Integrand size = 244, antiderivative size = 23 \[ \int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx=(3+x) \left (4+x+\frac {x+\log (x)}{-3+x+\log (3+x)}\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(23)=46\).
Time = 0.09 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.26 \[ \int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx=40 x+11 x^2+x^3+\frac {(3+x) (x+\log (x))^2}{(-3+x+\log (3+x))^2}+\frac {2 (3+x) (4+x) (x+\log (x))}{-3+x+\log (3+x)} \]
Integrate[(216 - 900*x + 630*x^2 + 72*x^3 - 92*x^4 - x^5 + 3*x^6 + (-18 + 204*x - 52*x^2 - 20*x^3 + 2*x^4)*Log[x] + (-11*x - x^2)*Log[x]^2 + (-144 + 906*x - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 + (6 - 108*x - 8*x^2 + 6*x^3)* Log[x] + x*Log[x]^2)*Log[3 + x] + (24 - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + (14*x + 4*x^2)*Log[x])*Log[3 + x]^2 + (40*x + 22*x^2 + 3*x^3)*Log[3 + x]^3 )/(-27*x + 27*x^2 - 9*x^3 + x^4 + (27*x - 18*x^2 + 3*x^3)*Log[3 + x] + (-9 *x + 3*x^2)*Log[3 + x]^2 + x*Log[3 + x]^3),x]
40*x + 11*x^2 + x^3 + ((3 + x)*(x + Log[x])^2)/(-3 + x + Log[3 + x])^2 + ( 2*(3 + x)*(4 + x)*(x + Log[x]))/(-3 + x + Log[3 + x])
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.
| \(\displaystyle \int \frac {3 x^6-x^5-92 x^4+72 x^3+630 x^2+\left (-x^2-11 x\right ) \log ^2(x)+\left (3 x^3+22 x^2+40 x\right ) \log ^3(x+3)+\left (9 x^4+45 x^3-48 x^2+\left (4 x^2+14 x\right ) \log (x)-322 x+24\right ) \log ^2(x+3)+\left (2 x^4-20 x^3-52 x^2+204 x-18\right ) \log (x)+\left (9 x^5+22 x^4-184 x^3-254 x^2+\left (6 x^3-8 x^2-108 x+6\right ) \log (x)+906 x+x \log ^2(x)-144\right ) \log (x+3)-900 x+216}{x^4-9 x^3+27 x^2+\left (3 x^2-9 x\right ) \log ^2(x+3)+\left (3 x^3-18 x^2+27 x\right ) \log (x+3)-27 x+x \log ^3(x+3)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-3 x^6+x^5+92 x^4-72 x^3-630 x^2-\left (-x^2-11 x\right ) \log ^2(x)-\left (3 x^3+22 x^2+40 x\right ) \log ^3(x+3)-\left (9 x^4+45 x^3-48 x^2+\left (4 x^2+14 x\right ) \log (x)-322 x+24\right ) \log ^2(x+3)-\left (2 x^4-20 x^3-52 x^2+204 x-18\right ) \log (x)-\left (9 x^5+22 x^4-184 x^3-254 x^2+\left (6 x^3-8 x^2-108 x+6\right ) \log (x)+906 x+x \log ^2(x)-144\right ) \log (x+3)+900 x-216}{x (-x-\log (x+3)+3)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (3 x^2+\frac {2 \left (3 x^3+15 x^2+2 x^2 \log (x)+19 x+7 x \log (x)+12\right )}{x (x+\log (x+3)-3)}+\frac {-2 x^4-13 x^3-2 x^3 \log (x)-24 x^2-12 x^2 \log (x)+6 x+x \log ^2(x)-24 x \log (x)+6 \log (x)}{x (x+\log (x+3)-3)^2}+22 x-\frac {2 (x+4) (x+\log (x))^2}{(x+\log (x+3)-3)^3}+40\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \int \frac {x^3}{(x+\log (x+3)-3)^3}dx-2 \int \frac {x^3}{(x+\log (x+3)-3)^2}dx-8 \int \frac {x^2}{(x+\log (x+3)-3)^3}dx-4 \int \frac {x^2 \log (x)}{(x+\log (x+3)-3)^3}dx-13 \int \frac {x^2}{(x+\log (x+3)-3)^2}dx-2 \int \frac {x^2 \log (x)}{(x+\log (x+3)-3)^2}dx+6 \int \frac {x^2}{x+\log (x+3)-3}dx-8 \int \frac {\log ^2(x)}{(x+\log (x+3)-3)^3}dx-2 \int \frac {x \log ^2(x)}{(x+\log (x+3)-3)^3}dx+\int \frac {\log ^2(x)}{(x+\log (x+3)-3)^2}dx-16 \int \frac {x \log (x)}{(x+\log (x+3)-3)^3}dx+6 \int \frac {1}{(x+\log (x+3)-3)^2}dx-24 \int \frac {x}{(x+\log (x+3)-3)^2}dx-24 \int \frac {\log (x)}{(x+\log (x+3)-3)^2}dx+6 \int \frac {\log (x)}{x (x+\log (x+3)-3)^2}dx-12 \int \frac {x \log (x)}{(x+\log (x+3)-3)^2}dx+38 \int \frac {1}{x+\log (x+3)-3}dx+24 \int \frac {1}{x (x+\log (x+3)-3)}dx+30 \int \frac {x}{x+\log (x+3)-3}dx+14 \int \frac {\log (x)}{x+\log (x+3)-3}dx+4 \int \frac {x \log (x)}{x+\log (x+3)-3}dx+x^3+11 x^2+40 x\) |
Int[(216 - 900*x + 630*x^2 + 72*x^3 - 92*x^4 - x^5 + 3*x^6 + (-18 + 204*x - 52*x^2 - 20*x^3 + 2*x^4)*Log[x] + (-11*x - x^2)*Log[x]^2 + (-144 + 906*x - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 + (6 - 108*x - 8*x^2 + 6*x^3)*Log[x] + x*Log[x]^2)*Log[3 + x] + (24 - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + (14*x + 4*x^2)*Log[x])*Log[3 + x]^2 + (40*x + 22*x^2 + 3*x^3)*Log[3 + x]^3)/(-27 *x + 27*x^2 - 9*x^3 + x^4 + (27*x - 18*x^2 + 3*x^3)*Log[3 + x] + (-9*x + 3 *x^2)*Log[3 + x]^2 + x*Log[3 + x]^3),x]
3.20.46.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(92\) vs. \(2(23)=46\).
Time = 2.13 (sec) , antiderivative size = 93, normalized size of antiderivative = 4.04
| method | result | size |
| risch | \(x^{3}+11 x^{2}+40 x +\frac {\left (2 x^{3}+2 x^{2} \ln \left (x \right )+2 \ln \left (3+x \right ) x^{2}+2 \ln \left (3+x \right ) \ln \left (x \right ) x +3 x^{2}+4 x \ln \left (x \right )+8 x \ln \left (3+x \right )+\ln \left (x \right )^{2}+8 \ln \left (3+x \right ) \ln \left (x \right )-24 x -24 \ln \left (x \right )\right ) \left (3+x \right )}{\left (\ln \left (3+x \right )+x -3\right )^{2}}\) | \(93\) |
| parallelrisch | \(-\frac {2160-2 \ln \left (3+x \right )^{2} x^{3}-4 \ln \left (3+x \right ) x^{4}-22 x^{2} \ln \left (3+x \right )^{2}-36 \ln \left (3+x \right ) x^{3}-80 x \ln \left (3+x \right )^{2}-48 \ln \left (3+x \right ) \ln \left (x \right )-2016 x -56 \ln \left (3+x \right ) x^{2}-2 x \ln \left (x \right )^{2}+24 x \ln \left (x \right )-1440 \ln \left (3+x \right )+912 x \ln \left (3+x \right )-2 x^{5}+144 \ln \left (x \right )-6 \ln \left (x \right )^{2}-14 x^{4}+16 x^{3}+552 x^{2}-4 x^{3} \ln \left (x \right )-20 x^{2} \ln \left (x \right )+240 \ln \left (3+x \right )^{2}-4 \ln \left (3+x \right ) \ln \left (x \right ) x^{2}-28 \ln \left (3+x \right ) \ln \left (x \right ) x}{2 \left (x^{2}+2 x \ln \left (3+x \right )+\ln \left (3+x \right )^{2}-6 x -6 \ln \left (3+x \right )+9\right )}\) | \(200\) |
int(((3*x^3+22*x^2+40*x)*ln(3+x)^3+((4*x^2+14*x)*ln(x)+9*x^4+45*x^3-48*x^2 -322*x+24)*ln(3+x)^2+(x*ln(x)^2+(6*x^3-8*x^2-108*x+6)*ln(x)+9*x^5+22*x^4-1 84*x^3-254*x^2+906*x-144)*ln(3+x)+(-x^2-11*x)*ln(x)^2+(2*x^4-20*x^3-52*x^2 +204*x-18)*ln(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/(x*ln(3+x)^3+( 3*x^2-9*x)*ln(3+x)^2+(3*x^3-18*x^2+27*x)*ln(3+x)+x^4-9*x^3+27*x^2-27*x),x, method=_RETURNVERBOSE)
x^3+11*x^2+40*x+(2*x^3+2*x^2*ln(x)+2*ln(3+x)*x^2+2*ln(3+x)*ln(x)*x+3*x^2+4 *x*ln(x)+8*x*ln(3+x)+ln(x)^2+8*ln(3+x)*ln(x)-24*x-24*ln(x))*(3+x)/(ln(3+x) +x-3)^2
Leaf count of result is larger than twice the leaf count of optimal. 126 vs. \(2 (23) = 46\).
Time = 0.24 (sec) , antiderivative size = 126, normalized size of antiderivative = 5.48 \[ \int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx=\frac {x^{5} + 7 \, x^{4} - 8 \, x^{3} + {\left (x^{3} + 11 \, x^{2} + 40 \, x\right )} \log \left (x + 3\right )^{2} + {\left (x + 3\right )} \log \left (x\right )^{2} - 156 \, x^{2} + 2 \, {\left (x^{4} + 9 \, x^{3} + 14 \, x^{2} + {\left (x^{2} + 7 \, x + 12\right )} \log \left (x\right ) - 108 \, x\right )} \log \left (x + 3\right ) + 2 \, {\left (x^{3} + 5 \, x^{2} - 6 \, x - 36\right )} \log \left (x\right ) + 288 \, x}{x^{2} + 2 \, {\left (x - 3\right )} \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} - 6 \, x + 9} \]
integrate(((3*x^3+22*x^2+40*x)*log(3+x)^3+((4*x^2+14*x)*log(x)+9*x^4+45*x^ 3-48*x^2-322*x+24)*log(3+x)^2+(x*log(x)^2+(6*x^3-8*x^2-108*x+6)*log(x)+9*x ^5+22*x^4-184*x^3-254*x^2+906*x-144)*log(3+x)+(-x^2-11*x)*log(x)^2+(2*x^4- 20*x^3-52*x^2+204*x-18)*log(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/ (x*log(3+x)^3+(3*x^2-9*x)*log(3+x)^2+(3*x^3-18*x^2+27*x)*log(3+x)+x^4-9*x^ 3+27*x^2-27*x),x, algorithm=\
(x^5 + 7*x^4 - 8*x^3 + (x^3 + 11*x^2 + 40*x)*log(x + 3)^2 + (x + 3)*log(x) ^2 - 156*x^2 + 2*(x^4 + 9*x^3 + 14*x^2 + (x^2 + 7*x + 12)*log(x) - 108*x)* log(x + 3) + 2*(x^3 + 5*x^2 - 6*x - 36)*log(x) + 288*x)/(x^2 + 2*(x - 3)*l og(x + 3) + log(x + 3)^2 - 6*x + 9)
Leaf count of result is larger than twice the leaf count of optimal. 136 vs. \(2 (20) = 40\).
Time = 0.14 (sec) , antiderivative size = 136, normalized size of antiderivative = 5.91 \[ \int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx=x^{3} + 11 x^{2} + 40 x + \frac {2 x^{4} + 2 x^{3} \log {\left (x \right )} + 9 x^{3} + 10 x^{2} \log {\left (x \right )} - 15 x^{2} + x \log {\left (x \right )}^{2} - 12 x \log {\left (x \right )} - 72 x + \left (2 x^{3} + 2 x^{2} \log {\left (x \right )} + 14 x^{2} + 14 x \log {\left (x \right )} + 24 x + 24 \log {\left (x \right )}\right ) \log {\left (x + 3 \right )} + 3 \log {\left (x \right )}^{2} - 72 \log {\left (x \right )}}{x^{2} - 6 x + \left (2 x - 6\right ) \log {\left (x + 3 \right )} + \log {\left (x + 3 \right )}^{2} + 9} \]
integrate(((3*x**3+22*x**2+40*x)*ln(3+x)**3+((4*x**2+14*x)*ln(x)+9*x**4+45 *x**3-48*x**2-322*x+24)*ln(3+x)**2+(x*ln(x)**2+(6*x**3-8*x**2-108*x+6)*ln( x)+9*x**5+22*x**4-184*x**3-254*x**2+906*x-144)*ln(3+x)+(-x**2-11*x)*ln(x)* *2+(2*x**4-20*x**3-52*x**2+204*x-18)*ln(x)+3*x**6-x**5-92*x**4+72*x**3+630 *x**2-900*x+216)/(x*ln(3+x)**3+(3*x**2-9*x)*ln(3+x)**2+(3*x**3-18*x**2+27* x)*ln(3+x)+x**4-9*x**3+27*x**2-27*x),x)
x**3 + 11*x**2 + 40*x + (2*x**4 + 2*x**3*log(x) + 9*x**3 + 10*x**2*log(x) - 15*x**2 + x*log(x)**2 - 12*x*log(x) - 72*x + (2*x**3 + 2*x**2*log(x) + 1 4*x**2 + 14*x*log(x) + 24*x + 24*log(x))*log(x + 3) + 3*log(x)**2 - 72*log (x))/(x**2 - 6*x + (2*x - 6)*log(x + 3) + log(x + 3)**2 + 9)
Leaf count of result is larger than twice the leaf count of optimal. 126 vs. \(2 (23) = 46\).
Time = 0.24 (sec) , antiderivative size = 126, normalized size of antiderivative = 5.48 \[ \int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx=\frac {x^{5} + 7 \, x^{4} - 8 \, x^{3} + {\left (x^{3} + 11 \, x^{2} + 40 \, x\right )} \log \left (x + 3\right )^{2} + {\left (x + 3\right )} \log \left (x\right )^{2} - 156 \, x^{2} + 2 \, {\left (x^{4} + 9 \, x^{3} + 14 \, x^{2} + {\left (x^{2} + 7 \, x + 12\right )} \log \left (x\right ) - 108 \, x\right )} \log \left (x + 3\right ) + 2 \, {\left (x^{3} + 5 \, x^{2} - 6 \, x - 36\right )} \log \left (x\right ) + 288 \, x}{x^{2} + 2 \, {\left (x - 3\right )} \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} - 6 \, x + 9} \]
integrate(((3*x^3+22*x^2+40*x)*log(3+x)^3+((4*x^2+14*x)*log(x)+9*x^4+45*x^ 3-48*x^2-322*x+24)*log(3+x)^2+(x*log(x)^2+(6*x^3-8*x^2-108*x+6)*log(x)+9*x ^5+22*x^4-184*x^3-254*x^2+906*x-144)*log(3+x)+(-x^2-11*x)*log(x)^2+(2*x^4- 20*x^3-52*x^2+204*x-18)*log(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/ (x*log(3+x)^3+(3*x^2-9*x)*log(3+x)^2+(3*x^3-18*x^2+27*x)*log(3+x)+x^4-9*x^ 3+27*x^2-27*x),x, algorithm=\
(x^5 + 7*x^4 - 8*x^3 + (x^3 + 11*x^2 + 40*x)*log(x + 3)^2 + (x + 3)*log(x) ^2 - 156*x^2 + 2*(x^4 + 9*x^3 + 14*x^2 + (x^2 + 7*x + 12)*log(x) - 108*x)* log(x + 3) + 2*(x^3 + 5*x^2 - 6*x - 36)*log(x) + 288*x)/(x^2 + 2*(x - 3)*l og(x + 3) + log(x + 3)^2 - 6*x + 9)
Leaf count of result is larger than twice the leaf count of optimal. 149 vs. \(2 (23) = 46\).
Time = 0.32 (sec) , antiderivative size = 149, normalized size of antiderivative = 6.48 \[ \int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx=x^{3} + 11 \, x^{2} + 40 \, x + \frac {2 \, x^{4} + 2 \, x^{3} \log \left (x + 3\right ) + 2 \, x^{3} \log \left (x\right ) + 2 \, x^{2} \log \left (x + 3\right ) \log \left (x\right ) + 9 \, x^{3} + 14 \, x^{2} \log \left (x + 3\right ) + 10 \, x^{2} \log \left (x\right ) + 14 \, x \log \left (x + 3\right ) \log \left (x\right ) + x \log \left (x\right )^{2} - 15 \, x^{2} + 24 \, x \log \left (x + 3\right ) - 12 \, x \log \left (x\right ) + 24 \, \log \left (x + 3\right ) \log \left (x\right ) + 3 \, \log \left (x\right )^{2} - 72 \, x - 72 \, \log \left (x\right )}{x^{2} + 2 \, x \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} - 6 \, x - 6 \, \log \left (x + 3\right ) + 9} \]
integrate(((3*x^3+22*x^2+40*x)*log(3+x)^3+((4*x^2+14*x)*log(x)+9*x^4+45*x^ 3-48*x^2-322*x+24)*log(3+x)^2+(x*log(x)^2+(6*x^3-8*x^2-108*x+6)*log(x)+9*x ^5+22*x^4-184*x^3-254*x^2+906*x-144)*log(3+x)+(-x^2-11*x)*log(x)^2+(2*x^4- 20*x^3-52*x^2+204*x-18)*log(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/ (x*log(3+x)^3+(3*x^2-9*x)*log(3+x)^2+(3*x^3-18*x^2+27*x)*log(3+x)+x^4-9*x^ 3+27*x^2-27*x),x, algorithm=\
x^3 + 11*x^2 + 40*x + (2*x^4 + 2*x^3*log(x + 3) + 2*x^3*log(x) + 2*x^2*log (x + 3)*log(x) + 9*x^3 + 14*x^2*log(x + 3) + 10*x^2*log(x) + 14*x*log(x + 3)*log(x) + x*log(x)^2 - 15*x^2 + 24*x*log(x + 3) - 12*x*log(x) + 24*log(x + 3)*log(x) + 3*log(x)^2 - 72*x - 72*log(x))/(x^2 + 2*x*log(x + 3) + log( x + 3)^2 - 6*x - 6*log(x + 3) + 9)
Timed out. \[ \int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx=\int \frac {{\ln \left (x+3\right )}^2\,\left (\ln \left (x\right )\,\left (4\,x^2+14\,x\right )-322\,x-48\,x^2+45\,x^3+9\,x^4+24\right )-\ln \left (x\right )\,\left (-2\,x^4+20\,x^3+52\,x^2-204\,x+18\right )-900\,x+{\ln \left (x+3\right )}^3\,\left (3\,x^3+22\,x^2+40\,x\right )-{\ln \left (x\right )}^2\,\left (x^2+11\,x\right )+\ln \left (x+3\right )\,\left (906\,x+x\,{\ln \left (x\right )}^2-254\,x^2-184\,x^3+22\,x^4+9\,x^5-\ln \left (x\right )\,\left (-6\,x^3+8\,x^2+108\,x-6\right )-144\right )+630\,x^2+72\,x^3-92\,x^4-x^5+3\,x^6+216}{\ln \left (x+3\right )\,\left (3\,x^3-18\,x^2+27\,x\right )-27\,x-{\ln \left (x+3\right )}^2\,\left (9\,x-3\,x^2\right )+x\,{\ln \left (x+3\right )}^3+27\,x^2-9\,x^3+x^4} \,d x \]
int((log(x + 3)^2*(log(x)*(14*x + 4*x^2) - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + 24) - log(x)*(52*x^2 - 204*x + 20*x^3 - 2*x^4 + 18) - 900*x + log(x + 3 )^3*(40*x + 22*x^2 + 3*x^3) - log(x)^2*(11*x + x^2) + log(x + 3)*(906*x + x*log(x)^2 - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 - log(x)*(108*x + 8*x^2 - 6*x^3 - 6) - 144) + 630*x^2 + 72*x^3 - 92*x^4 - x^5 + 3*x^6 + 216)/(log(x + 3)*(27*x - 18*x^2 + 3*x^3) - 27*x - log(x + 3)^2*(9*x - 3*x^2) + x*log(x + 3)^3 + 27*x^2 - 9*x^3 + x^4),x)
int((log(x + 3)^2*(log(x)*(14*x + 4*x^2) - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + 24) - log(x)*(52*x^2 - 204*x + 20*x^3 - 2*x^4 + 18) - 900*x + log(x + 3 )^3*(40*x + 22*x^2 + 3*x^3) - log(x)^2*(11*x + x^2) + log(x + 3)*(906*x + x*log(x)^2 - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 - log(x)*(108*x + 8*x^2 - 6*x^3 - 6) - 144) + 630*x^2 + 72*x^3 - 92*x^4 - x^5 + 3*x^6 + 216)/(log(x + 3)*(27*x - 18*x^2 + 3*x^3) - 27*x - log(x + 3)^2*(9*x - 3*x^2) + x*log(x + 3)^3 + 27*x^2 - 9*x^3 + x^4), x)