x**7 - 240*x**5 - 241*x**3 - 98*x),x) + 40*int( log(x)**3/(log(x)**6*x + 5*log(x)**5*x**3 + 7*log(x)**5*x + 10*log(x)**4*x **5 + 25*log(x)**4*x**3 + 10*log(x)**4*x + 10*log(x)**3*x**7 + 30*log(x)** 3*x**5 - 40*log(x)**3*x + 5*log(x)**2*x**9 + 10*log(x)**2*x**7 - 60*log(x) **2*x**5 - 200*log(x)**2*x**3 - 160*log(x)**2*x + log(x)*x**11 - 5*log(x)* x**9 - 80*log(x)*x**7 - 280*log(x)*x**5 - 400*log(x)*x**3 - 209*log(x)*x - 3*x**11 - 30*x**9 - 120*x**7 - 240*x**5 - 241*x**3 - 98*x),x) + 80*int(lo g(x)**2/(log(x)**6*x + 5*log(x)**5*x**3 + 7*log(x)**5*x + 10*log(x)**4*x** 5 + 25*log(x)**4*x**3 + 10*log(x)**4*x + 10*log(x)**3*x**7 + 30*log(x)*...