Integrand size = 206, antiderivative size = 31 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\left (\frac {e^6}{3}-x-x^2\right )^2 (3-x+\log (-7+\log (-4+x))) \] Output:
(3-x+ln(ln(-4+x)-7))*(1/3*exp(3)^2-x-x^2)^2
Leaf count is larger than twice the leaf count of optimal. \(90\) vs. \(2(31)=62\).
Time = 0.07 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.90 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\frac {1}{9} \left (-e^6 \left (18+e^6\right ) x-3 \left (-9+4 e^6\right ) x^2+3 \left (15+2 e^6\right ) x^3+9 x^4-9 x^5+e^{12} \log (7-\log (-4+x))-3 x (1+x) \left (2 e^6-3 x-3 x^2\right ) \log (-7+\log (-4+x))\right ) \] Input:
Integrate[(1512*x + 3411*x^2 + 81*x^3 - 1503*x^4 + 315*x^5 + E^12*(-27 + 7 *x) + E^6*(-504 - 552*x + 666*x^2 - 126*x^3) + (E^12*(4 - x) - 216*x - 486 *x^2 - 9*x^3 + 216*x^4 - 45*x^5 + E^6*(72 + 78*x - 96*x^2 + 18*x^3))*Log[- 4 + x] + (504*x + 1386*x^2 + 630*x^3 - 252*x^4 + E^6*(-168 - 294*x + 84*x^ 2) + (-72*x - 198*x^2 - 90*x^3 + 36*x^4 + E^6*(24 + 42*x - 12*x^2))*Log[-4 + x])*Log[-7 + Log[-4 + x]])/(252 - 63*x + (-36 + 9*x)*Log[-4 + x]),x]
Output:
(-(E^6*(18 + E^6)*x) - 3*(-9 + 4*E^6)*x^2 + 3*(15 + 2*E^6)*x^3 + 9*x^4 - 9 *x^5 + E^12*Log[7 - Log[-4 + x]] - 3*x*(1 + x)*(2*E^6 - 3*x - 3*x^2)*Log[- 7 + Log[-4 + x]])/9
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.
| \(\displaystyle \int \frac {315 x^5-1503 x^4+81 x^3+3411 x^2+e^6 \left (-126 x^3+666 x^2-552 x-504\right )+\left (-252 x^4+630 x^3+1386 x^2+e^6 \left (84 x^2-294 x-168\right )+\left (36 x^4-90 x^3-198 x^2+e^6 \left (-12 x^2+42 x+24\right )-72 x\right ) \log (x-4)+504 x\right ) \log (\log (x-4)-7)+\left (-45 x^5+216 x^4-9 x^3-486 x^2+e^6 \left (18 x^3-96 x^2+78 x+72\right )-216 x+e^{12} (4-x)\right ) \log (x-4)+1512 x+e^{12} (7 x-27)}{-63 x+(9 x-36) \log (x-4)+252} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-3 x^2-3 x+e^6\right ) \left (-105 x^3+606 x^2+42 \left (2 x^2-7 x-4\right ) \log (\log (x-4)-7)-(x-4) \log (x-4) \left (-15 x^2+27 x+6 (2 x+1) \log (\log (x-4)-7)+e^6+18\right )-633 \left (1-\frac {7 e^6}{633}\right ) x-504 \left (1+\frac {3 e^6}{56}\right )\right )}{9 (4-x) (7-\log (x-4))}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{9} \int -\frac {\left (-3 x^2-3 x+e^6\right ) \left (105 x^3-606 x^2+\left (633-7 e^6\right ) x+42 \left (-2 x^2+7 x+4\right ) \log (\log (x-4)-7)-(4-x) \log (x-4) \left (-15 x^2+27 x+6 (2 x+1) \log (\log (x-4)-7)+e^6+18\right )+9 \left (56+3 e^6\right )\right )}{(4-x) (7-\log (x-4))}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{9} \int \frac {\left (-3 x^2-3 x+e^6\right ) \left (105 x^3-606 x^2+\left (633-7 e^6\right ) x+42 \left (-2 x^2+7 x+4\right ) \log (\log (x-4)-7)-(4-x) \log (x-4) \left (-15 x^2+27 x+6 (2 x+1) \log (\log (x-4)-7)+e^6+18\right )+9 \left (56+3 e^6\right )\right )}{(4-x) (7-\log (x-4))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{9} \int \left (-\frac {105 \left (3 x^2+3 x-e^6\right ) x^3}{(x-4) (\log (x-4)-7)}+\frac {15 \left (3 x^2+3 x-e^6\right ) \log (x-4) x^2}{\log (x-4)-7}+\frac {606 \left (3 x^2+3 x-e^6\right ) x^2}{(x-4) (\log (x-4)-7)}-\frac {27 \left (3 x^2+3 x-e^6\right ) \log (x-4) x}{\log (x-4)-7}-\frac {\left (-633+7 e^6\right ) \left (-3 x^2-3 x+e^6\right ) x}{(x-4) (\log (x-4)-7)}+\frac {18 \left (1+\frac {e^6}{18}\right ) \left (-3 x^2-3 x+e^6\right ) \log (x-4)}{\log (x-4)-7}-6 (2 x+1) \left (3 x^2+3 x-e^6\right ) \log (\log (x-4)-7)+\frac {9 \left (56+3 e^6\right ) \left (-3 x^2-3 x+e^6\right )}{(x-4) (\log (x-4)-7)}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{9} \left (-6 e^6 \text {Subst}(\int \log (\log (x)-7)dx,x,x-4)+36 \int x^3 \log (\log (x-4)-7)dx+54 \int x^2 \log (\log (x-4)-7)dx+6 \left (3-2 e^6\right ) \int x \log (\log (x-4)-7)dx+9 e^{28} \operatorname {ExpIntegralEi}(-4 (7-\log (x-4)))+21 e^{21} \left (18+e^6\right ) \operatorname {ExpIntegralEi}(-3 (7-\log (x-4)))-105 e^{21} \left (324-e^6\right ) \operatorname {ExpIntegralEi}(-3 (7-\log (x-4)))+105 e^{21} \left (60-e^6\right ) \operatorname {ExpIntegralEi}(-3 (7-\log (x-4)))+3 e^{21} \left (633-7 e^6\right ) \operatorname {ExpIntegralEi}(-3 (7-\log (x-4)))+25605 e^{21} \operatorname {ExpIntegralEi}(-3 (7-\log (x-4)))+27 e^{14} \left (56+3 e^6\right ) \operatorname {ExpIntegralEi}(-2 (7-\log (x-4)))+189 e^{14} \left (18+e^6\right ) \operatorname {ExpIntegralEi}(-2 (7-\log (x-4)))+189 e^{14} \left (168-e^6\right ) \operatorname {ExpIntegralEi}(-2 (7-\log (x-4)))-840 e^{14} \left (114-e^6\right ) \operatorname {ExpIntegralEi}(-2 (7-\log (x-4)))+654 e^{14} \left (60-e^6\right ) \operatorname {ExpIntegralEi}(-2 (7-\log (x-4)))+39 e^{14} \left (633-7 e^6\right ) \operatorname {ExpIntegralEi}(-2 (7-\log (x-4)))-3744 e^{14} \operatorname {ExpIntegralEi}(-2 (7-\log (x-4)))+243 e^7 \left (56+3 e^6\right ) \operatorname {ExpIntegralEi}(\log (x-4)-7)+7 e^7 \left (60-e^6\right ) \left (18+e^6\right ) \operatorname {ExpIntegralEi}(\log (x-4)-7)+e^7 \left (633-7 e^6\right ) \left (168-e^6\right ) \operatorname {ExpIntegralEi}(\log (x-4)-7)-732 e^7 \left (60-e^6\right ) \operatorname {ExpIntegralEi}(\log (x-4)-7)-80352 e^7 \operatorname {ExpIntegralEi}(\log (x-4)-7)-9 x^5+9 x^4+\left (18+e^6\right ) x^3+5 e^6 x^3+27 x^3+\frac {3}{2} \left (18+e^6\right ) x^2-\frac {27 e^6 x^2}{2}-e^6 \left (18+e^6\right ) x+9 \left (60-e^6\right ) \left (56+3 e^6\right ) \log (7-\log (x-4))+4 \left (633-7 e^6\right ) \left (60-e^6\right ) \log (7-\log (x-4))-2976 \left (60-e^6\right ) \log (7-\log (x-4))\right )\) |
Input:
Int[(1512*x + 3411*x^2 + 81*x^3 - 1503*x^4 + 315*x^5 + E^12*(-27 + 7*x) + E^6*(-504 - 552*x + 666*x^2 - 126*x^3) + (E^12*(4 - x) - 216*x - 486*x^2 - 9*x^3 + 216*x^4 - 45*x^5 + E^6*(72 + 78*x - 96*x^2 + 18*x^3))*Log[-4 + x] + (504*x + 1386*x^2 + 630*x^3 - 252*x^4 + E^6*(-168 - 294*x + 84*x^2) + ( -72*x - 198*x^2 - 90*x^3 + 36*x^4 + E^6*(24 + 42*x - 12*x^2))*Log[-4 + x]) *Log[-7 + Log[-4 + x]])/(252 - 63*x + (-36 + 9*x)*Log[-4 + x]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(30)=60\).
Time = 1.56 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.13
| method | result | size |
| risch | \(\frac {\left ({\mathrm e}^{6}-3 x^{2}-3 x \right )^{2} \ln \left (\ln \left (x -4\right )-7\right )}{9}-x^{5}+x^{4}+\frac {2 x^{3} {\mathrm e}^{6}}{3}+5 x^{3}-\frac {4 x^{2} {\mathrm e}^{6}}{3}+3 x^{2}-\frac {x \,{\mathrm e}^{12}}{9}-2 x \,{\mathrm e}^{6}\) | \(66\) |
| parallelrisch | \(-\frac {x \,{\mathrm e}^{12}}{9}+\frac {\ln \left (\ln \left (x -4\right )-7\right ) {\mathrm e}^{12}}{9}+\frac {2 x^{3} {\mathrm e}^{6}}{3}-\frac {2 \ln \left (\ln \left (x -4\right )-7\right ) {\mathrm e}^{6} x^{2}}{3}-x^{5}+\ln \left (\ln \left (x -4\right )-7\right ) x^{4}-\frac {8 \,{\mathrm e}^{12}}{9}-\frac {4 x^{2} {\mathrm e}^{6}}{3}-\frac {2 \ln \left (\ln \left (x -4\right )-7\right ) {\mathrm e}^{6} x}{3}+x^{4}+2 \ln \left (\ln \left (x -4\right )-7\right ) x^{3}-2 x \,{\mathrm e}^{6}+5 x^{3}+\ln \left (\ln \left (x -4\right )-7\right ) x^{2}+\frac {16 \,{\mathrm e}^{6}}{3}+3 x^{2}-48\) | \(142\) |
| default | \(400-2 x \,{\mathrm e}^{6}-\frac {4 x^{2} {\mathrm e}^{6}}{3}+\frac {2 x^{3} {\mathrm e}^{6}}{3}-\frac {x \,{\mathrm e}^{12}}{9}+400 \ln \left (\ln \left (x -4\right )-7\right )+\frac {4 \,{\mathrm e}^{12}}{9}-\frac {40 \,{\mathrm e}^{6}}{3}+3 x^{2}+5 x^{3}+x^{4}-x^{5}+\frac {\ln \left (\ln \left (x -4\right )-7\right ) {\mathrm e}^{12}}{9}+6 \left (\frac {\left (x -4\right )^{3}}{3}+4 \left (x -4\right )^{2}+16 x -64\right ) \ln \left (\ln \left (x -4\right )-7\right )+4 \left (\frac {\left (x -4\right )^{4}}{4}+4 \left (x -4\right )^{3}+24 \left (x -4\right )^{2}+64 x -256\right ) \ln \left (\ln \left (x -4\right )-7\right )+2 \left (\frac {\left (x -4\right )^{2}}{2}+4 x -16\right ) \ln \left (\ln \left (x -4\right )-7\right )-\frac {2 \ln \left (\ln \left (x -4\right )-7\right ) {\mathrm e}^{6} x}{3}-\frac {2 \ln \left (\ln \left (x -4\right )-7\right ) {\mathrm e}^{6} x^{2}}{3}\) | \(201\) |
Input:
int(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*ln(x-4)+(84* x^2-294*x-168)*exp(3)^2-252*x^4+630*x^3+1386*x^2+504*x)*ln(ln(x-4)-7)+((-x +4)*exp(3)^4+(18*x^3-96*x^2+78*x+72)*exp(3)^2-45*x^5+216*x^4-9*x^3-486*x^2 -216*x)*ln(x-4)+(7*x-27)*exp(3)^4+(-126*x^3+666*x^2-552*x-504)*exp(3)^2+31 5*x^5-1503*x^4+81*x^3+3411*x^2+1512*x)/((9*x-36)*ln(x-4)-63*x+252),x,metho d=_RETURNVERBOSE)
Output:
1/9*(exp(6)-3*x^2-3*x)^2*ln(ln(x-4)-7)-x^5+x^4+2/3*x^3*exp(6)+5*x^3-4/3*x^ 2*exp(6)+3*x^2-1/9*x*exp(12)-2*x*exp(6)
Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (29) = 58\).
Time = 0.09 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.45 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} + 5 \, x^{3} + 3 \, x^{2} - \frac {1}{9} \, x e^{12} + \frac {2}{3} \, {\left (x^{3} - 2 \, x^{2} - 3 \, x\right )} e^{6} + \frac {1}{9} \, {\left (9 \, x^{4} + 18 \, x^{3} + 9 \, x^{2} - 6 \, {\left (x^{2} + x\right )} e^{6} + e^{12}\right )} \log \left (\log \left (x - 4\right ) - 7\right ) \] Input:
integrate(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*log(-4 +x)+(84*x^2-294*x-168)*exp(3)^2-252*x^4+630*x^3+1386*x^2+504*x)*log(log(-4 +x)-7)+((-x+4)*exp(3)^4+(18*x^3-96*x^2+78*x+72)*exp(3)^2-45*x^5+216*x^4-9* x^3-486*x^2-216*x)*log(-4+x)+(7*x-27)*exp(3)^4+(-126*x^3+666*x^2-552*x-504 )*exp(3)^2+315*x^5-1503*x^4+81*x^3+3411*x^2+1512*x)/((9*x-36)*log(-4+x)-63 *x+252),x, algorithm="fricas")
Output:
-x^5 + x^4 + 5*x^3 + 3*x^2 - 1/9*x*e^12 + 2/3*(x^3 - 2*x^2 - 3*x)*e^6 + 1/ 9*(9*x^4 + 18*x^3 + 9*x^2 - 6*(x^2 + x)*e^6 + e^12)*log(log(x - 4) - 7)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (22) = 44\).
Time = 0.58 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=- x^{5} + x^{4} + x^{3} \cdot \left (5 + \frac {2 e^{6}}{3}\right ) + x^{2} \cdot \left (3 - \frac {4 e^{6}}{3}\right ) + x \left (- \frac {e^{12}}{9} - 2 e^{6}\right ) + \left (x^{4} + 2 x^{3} - \frac {2 x^{2} e^{6}}{3} + x^{2} - \frac {2 x e^{6}}{3} - \frac {1328}{15} + \frac {44 e^{6}}{9}\right ) \log {\left (\log {\left (x - 4 \right )} - 7 \right )} + \frac {\left (- 220 e^{6} + 3984 + 5 e^{12}\right ) \log {\left (\log {\left (x - 4 \right )} - 7 \right )}}{45} \] Input:
integrate(((((-12*x**2+42*x+24)*exp(3)**2+36*x**4-90*x**3-198*x**2-72*x)*l n(-4+x)+(84*x**2-294*x-168)*exp(3)**2-252*x**4+630*x**3+1386*x**2+504*x)*l n(ln(-4+x)-7)+((-x+4)*exp(3)**4+(18*x**3-96*x**2+78*x+72)*exp(3)**2-45*x** 5+216*x**4-9*x**3-486*x**2-216*x)*ln(-4+x)+(7*x-27)*exp(3)**4+(-126*x**3+6 66*x**2-552*x-504)*exp(3)**2+315*x**5-1503*x**4+81*x**3+3411*x**2+1512*x)/ ((9*x-36)*ln(-4+x)-63*x+252),x)
Output:
-x**5 + x**4 + x**3*(5 + 2*exp(6)/3) + x**2*(3 - 4*exp(6)/3) + x*(-exp(12) /9 - 2*exp(6)) + (x**4 + 2*x**3 - 2*x**2*exp(6)/3 + x**2 - 2*x*exp(6)/3 - 1328/15 + 44*exp(6)/9)*log(log(x - 4) - 7) + (-220*exp(6) + 3984 + 5*exp(1 2))*log(log(x - 4) - 7)/45
Leaf count of result is larger than twice the leaf count of optimal. 287 vs. \(2 (29) = 58\).
Time = 0.10 (sec) , antiderivative size = 287, normalized size of antiderivative = 9.26 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} + \frac {1}{3} \, x^{3} {\left (2 \, e^{6} + 15\right )} - \frac {1}{3} \, x^{2} {\left (4 \, e^{6} - 9\right )} - \frac {8}{3} \, {\left ({\left (\log \left (x - 4\right ) - 7\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) + 7\right )} e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + \frac {4}{9} \, e^{12} \log \left (x - 4\right ) \log \left (\log \left (x - 4\right ) - 7\right ) + 8 \, e^{6} \log \left (x - 4\right ) \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {28}{3} \, e^{6} \log \left (\log \left (x - 4\right ) - 7\right )^{2} - \frac {1}{9} \, x {\left (e^{12} + 18 \, e^{6}\right )} - \frac {4}{9} \, {\left ({\left (\log \left (x - 4\right ) - 7\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) + 7\right )} e^{12} - 8 \, {\left ({\left (\log \left (x - 4\right ) - 7\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - \log \left (x - 4\right ) + 7\right )} e^{6} - \frac {4}{3} \, {\left (7 \, \log \left (\log \left (x - 4\right ) - 7\right )^{2} + 2 \, \log \left (x - 4\right )\right )} e^{6} - \frac {4}{9} \, {\left (e^{12} + 12 \, e^{6}\right )} \log \left (x - 4\right ) + \frac {1}{3} \, {\left (3 \, x^{4} + 6 \, x^{3} - x^{2} {\left (2 \, e^{6} - 3\right )} - 2 \, x e^{6} - 8 \, e^{6} \log \left (x - 4\right ) + 56 \, e^{6}\right )} \log \left (\log \left (x - 4\right ) - 7\right ) - 3 \, e^{12} \log \left (\log \left (x - 4\right ) - 7\right ) - 56 \, e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) \] Input:
integrate(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*log(-4 +x)+(84*x^2-294*x-168)*exp(3)^2-252*x^4+630*x^3+1386*x^2+504*x)*log(log(-4 +x)-7)+((-x+4)*exp(3)^4+(18*x^3-96*x^2+78*x+72)*exp(3)^2-45*x^5+216*x^4-9* x^3-486*x^2-216*x)*log(-4+x)+(7*x-27)*exp(3)^4+(-126*x^3+666*x^2-552*x-504 )*exp(3)^2+315*x^5-1503*x^4+81*x^3+3411*x^2+1512*x)/((9*x-36)*log(-4+x)-63 *x+252),x, algorithm="maxima")
Output:
-x^5 + x^4 + 1/3*x^3*(2*e^6 + 15) - 1/3*x^2*(4*e^6 - 9) - 8/3*((log(x - 4) - 7)*log(log(x - 4) - 7) - log(x - 4)*log(log(x - 4) - 7) - log(x - 4) + 7)*e^6*log(log(x - 4) - 7) + 4/9*e^12*log(x - 4)*log(log(x - 4) - 7) + 8*e ^6*log(x - 4)*log(log(x - 4) - 7) - 28/3*e^6*log(log(x - 4) - 7)^2 - 1/9*x *(e^12 + 18*e^6) - 4/9*((log(x - 4) - 7)*log(log(x - 4) - 7) - log(x - 4) + 7)*e^12 - 8*((log(x - 4) - 7)*log(log(x - 4) - 7) - log(x - 4) + 7)*e^6 - 4/3*(7*log(log(x - 4) - 7)^2 + 2*log(x - 4))*e^6 - 4/9*(e^12 + 12*e^6)*l og(x - 4) + 1/3*(3*x^4 + 6*x^3 - x^2*(2*e^6 - 3) - 2*x*e^6 - 8*e^6*log(x - 4) + 56*e^6)*log(log(x - 4) - 7) - 3*e^12*log(log(x - 4) - 7) - 56*e^6*lo g(log(x - 4) - 7)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (29) = 58\).
Time = 0.17 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} \log \left (\log \left (x - 4\right ) - 7\right ) + x^{4} + \frac {2}{3} \, x^{3} e^{6} + 2 \, x^{3} \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {2}{3} \, x^{2} e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + 5 \, x^{3} - \frac {4}{3} \, x^{2} e^{6} + x^{2} \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {2}{3} \, x e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + 3 \, x^{2} - \frac {1}{9} \, x e^{12} - 2 \, x e^{6} + \frac {1}{9} \, e^{12} \log \left (\log \left (x - 4\right ) - 7\right ) \] Input:
integrate(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*log(-4 +x)+(84*x^2-294*x-168)*exp(3)^2-252*x^4+630*x^3+1386*x^2+504*x)*log(log(-4 +x)-7)+((-x+4)*exp(3)^4+(18*x^3-96*x^2+78*x+72)*exp(3)^2-45*x^5+216*x^4-9* x^3-486*x^2-216*x)*log(-4+x)+(7*x-27)*exp(3)^4+(-126*x^3+666*x^2-552*x-504 )*exp(3)^2+315*x^5-1503*x^4+81*x^3+3411*x^2+1512*x)/((9*x-36)*log(-4+x)-63 *x+252),x, algorithm="giac")
Output:
-x^5 + x^4*log(log(x - 4) - 7) + x^4 + 2/3*x^3*e^6 + 2*x^3*log(log(x - 4) - 7) - 2/3*x^2*e^6*log(log(x - 4) - 7) + 5*x^3 - 4/3*x^2*e^6 + x^2*log(log (x - 4) - 7) - 2/3*x*e^6*log(log(x - 4) - 7) + 3*x^2 - 1/9*x*e^12 - 2*x*e^ 6 + 1/9*e^12*log(log(x - 4) - 7)
Time = 3.01 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.87 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=x^3\,\left (\frac {2\,{\mathrm {e}}^6}{3}+5\right )-x^2\,\left (\frac {4\,{\mathrm {e}}^6}{3}-3\right )-x\,\left (2\,{\mathrm {e}}^6+\frac {{\mathrm {e}}^{12}}{9}\right )-\ln \left (\ln \left (x-4\right )-7\right )\,\left (\frac {2\,x\,{\mathrm {e}}^6}{3}+\frac {x^2\,\left (2\,{\mathrm {e}}^6-3\right )}{3}-2\,x^3-x^4\right )+\frac {\ln \left (\ln \left (x-4\right )-7\right )\,{\mathrm {e}}^{12}}{9}+x^4-x^5 \] Input:
int((1512*x + log(log(x - 4) - 7)*(504*x - exp(6)*(294*x - 84*x^2 + 168) - log(x - 4)*(72*x - exp(6)*(42*x - 12*x^2 + 24) + 198*x^2 + 90*x^3 - 36*x^ 4) + 1386*x^2 + 630*x^3 - 252*x^4) - exp(6)*(552*x - 666*x^2 + 126*x^3 + 5 04) - log(x - 4)*(216*x - exp(6)*(78*x - 96*x^2 + 18*x^3 + 72) + exp(12)*( x - 4) + 486*x^2 + 9*x^3 - 216*x^4 + 45*x^5) + 3411*x^2 + 81*x^3 - 1503*x^ 4 + 315*x^5 + exp(12)*(7*x - 27))/(log(x - 4)*(9*x - 36) - 63*x + 252),x)
Output:
x^3*((2*exp(6))/3 + 5) - x^2*((4*exp(6))/3 - 3) - x*(2*exp(6) + exp(12)/9) - log(log(x - 4) - 7)*((2*x*exp(6))/3 + (x^2*(2*exp(6) - 3))/3 - 2*x^3 - x^4) + (log(log(x - 4) - 7)*exp(12))/9 + x^4 - x^5
Time = 0.19 (sec) , antiderivative size = 121, normalized size of antiderivative = 3.90 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\frac {\mathrm {log}\left (\mathrm {log}\left (x -4\right )-7\right ) e^{12}}{9}-\frac {2 \,\mathrm {log}\left (\mathrm {log}\left (x -4\right )-7\right ) e^{6} x^{2}}{3}-\frac {2 \,\mathrm {log}\left (\mathrm {log}\left (x -4\right )-7\right ) e^{6} x}{3}+\mathrm {log}\left (\mathrm {log}\left (x -4\right )-7\right ) x^{4}+2 \,\mathrm {log}\left (\mathrm {log}\left (x -4\right )-7\right ) x^{3}+\mathrm {log}\left (\mathrm {log}\left (x -4\right )-7\right ) x^{2}-\frac {e^{12} x}{9}+\frac {2 e^{6} x^{3}}{3}-\frac {4 e^{6} x^{2}}{3}-2 e^{6} x -x^{5}+x^{4}+5 x^{3}+3 x^{2} \] Input:
int(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*log(-4+x)+(8 4*x^2-294*x-168)*exp(3)^2-252*x^4+630*x^3+1386*x^2+504*x)*log(log(-4+x)-7) +((-x+4)*exp(3)^4+(18*x^3-96*x^2+78*x+72)*exp(3)^2-45*x^5+216*x^4-9*x^3-48 6*x^2-216*x)*log(-4+x)+(7*x-27)*exp(3)^4+(-126*x^3+666*x^2-552*x-504)*exp( 3)^2+315*x^5-1503*x^4+81*x^3+3411*x^2+1512*x)/((9*x-36)*log(-4+x)-63*x+252 ),x)
Output:
(log(log(x - 4) - 7)*e**12 - 6*log(log(x - 4) - 7)*e**6*x**2 - 6*log(log(x - 4) - 7)*e**6*x + 9*log(log(x - 4) - 7)*x**4 + 18*log(log(x - 4) - 7)*x* *3 + 9*log(log(x - 4) - 7)*x**2 - e**12*x + 6*e**6*x**3 - 12*e**6*x**2 - 1 8*e**6*x - 9*x**5 + 9*x**4 + 45*x**3 + 27*x**2)/9