Integrand size = 159, antiderivative size = 33 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2}{e^4 \left (\frac {e^{10}}{x^4}+2 x\right ) \log \left (x \left (3-x-x^2\right )\right )} \] Output:
2/exp(4)/(exp(5)^2/x^4+2*x)/ln(x*(-x^2-x+3))
Time = 0.05 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.94 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 x^4}{e^4 \left (e^{10}+2 x^5\right ) \log \left (-x \left (-3+x+x^2\right )\right )} \] Input:
Integrate[(12*x^8 - 8*x^9 - 12*x^10 + E^10*(6*x^3 - 4*x^4 - 6*x^5) + (12*x ^8 - 4*x^9 - 4*x^10 + E^10*(-24*x^3 + 8*x^4 + 8*x^5))*Log[3*x - x^2 - x^3] )/((E^24*(-3 + x + x^2) + E^14*(-12*x^5 + 4*x^6 + 4*x^7) + E^4*(-12*x^10 + 4*x^11 + 4*x^12))*Log[3*x - x^2 - x^3]^2),x]
Output:
(2*x^4)/(E^4*(E^10 + 2*x^5)*Log[-(x*(-3 + x + 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.
| \(\displaystyle \int \frac {-12 x^{10}-8 x^9+12 x^8+e^{10} \left (-6 x^5-4 x^4+6 x^3\right )+\left (-4 x^{10}-4 x^9+12 x^8+e^{10} \left (8 x^5+8 x^4-24 x^3\right )\right ) \log \left (-x^3-x^2+3 x\right )}{\left (e^{24} \left (x^2+x-3\right )+e^4 \left (4 x^{12}+4 x^{11}-12 x^{10}\right )+e^{14} \left (4 x^7+4 x^6-12 x^5\right )\right ) \log ^2\left (-x^3-x^2+3 x\right )} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (-76 \left (61-e^{10}\right ) x-e^{20}+160 e^{10}-10732\right ) \left (-12 x^{10}-8 x^9+12 x^8+e^{10} \left (-6 x^5-4 x^4+6 x^3\right )+\left (-4 x^{10}-4 x^9+12 x^8+e^{10} \left (8 x^5+8 x^4-24 x^3\right )\right ) \log \left (-x^3-x^2+3 x\right )\right )}{e^4 \left (972+122 e^{10}-e^{20}\right )^2 \left (-x^2-x+3\right ) \log ^2\left (-x^3-x^2+3 x\right )}+\frac {2 \left (-76 \left (61-e^{10}\right ) x^4-\left (6096-84 e^{10}+e^{20}\right ) x^3-\left (7812-144 e^{10}-e^{20}\right ) x^2-4 \left (2619-27 e^{10}+e^{20}\right ) x+7 e^{20}+324 e^{10}-12960\right ) \left (-12 x^{10}-8 x^9+12 x^8+e^{10} \left (-6 x^5-4 x^4+6 x^3\right )+\left (-4 x^{10}-4 x^9+12 x^8+e^{10} \left (8 x^5+8 x^4-24 x^3\right )\right ) \log \left (-x^3-x^2+3 x\right )\right )}{e^4 \left (972+122 e^{10}-e^{20}\right )^2 \left (2 x^5+e^{10}\right ) \log ^2\left (-x^3-x^2+3 x\right )}+\frac {2 \left (-38 x^4-\left (42-e^{10}\right ) x^3-\left (72+e^{10}\right ) x^2-2 \left (27-2 e^{10}\right ) x-7 e^{10}-162\right ) \left (-12 x^{10}-8 x^9+12 x^8+e^{10} \left (-6 x^5-4 x^4+6 x^3\right )+\left (-4 x^{10}-4 x^9+12 x^8+e^{10} \left (8 x^5+8 x^4-24 x^3\right )\right ) \log \left (-x^3-x^2+3 x\right )\right )}{e^4 \left (972+122 e^{10}-e^{20}\right ) \left (2 x^5+e^{10}\right )^2 \log ^2\left (-x^3-x^2+3 x\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^3 \left (\left (3 x^2+2 x-3\right ) \left (2 x^5+e^{10}\right )+2 \left (x^2+x-3\right ) \left (x^5-2 e^{10}\right ) \log \left (-x \left (x^2+x-3\right )\right )\right )}{e^4 \left (-x^2-x+3\right ) \left (2 x^5+e^{10}\right )^2 \log ^2\left (x \left (-x^2-x+3\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2 \int -\frac {x^3 \left (\left (-3 x^2-2 x+3\right ) \left (2 x^5+e^{10}\right )-2 \left (-x^2-x+3\right ) \left (2 e^{10}-x^5\right ) \log \left (x \left (-x^2-x+3\right )\right )\right )}{\left (-x^2-x+3\right ) \left (2 x^5+e^{10}\right )^2 \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{e^4}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {2 \int \frac {x^3 \left (\left (-3 x^2-2 x+3\right ) \left (2 x^5+e^{10}\right )-2 \left (-x^2-x+3\right ) \left (2 e^{10}-x^5\right ) \log \left (x \left (-x^2-x+3\right )\right )\right )}{\left (-x^2-x+3\right ) \left (2 x^5+e^{10}\right )^2 \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{e^4}\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -\frac {2 \int \left (\frac {2 \left (x^5-2 e^{10}\right ) x^3}{\left (2 x^5+e^{10}\right )^2 \log \left (x \left (-x^2-x+3\right )\right )}+\frac {\left (-3 x^2-2 x+3\right ) x^3}{\left (-x^2-x+3\right ) \left (2 x^5+e^{10}\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}\right )dx}{e^4}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {2 \left (-\frac {\left (13+\sqrt {13}\right ) \left (162-31 e^{10}\right ) \int \frac {1}{\left (-2 x-\sqrt {13}-1\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{13 \left (972+122 e^{10}-e^{20}\right )}-\frac {12 \left (189+5 e^{10}\right ) \int \frac {1}{\left (-2 x+\sqrt {13}-1\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{\sqrt {13} \left (972+122 e^{10}-e^{20}\right )}-\frac {\left (13-\sqrt {13}\right ) \left (162-31 e^{10}\right ) \int \frac {1}{\left (-2 x+\sqrt {13}-1\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{13 \left (972+122 e^{10}-e^{20}\right )}-\frac {12 \left (189+5 e^{10}\right ) \int \frac {1}{\left (2 x+\sqrt {13}+1\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{\sqrt {13} \left (972+122 e^{10}-e^{20}\right )}-\frac {(-1)^{2/5} \left (972+244 e^{10}-3 e^{20}\right ) \int \frac {1}{\left (e^2-\sqrt [5]{-2} x\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2 \left (972+122 e^{10}-e^{20}\right )}-\frac {(-1)^{3/5} e^6 \left (186+e^{10}\right ) \int \frac {1}{\left (e^2-\sqrt [5]{-2} x\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{2/5} \left (972+122 e^{10}-e^{20}\right )}-\frac {(-1)^{4/5} e^4 \left (180-7 e^{10}\right ) \int \frac {1}{\left (e^2-\sqrt [5]{-2} x\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \sqrt [5]{2} \left (972+122 e^{10}-e^{20}\right )}-\frac {2 e^2 \left (189+5 e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{-2} x-e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {2 e^2 \left (189+5 e^{10}\right ) \int \frac {1}{\left (-\sqrt [5]{2} x-e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {\left (972+244 e^{10}-3 e^{20}\right ) \int \frac {1}{\left (\sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2 \left (972+122 e^{10}-e^{20}\right )}+\frac {e^6 \left (186+e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{2/5} \left (972+122 e^{10}-e^{20}\right )}-\frac {e^4 \left (180-7 e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \sqrt [5]{2} \left (972+122 e^{10}-e^{20}\right )}-\frac {\sqrt [5]{2} \left (162-31 e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {\sqrt [5]{2} \left (162-31 e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{2} x-\sqrt [5]{-1} e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {\sqrt [5]{2} \left (162-31 e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{2} x+(-1)^{2/5} e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {\sqrt [5]{2} \left (162-31 e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{2} x-(-1)^{3/5} e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {\sqrt [5]{2} \left (162-31 e^{10}\right ) \int \frac {1}{\left (\sqrt [5]{2} x+(-1)^{4/5} e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {2 e^2 \left (189+5 e^{10}\right ) \int \frac {1}{\left (-(-1)^{2/5} \sqrt [5]{2} x-e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {(-1)^{4/5} \left (972+244 e^{10}-3 e^{20}\right ) \int \frac {1}{\left ((-1)^{2/5} \sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2 \left (972+122 e^{10}-e^{20}\right )}-\frac {\sqrt [5]{-1} e^6 \left (186+e^{10}\right ) \int \frac {1}{\left ((-1)^{2/5} \sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{2/5} \left (972+122 e^{10}-e^{20}\right )}+\frac {(-1)^{3/5} e^4 \left (180-7 e^{10}\right ) \int \frac {1}{\left ((-1)^{2/5} \sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \sqrt [5]{2} \left (972+122 e^{10}-e^{20}\right )}+\frac {\sqrt [5]{-1} \left (972+244 e^{10}-3 e^{20}\right ) \int \frac {1}{\left (e^2-(-1)^{3/5} \sqrt [5]{2} x\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2 \left (972+122 e^{10}-e^{20}\right )}+\frac {(-1)^{4/5} e^6 \left (186+e^{10}\right ) \int \frac {1}{\left (e^2-(-1)^{3/5} \sqrt [5]{2} x\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{2/5} \left (972+122 e^{10}-e^{20}\right )}-\frac {(-1)^{2/5} e^4 \left (180-7 e^{10}\right ) \int \frac {1}{\left (e^2-(-1)^{3/5} \sqrt [5]{2} x\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \sqrt [5]{2} \left (972+122 e^{10}-e^{20}\right )}-\frac {2 e^2 \left (189+5 e^{10}\right ) \int \frac {1}{\left ((-1)^{3/5} \sqrt [5]{2} x-e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {2 e^2 \left (189+5 e^{10}\right ) \int \frac {1}{\left (-(-1)^{4/5} \sqrt [5]{2} x-e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}+\frac {\left (-\frac {1}{2}\right )^{3/5} \left (972+244 e^{10}-3 e^{20}\right ) \int \frac {1}{\left ((-1)^{4/5} \sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 e^2 \left (972+122 e^{10}-e^{20}\right )}+\frac {\left (-\frac {1}{2}\right )^{2/5} e^6 \left (186+e^{10}\right ) \int \frac {1}{\left ((-1)^{4/5} \sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}+\frac {\sqrt [5]{-\frac {1}{2}} e^4 \left (180-7 e^{10}\right ) \int \frac {1}{\left ((-1)^{4/5} \sqrt [5]{2} x+e^2\right ) \log ^2\left (x \left (-x^2-x+3\right )\right )}dx}{5 \left (972+122 e^{10}-e^{20}\right )}-\frac {(-1)^{2/5} \int \frac {1}{\left (e^2-\sqrt [5]{-2} x\right ) \log \left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2}-\frac {\int \frac {1}{\left (\sqrt [5]{2} x+e^2\right ) \log \left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2}-\frac {(-1)^{4/5} \int \frac {1}{\left ((-1)^{2/5} \sqrt [5]{2} x+e^2\right ) \log \left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2}+\frac {\sqrt [5]{-1} \int \frac {1}{\left (e^2-(-1)^{3/5} \sqrt [5]{2} x\right ) \log \left (x \left (-x^2-x+3\right )\right )}dx}{5\ 2^{3/5} e^2}+\frac {\left (-\frac {1}{2}\right )^{3/5} \int \frac {1}{\left ((-1)^{4/5} \sqrt [5]{2} x+e^2\right ) \log \left (x \left (-x^2-x+3\right )\right )}dx}{5 e^2}-5 e^{10} \int \frac {x^3}{\left (2 x^5+e^{10}\right )^2 \log \left (x \left (-x^2-x+3\right )\right )}dx\right )}{e^4}\) |
Input:
Int[(12*x^8 - 8*x^9 - 12*x^10 + E^10*(6*x^3 - 4*x^4 - 6*x^5) + (12*x^8 - 4 *x^9 - 4*x^10 + E^10*(-24*x^3 + 8*x^4 + 8*x^5))*Log[3*x - x^2 - x^3])/((E^ 24*(-3 + x + x^2) + E^14*(-12*x^5 + 4*x^6 + 4*x^7) + E^4*(-12*x^10 + 4*x^1 1 + 4*x^12))*Log[3*x - x^2 - x^3]^2),x]
Output:
$Aborted
Time = 5.67 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06
| method | result | size |
| risch | \(\frac {2 x^{4} {\mathrm e}^{-4}}{\left ({\mathrm e}^{10}+2 x^{5}\right ) \ln \left (-x^{3}-x^{2}+3 x \right )}\) | \(35\) |
| parallelrisch | \(\frac {2 x^{4} {\mathrm e}^{-4}}{\left ({\mathrm e}^{10}+2 x^{5}\right ) \ln \left (-x^{3}-x^{2}+3 x \right )}\) | \(39\) |
Input:
int((((8*x^5+8*x^4-24*x^3)*exp(5)^2-4*x^10-4*x^9+12*x^8)*ln(-x^3-x^2+3*x)+ (-6*x^5-4*x^4+6*x^3)*exp(5)^2-12*x^10-8*x^9+12*x^8)/((x^2+x-3)*exp(4)*exp( 5)^4+(4*x^7+4*x^6-12*x^5)*exp(4)*exp(5)^2+(4*x^12+4*x^11-12*x^10)*exp(4))/ ln(-x^3-x^2+3*x)^2,x,method=_RETURNVERBOSE)
Output:
2*x^4*exp(-4)/(exp(10)+2*x^5)/ln(-x^3-x^2+3*x)
Time = 0.08 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 \, x^{4}}{{\left (2 \, x^{5} e^{4} + e^{14}\right )} \log \left (-x^{3} - x^{2} + 3 \, x\right )} \] Input:
integrate((((8*x^5+8*x^4-24*x^3)*exp(5)^2-4*x^10-4*x^9+12*x^8)*log(-x^3-x^ 2+3*x)+(-6*x^5-4*x^4+6*x^3)*exp(5)^2-12*x^10-8*x^9+12*x^8)/((x^2+x-3)*exp( 4)*exp(5)^4+(4*x^7+4*x^6-12*x^5)*exp(4)*exp(5)^2+(4*x^12+4*x^11-12*x^10)*e xp(4))/log(-x^3-x^2+3*x)^2,x, algorithm="fricas")
Output:
2*x^4/((2*x^5*e^4 + e^14)*log(-x^3 - x^2 + 3*x))
Time = 0.12 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.82 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 x^{4}}{\left (2 x^{5} e^{4} + e^{14}\right ) \log {\left (- x^{3} - x^{2} + 3 x \right )}} \] Input:
integrate((((8*x**5+8*x**4-24*x**3)*exp(5)**2-4*x**10-4*x**9+12*x**8)*ln(- x**3-x**2+3*x)+(-6*x**5-4*x**4+6*x**3)*exp(5)**2-12*x**10-8*x**9+12*x**8)/ ((x**2+x-3)*exp(4)*exp(5)**4+(4*x**7+4*x**6-12*x**5)*exp(4)*exp(5)**2+(4*x **12+4*x**11-12*x**10)*exp(4))/ln(-x**3-x**2+3*x)**2,x)
Output:
2*x**4/((2*x**5*exp(4) + exp(14))*log(-x**3 - x**2 + 3*x))
Time = 0.10 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.30 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 \, x^{4}}{{\left (2 \, x^{5} e^{4} + e^{14}\right )} \log \left (-x^{2} - x + 3\right ) + {\left (2 \, x^{5} e^{4} + e^{14}\right )} \log \left (x\right )} \] Input:
integrate((((8*x^5+8*x^4-24*x^3)*exp(5)^2-4*x^10-4*x^9+12*x^8)*log(-x^3-x^ 2+3*x)+(-6*x^5-4*x^4+6*x^3)*exp(5)^2-12*x^10-8*x^9+12*x^8)/((x^2+x-3)*exp( 4)*exp(5)^4+(4*x^7+4*x^6-12*x^5)*exp(4)*exp(5)^2+(4*x^12+4*x^11-12*x^10)*e xp(4))/log(-x^3-x^2+3*x)^2,x, algorithm="maxima")
Output:
2*x^4/((2*x^5*e^4 + e^14)*log(-x^2 - x + 3) + (2*x^5*e^4 + e^14)*log(x))
Time = 0.28 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.45 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 \, x^{4}}{2 \, x^{5} e^{4} \log \left (-x^{3} - x^{2} + 3 \, x\right ) + e^{14} \log \left (-x^{3} - x^{2} + 3 \, x\right )} \] Input:
integrate((((8*x^5+8*x^4-24*x^3)*exp(5)^2-4*x^10-4*x^9+12*x^8)*log(-x^3-x^ 2+3*x)+(-6*x^5-4*x^4+6*x^3)*exp(5)^2-12*x^10-8*x^9+12*x^8)/((x^2+x-3)*exp( 4)*exp(5)^4+(4*x^7+4*x^6-12*x^5)*exp(4)*exp(5)^2+(4*x^12+4*x^11-12*x^10)*e xp(4))/log(-x^3-x^2+3*x)^2,x, algorithm="giac")
Output:
2*x^4/(2*x^5*e^4*log(-x^3 - x^2 + 3*x) + e^14*log(-x^3 - x^2 + 3*x))
Time = 3.37 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2\,x^4\,{\mathrm {e}}^{-4}}{\ln \left (-x^3-x^2+3\,x\right )\,\left (2\,x^5+{\mathrm {e}}^{10}\right )} \] Input:
int(-(exp(10)*(4*x^4 - 6*x^3 + 6*x^5) - log(3*x - x^2 - x^3)*(exp(10)*(8*x ^4 - 24*x^3 + 8*x^5) + 12*x^8 - 4*x^9 - 4*x^10) - 12*x^8 + 8*x^9 + 12*x^10 )/(log(3*x - x^2 - x^3)^2*(exp(24)*(x + x^2 - 3) + exp(14)*(4*x^6 - 12*x^5 + 4*x^7) + exp(4)*(4*x^11 - 12*x^10 + 4*x^12))),x)
Output:
(2*x^4*exp(-4))/(log(3*x - x^2 - x^3)*(exp(10) + 2*x^5))
Time = 0.20 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.09 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 x^{4}}{\mathrm {log}\left (-x^{3}-x^{2}+3 x \right ) e^{4} \left (e^{10}+2 x^{5}\right )} \] Input:
int((((8*x^5+8*x^4-24*x^3)*exp(5)^2-4*x^10-4*x^9+12*x^8)*log(-x^3-x^2+3*x) +(-6*x^5-4*x^4+6*x^3)*exp(5)^2-12*x^10-8*x^9+12*x^8)/((x^2+x-3)*exp(4)*exp (5)^4+(4*x^7+4*x^6-12*x^5)*exp(4)*exp(5)^2+(4*x^12+4*x^11-12*x^10)*exp(4)) /log(-x^3-x^2+3*x)^2,x)
Output:
(2*x**4)/(log( - x**3 - x**2 + 3*x)*e**4*(e**10 + 2*x**5))