\(\int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 (-504-552 x+666 x^2-126 x^3)+(e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 (72+78 x-96 x^2+18 x^3)) \log (-4+x)+(504 x+1386 x^2+630 x^3-252 x^4+e^6 (-168-294 x+84 x^2)+(-72 x-198 x^2-90 x^3+36 x^4+e^6 (24+42 x-12 x^2)) \log (-4+x)) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx\) [3753]

Optimal result

Integrand size = 206, antiderivative size = 31 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\left (\frac {e^6}{3}-x-x^2\right )^2 (3-x+\log (-7+\log (-4+x))) \]

[Out]

(3-x+ln(ln(x-4)-7))*(1/3*exp(3)^2-x-x^2)^2

Rubi [F]

\[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx \]

[In]

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]

[Out]

-1/9*(E^6*(18 + E^6)*x) - (3*E^6*x^2)/2 + ((18 + E^6)*x^2)/6 + 3*x^3 + (5*E^6*x^3)/9 + ((18 + E^6)*x^3)/9 + x^
4 - x^5 + E^28*ExpIntegralEi[-4*(7 - Log[-4 + x])] + 2845*E^21*ExpIntegralEi[-3*(7 - Log[-4 + x])] + (E^21*(63
3 - 7*E^6)*ExpIntegralEi[-3*(7 - Log[-4 + x])])/3 + (35*E^21*(60 - E^6)*ExpIntegralEi[-3*(7 - Log[-4 + x])])/3
- (35*E^21*(324 - E^6)*ExpIntegralEi[-3*(7 - Log[-4 + x])])/3 + (7*E^21*(18 + E^6)*ExpIntegralEi[-3*(7 - Log[
-4 + x])])/3 - 416*E^14*ExpIntegralEi[-2*(7 - Log[-4 + x])] + (13*E^14*(633 - 7*E^6)*ExpIntegralEi[-2*(7 - Log
[-4 + x])])/3 + (218*E^14*(60 - E^6)*ExpIntegralEi[-2*(7 - Log[-4 + x])])/3 - (280*E^14*(114 - E^6)*ExpIntegra
lEi[-2*(7 - Log[-4 + x])])/3 + 21*E^14*(168 - E^6)*ExpIntegralEi[-2*(7 - Log[-4 + x])] + 21*E^14*(18 + E^6)*Ex
pIntegralEi[-2*(7 - Log[-4 + x])] + 3*E^14*(56 + 3*E^6)*ExpIntegralEi[-2*(7 - Log[-4 + x])] - 8928*E^7*ExpInte
gralEi[-7 + Log[-4 + x]] - (244*E^7*(60 - E^6)*ExpIntegralEi[-7 + Log[-4 + x]])/3 + (E^7*(633 - 7*E^6)*(168 -
E^6)*ExpIntegralEi[-7 + Log[-4 + x]])/9 + (7*E^7*(60 - E^6)*(18 + E^6)*ExpIntegralEi[-7 + Log[-4 + x]])/9 + 27
*E^7*(56 + 3*E^6)*ExpIntegralEi[-7 + Log[-4 + x]] - (992*(60 - E^6)*Log[7 - Log[-4 + x]])/3 + (4*(633 - 7*E^6)
*(60 - E^6)*Log[7 - Log[-4 + x]])/9 + (60 - E^6)*(56 + 3*E^6)*Log[7 - Log[-4 + x]] + (2*(3 - 2*E^6)*Defer[Int]
[x*Log[-7 + Log[-4 + x]], x])/3 + 6*Defer[Int][x^2*Log[-7 + Log[-4 + x]], x] + 4*Defer[Int][x^3*Log[-7 + Log[-
4 + x]], x] - (2*E^6*Defer[Subst][Defer[Int][Log[-7 + Log[x]], x], x, -4 + x])/3

Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (e^6-3 x-3 x^2\right ) \left (-504 \left (1+\frac {3 e^6}{56}\right )-633 \left (1-\frac {7 e^6}{633}\right ) x+606 x^2-105 x^3+42 \left (-4-7 x+2 x^2\right ) \log (-7+\log (-4+x))-(-4+x) \log (-4+x) \left (18+e^6+27 x-15 x^2+6 (1+2 x) \log (-7+\log (-4+x))\right )\right )}{9 (4-x) (7-\log (-4+x))} \, dx \\ & = \frac {1}{9} \int \frac {\left (e^6-3 x-3 x^2\right ) \left (-504 \left (1+\frac {3 e^6}{56}\right )-633 \left (1-\frac {7 e^6}{633}\right ) x+606 x^2-105 x^3+42 \left (-4-7 x+2 x^2\right ) \log (-7+\log (-4+x))-(-4+x) \log (-4+x) \left (18+e^6+27 x-15 x^2+6 (1+2 x) \log (-7+\log (-4+x))\right )\right )}{(4-x) (7-\log (-4+x))} \, dx \\ & = \frac {1}{9} \int \left (-\frac {9 \left (56+3 e^6\right ) \left (e^6-3 x-3 x^2\right )}{(-4+x) (-7+\log (-4+x))}+\frac {\left (-633+7 e^6\right ) x \left (e^6-3 x-3 x^2\right )}{(-4+x) (-7+\log (-4+x))}-\frac {606 x^2 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))}+\frac {105 x^3 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))}-\frac {18 \left (1+\frac {e^6}{18}\right ) \left (e^6-3 x-3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)}+\frac {27 x \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)}-\frac {15 x^2 \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)}+6 (1+2 x) \left (-e^6+3 x+3 x^2\right ) \log (-7+\log (-4+x))\right ) \, dx \\ & = \frac {2}{3} \int (1+2 x) \left (-e^6+3 x+3 x^2\right ) \log (-7+\log (-4+x)) \, dx-\frac {5}{3} \int \frac {x^2 \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)} \, dx+3 \int \frac {x \left (-e^6+3 x+3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)} \, dx+\frac {35}{3} \int \frac {x^3 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))} \, dx-\frac {202}{3} \int \frac {x^2 \left (-e^6+3 x+3 x^2\right )}{(-4+x) (-7+\log (-4+x))} \, dx+\left (-56-3 e^6\right ) \int \frac {e^6-3 x-3 x^2}{(-4+x) (-7+\log (-4+x))} \, dx+\frac {1}{9} \left (-18-e^6\right ) \int \frac {\left (e^6-3 x-3 x^2\right ) \log (-4+x)}{-7+\log (-4+x)} \, dx+\frac {1}{9} \left (-633+7 e^6\right ) \int \frac {x \left (e^6-3 x-3 x^2\right )}{(-4+x) (-7+\log (-4+x))} \, dx \\ & = \frac {2}{3} \int \left (-e^6 \log (-7+\log (-4+x))-\left (-3+2 e^6\right ) x \log (-7+\log (-4+x))+9 x^2 \log (-7+\log (-4+x))+6 x^3 \log (-7+\log (-4+x))\right ) \, dx-\frac {5}{3} \int \left (x^2 \left (-e^6+3 x+3 x^2\right )+\frac {7 x^2 \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)}\right ) \, dx+3 \int \left (x \left (-e^6+3 x+3 x^2\right )+\frac {7 x \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)}\right ) \, dx+\frac {35}{3} \int \left (-\frac {16 \left (-60+e^6\right )}{-7+\log (-4+x)}-\frac {64 \left (-60+e^6\right )}{(-4+x) (-7+\log (-4+x))}-\frac {4 \left (-60+e^6\right ) x}{-7+\log (-4+x)}-\frac {\left (-60+e^6\right ) x^2}{-7+\log (-4+x)}+\frac {15 x^3}{-7+\log (-4+x)}+\frac {3 x^4}{-7+\log (-4+x)}\right ) \, dx-\frac {202}{3} \int \left (-\frac {4 \left (-60+e^6\right )}{-7+\log (-4+x)}-\frac {16 \left (-60+e^6\right )}{(-4+x) (-7+\log (-4+x))}-\frac {\left (-60+e^6\right ) x}{-7+\log (-4+x)}+\frac {15 x^2}{-7+\log (-4+x)}+\frac {3 x^3}{-7+\log (-4+x)}\right ) \, dx+\left (-56-3 e^6\right ) \int \left (-\frac {15}{-7+\log (-4+x)}+\frac {-60+e^6}{(-4+x) (-7+\log (-4+x))}-\frac {3 x}{-7+\log (-4+x)}\right ) \, dx+\frac {1}{9} \left (-18-e^6\right ) \int \left (e^6-3 x-3 x^2+\frac {7 \left (e^6-3 x-3 x^2\right )}{-7+\log (-4+x)}\right ) \, dx+\frac {1}{9} \left (-633+7 e^6\right ) \int \left (\frac {-168+e^6}{-7+\log (-4+x)}+\frac {4 \left (-60+e^6\right )}{(-4+x) (-7+\log (-4+x))}-\frac {39 (-4+x)}{-7+\log (-4+x)}-\frac {3 (-4+x)^2}{-7+\log (-4+x)}\right ) \, dx \\ & = -\frac {1}{9} e^6 \left (18+e^6\right ) x+\frac {1}{6} \left (18+e^6\right ) x^2+\frac {1}{9} \left (18+e^6\right ) x^3-\frac {5}{3} \int x^2 \left (-e^6+3 x+3 x^2\right ) \, dx+3 \int x \left (-e^6+3 x+3 x^2\right ) \, dx+4 \int x^3 \log (-7+\log (-4+x)) \, dx+6 \int x^2 \log (-7+\log (-4+x)) \, dx-\frac {35}{3} \int \frac {x^2 \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)} \, dx+21 \int \frac {x \left (-e^6+3 x+3 x^2\right )}{-7+\log (-4+x)} \, dx+35 \int \frac {x^4}{-7+\log (-4+x)} \, dx+175 \int \frac {x^3}{-7+\log (-4+x)} \, dx-202 \int \frac {x^3}{-7+\log (-4+x)} \, dx-1010 \int \frac {x^2}{-7+\log (-4+x)} \, dx-\frac {1}{3} \left (2 e^6\right ) \int \log (-7+\log (-4+x)) \, dx+\frac {1}{3} \left (633-7 e^6\right ) \int \frac {(-4+x)^2}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (13 \left (633-7 e^6\right )\right ) \int \frac {-4+x}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (2 \left (3-2 e^6\right )\right ) \int x \log (-7+\log (-4+x)) \, dx+\frac {1}{3} \left (35 \left (60-e^6\right )\right ) \int \frac {x^2}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (140 \left (60-e^6\right )\right ) \int \frac {x}{-7+\log (-4+x)} \, dx-\frac {1}{3} \left (202 \left (60-e^6\right )\right ) \int \frac {x}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (560 \left (60-e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx-\frac {1}{3} \left (808 \left (60-e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx+\frac {1}{3} \left (2240 \left (60-e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx-\frac {1}{3} \left (3232 \left (60-e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx+\frac {1}{9} \left (4 \left (633-7 e^6\right ) \left (60-e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx+\frac {1}{9} \left (\left (633-7 e^6\right ) \left (168-e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx-\frac {1}{9} \left (7 \left (18+e^6\right )\right ) \int \frac {e^6-3 x-3 x^2}{-7+\log (-4+x)} \, dx+\left (3 \left (56+3 e^6\right )\right ) \int \frac {x}{-7+\log (-4+x)} \, dx+\left (15 \left (56+3 e^6\right )\right ) \int \frac {1}{-7+\log (-4+x)} \, dx+\left (\left (60-e^6\right ) \left (56+3 e^6\right )\right ) \int \frac {1}{(-4+x) (-7+\log (-4+x))} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(90\) vs. \(2(31)=62\).

Time = 0.11 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.90 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=\frac {1}{9} \left (-e^6 \left (18+e^6\right ) x-3 \left (-9+4 e^6\right ) x^2+3 \left (15+2 e^6\right ) x^3+9 x^4-9 x^5+e^{12} \log (7-\log (-4+x))-3 x (1+x) \left (2 e^6-3 x-3 x^2\right ) \log (-7+\log (-4+x))\right ) \]

[In]

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 + 3
6*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
]

[Out]

(-(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

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(30)=60\).

Time = 7.64 (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	\(-\frac {x \,{\mathrm e}^{12}}{9}+\frac {{\mathrm e}^{12} \ln \left (\ln \left (x -4\right )-7\right )}{9}+\frac {2 x^{3} {\mathrm e}^{6}}{3}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x^{2}}{3}-x^{5}+\ln \left (\ln \left (x -4\right )-7\right ) x^{4}-\frac {8 \,{\mathrm e}^{12}}{9}-\frac {4 x^{2} {\mathrm e}^{6}}{3}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x}{3}+x^{4}+2 \ln \left (\ln \left (x -4\right )-7\right ) x^{3}-2 x \,{\mathrm e}^{6}+5 x^{3}+\ln \left (\ln \left (x -4\right )-7\right ) x^{2}+\frac {16 \,{\mathrm e}^{6}}{3}+3 x^{2}-48\)	\(142\)
default	\(400-2 x \,{\mathrm e}^{6}-\frac {x \,{\mathrm e}^{12}}{9}+\frac {2 x^{3} {\mathrm e}^{6}}{3}-\frac {4 x^{2} {\mathrm e}^{6}}{3}+400 \ln \left (\ln \left (x -4\right )-7\right )+\frac {4 \,{\mathrm e}^{12}}{9}-\frac {40 \,{\mathrm e}^{6}}{3}+x^{4}+5 x^{3}+3 x^{2}-x^{5}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x}{3}-\frac {2 \,{\mathrm e}^{6} \ln \left (\ln \left (x -4\right )-7\right ) x^{2}}{3}+\frac {{\mathrm e}^{12} \ln \left (\ln \left (x -4\right )-7\right )}{9}+2 \left (\frac {\left (x -4\right )^{2}}{2}+4 x -16\right ) \ln \left (\ln \left (x -4\right )-7\right )+6 \left (\frac {\left (x -4\right )^{3}}{3}+4 \left (x -4\right )^{2}+16 x -64\right ) \ln \left (\ln \left (x -4\right )-7\right )+4 \left (\frac {\left (x -4\right )^{4}}{4}+4 \left (x -4\right )^{3}+24 \left (x -4\right )^{2}+64 x -256\right ) \ln \left (\ln \left (x -4\right )-7\right )\)	\(201\)

[In]

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+315*x^5-1503*x^4+81*x^3+3411*x^2+151
2*x)/((9*x-36)*ln(x-4)-63*x+252),x,method=_RETURNVERBOSE)

[Out]

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)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (29) = 58\).

Time = 0.31 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.45 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} + 5 \, x^{3} + 3 \, x^{2} - \frac {1}{9} \, x e^{12} + \frac {2}{3} \, {\left (x^{3} - 2 \, x^{2} - 3 \, x\right )} e^{6} + \frac {1}{9} \, {\left (9 \, x^{4} + 18 \, x^{3} + 9 \, x^{2} - 6 \, {\left (x^{2} + x\right )} e^{6} + e^{12}\right )} \log \left (\log \left (x - 4\right ) - 7\right ) \]

[In]

integrate(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*log(x-4)+(84*x^2-294*x-168)*exp(3)^2-252*x
^4+630*x^3+1386*x^2+504*x)*log(log(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)*log(x-4)+(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+34
11*x^2+1512*x)/((9*x-36)*log(x-4)-63*x+252),x, algorithm="fricas")

[Out]

-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)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (22) = 44\).

Time = 0.60 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=- x^{5} + x^{4} + x^{3} \cdot \left (5 + \frac {2 e^{6}}{3}\right ) + x^{2} \cdot \left (3 - \frac {4 e^{6}}{3}\right ) + x \left (- \frac {e^{12}}{9} - 2 e^{6}\right ) + \left (x^{4} + 2 x^{3} - \frac {2 x^{2} e^{6}}{3} + x^{2} - \frac {2 x e^{6}}{3} - \frac {1328}{15} + \frac {44 e^{6}}{9}\right ) \log {\left (\log {\left (x - 4 \right )} - 7 \right )} + \frac {\left (- 220 e^{6} + 3984 + 5 e^{12}\right ) \log {\left (\log {\left (x - 4 \right )} - 7 \right )}}{45} \]

[In]

integrate(((((-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+315*x**5
-1503*x**4+81*x**3+3411*x**2+1512*x)/((9*x-36)*ln(x-4)-63*x+252),x)

[Out]

-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
(12))*log(log(x - 4) - 7)/45

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 287 vs. \(2 (29) = 58\).

Time = 0.23 (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 ) \]

[In]

integrate(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*log(x-4)+(84*x^2-294*x-168)*exp(3)^2-252*x
^4+630*x^3+1386*x^2+504*x)*log(log(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)*log(x-4)+(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+34
11*x^2+1512*x)/((9*x-36)*log(x-4)-63*x+252),x, algorithm="maxima")

[Out]

-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)*log(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*log(log(x - 4) - 7)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (29) = 58\).

Time = 0.31 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=-x^{5} + x^{4} \log \left (\log \left (x - 4\right ) - 7\right ) + x^{4} + \frac {2}{3} \, x^{3} e^{6} + 2 \, x^{3} \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {2}{3} \, x^{2} e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + 5 \, x^{3} - \frac {4}{3} \, x^{2} e^{6} + x^{2} \log \left (\log \left (x - 4\right ) - 7\right ) - \frac {2}{3} \, x e^{6} \log \left (\log \left (x - 4\right ) - 7\right ) + 3 \, x^{2} - \frac {1}{9} \, x e^{12} - 2 \, x e^{6} + \frac {1}{9} \, e^{12} \log \left (\log \left (x - 4\right ) - 7\right ) \]

[In]

integrate(((((-12*x^2+42*x+24)*exp(3)^2+36*x^4-90*x^3-198*x^2-72*x)*log(x-4)+(84*x^2-294*x-168)*exp(3)^2-252*x
^4+630*x^3+1386*x^2+504*x)*log(log(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)*log(x-4)+(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+34
11*x^2+1512*x)/((9*x-36)*log(x-4)-63*x+252),x, algorithm="giac")

[Out]

-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)

Mupad [B] (verification not implemented)

Time = 9.32 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.87 \[ \int \frac {1512 x+3411 x^2+81 x^3-1503 x^4+315 x^5+e^{12} (-27+7 x)+e^6 \left (-504-552 x+666 x^2-126 x^3\right )+\left (e^{12} (4-x)-216 x-486 x^2-9 x^3+216 x^4-45 x^5+e^6 \left (72+78 x-96 x^2+18 x^3\right )\right ) \log (-4+x)+\left (504 x+1386 x^2+630 x^3-252 x^4+e^6 \left (-168-294 x+84 x^2\right )+\left (-72 x-198 x^2-90 x^3+36 x^4+e^6 \left (24+42 x-12 x^2\right )\right ) \log (-4+x)\right ) \log (-7+\log (-4+x))}{252-63 x+(-36+9 x) \log (-4+x)} \, dx=x^3\,\left (\frac {2\,{\mathrm {e}}^6}{3}+5\right )-x^2\,\left (\frac {4\,{\mathrm {e}}^6}{3}-3\right )-x\,\left (2\,{\mathrm {e}}^6+\frac {{\mathrm {e}}^{12}}{9}\right )-\ln \left (\ln \left (x-4\right )-7\right )\,\left (\frac {2\,x\,{\mathrm {e}}^6}{3}+\frac {x^2\,\left (2\,{\mathrm {e}}^6-3\right )}{3}-2\,x^3-x^4\right )+\frac {\ln \left (\ln \left (x-4\right )-7\right )\,{\mathrm {e}}^{12}}{9}+x^4-x^5 \]

[In]

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 - 1
2*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 +
504) - 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)

[Out]

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