\(\int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} (6 x^3-4 x^4-6 x^5)+(12 x^8-4 x^9-4 x^{10}+e^{10} (-24 x^3+8 x^4+8 x^5)) \log (3 x-x^2-x^3)}{(e^{24} (-3+x+x^2)+e^{14} (-12 x^5+4 x^6+4 x^7)+e^4 (-12 x^{10}+4 x^{11}+4 x^{12})) \log ^2(3 x-x^2-x^3)} \, dx\) [2785]

Optimal result

Integrand size = 159, antiderivative size = 33 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2}{e^4 \left (\frac {e^{10}}{x^4}+2 x\right ) \log \left (x \left (3-x-x^2\right )\right )} \]

[Out]

2/exp(4)/(exp(5)^2/x^4+2*x)/ln(x*(-x^2-x+3))

Rubi [F]

\[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx \]

[In]

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
^11 + 4*x^12))*Log[3*x - x^2 - x^3]^2),x]

[Out]

(2*(13 + Sqrt[13])*(162 - 31*E^10)*Defer[Int][1/((-1 - Sqrt[13] - 2*x)*Log[x*(3 - x - x^2)]^2), x])/(13*E^4*(9
72 + 122*E^10 - E^20)) + (2*(13 - Sqrt[13])*(162 - 31*E^10)*Defer[Int][1/((-1 + Sqrt[13] - 2*x)*Log[x*(3 - x -
x^2)]^2), x])/(13*E^4*(972 + 122*E^10 - E^20)) + (24*(189 + 5*E^10)*Defer[Int][1/((-1 + Sqrt[13] - 2*x)*Log[x
*(3 - x - x^2)]^2), x])/(Sqrt[13]*E^4*(972 + 122*E^10 - E^20)) + (24*(189 + 5*E^10)*Defer[Int][1/((1 + Sqrt[13
] + 2*x)*Log[x*(3 - x - x^2)]^2), x])/(Sqrt[13]*E^4*(972 + 122*E^10 - E^20)) + ((-2)^(4/5)*(180 - 7*E^10)*Defe
r[Int][1/((E^2 - (-2)^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*(972 + 122*E^10 - E^20)) + ((-2)^(3/5)*E^2*(186
+ E^10)*Defer[Int][1/((E^2 - (-2)^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*(972 + 122*E^10 - E^20)) + ((-2)^(
2/5)*(972 + 244*E^10 - 3*E^20)*Defer[Int][1/((E^2 - (-2)^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^6*(972 + 1
22*E^10 - E^20)) + (4*(189 + 5*E^10)*Defer[Int][1/((-E^2 + (-2)^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^2*(
972 + 122*E^10 - E^20)) + (4*(189 + 5*E^10)*Defer[Int][1/((-E^2 - 2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E
^2*(972 + 122*E^10 - E^20)) + (2*2^(1/5)*(162 - 31*E^10)*Defer[Int][1/((E^2 + 2^(1/5)*x)*Log[x*(3 - x - x^2)]^
2), x])/(5*E^4*(972 + 122*E^10 - E^20)) + (2^(4/5)*(180 - 7*E^10)*Defer[Int][1/((E^2 + 2^(1/5)*x)*Log[x*(3 - x
- x^2)]^2), x])/(5*(972 + 122*E^10 - E^20)) - (2^(3/5)*E^2*(186 + E^10)*Defer[Int][1/((E^2 + 2^(1/5)*x)*Log[x
*(3 - x - x^2)]^2), x])/(5*(972 + 122*E^10 - E^20)) + (2^(2/5)*(972 + 244*E^10 - 3*E^20)*Defer[Int][1/((E^2 +
2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^6*(972 + 122*E^10 - E^20)) + (2*2^(1/5)*(162 - 31*E^10)*Defer[Int
][1/((-((-1)^(1/5)*E^2) + 2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^4*(972 + 122*E^10 - E^20)) + (2*2^(1/5)
*(162 - 31*E^10)*Defer[Int][1/(((-1)^(2/5)*E^2 + 2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^4*(972 + 122*E^1
0 - E^20)) + (2*2^(1/5)*(162 - 31*E^10)*Defer[Int][1/((-((-1)^(3/5)*E^2) + 2^(1/5)*x)*Log[x*(3 - x - x^2)]^2),
x])/(5*E^4*(972 + 122*E^10 - E^20)) + (2*2^(1/5)*(162 - 31*E^10)*Defer[Int][1/(((-1)^(4/5)*E^2 + 2^(1/5)*x)*L
og[x*(3 - x - x^2)]^2), x])/(5*E^4*(972 + 122*E^10 - E^20)) + (4*(189 + 5*E^10)*Defer[Int][1/((-E^2 - (-1)^(2/
5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^2*(972 + 122*E^10 - E^20)) - ((-1)^(3/5)*2^(4/5)*(180 - 7*E^10
)*Defer[Int][1/((E^2 + (-1)^(2/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*(972 + 122*E^10 - E^20)) + ((-1)^
(1/5)*2^(3/5)*E^2*(186 + E^10)*Defer[Int][1/((E^2 + (-1)^(2/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*(972
+ 122*E^10 - E^20)) + ((-1)^(4/5)*2^(2/5)*(972 + 244*E^10 - 3*E^20)*Defer[Int][1/((E^2 + (-1)^(2/5)*2^(1/5)*x
)*Log[x*(3 - x - x^2)]^2), x])/(5*E^6*(972 + 122*E^10 - E^20)) + ((-1)^(2/5)*2^(4/5)*(180 - 7*E^10)*Defer[Int]
[1/((E^2 - (-1)^(3/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*(972 + 122*E^10 - E^20)) - ((-1)^(4/5)*2^(3/5
)*E^2*(186 + E^10)*Defer[Int][1/((E^2 - (-1)^(3/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*(972 + 122*E^10
- E^20)) - ((-1)^(1/5)*2^(2/5)*(972 + 244*E^10 - 3*E^20)*Defer[Int][1/((E^2 - (-1)^(3/5)*2^(1/5)*x)*Log[x*(3 -
x - x^2)]^2), x])/(5*E^6*(972 + 122*E^10 - E^20)) + (4*(189 + 5*E^10)*Defer[Int][1/((-E^2 + (-1)^(3/5)*2^(1/5
)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^2*(972 + 122*E^10 - E^20)) + (4*(189 + 5*E^10)*Defer[Int][1/((-E^2 - (-
1)^(4/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^2*(972 + 122*E^10 - E^20)) - ((-1)^(1/5)*2^(4/5)*(180 -
7*E^10)*Defer[Int][1/((E^2 + (-1)^(4/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*(972 + 122*E^10 - E^20)) -
((-1)^(2/5)*2^(3/5)*E^2*(186 + E^10)*Defer[Int][1/((E^2 + (-1)^(4/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(
5*(972 + 122*E^10 - E^20)) - ((-1)^(3/5)*2^(2/5)*(972 + 244*E^10 - 3*E^20)*Defer[Int][1/((E^2 + (-1)^(4/5)*2^(
1/5)*x)*Log[x*(3 - x - x^2)]^2), x])/(5*E^6*(972 + 122*E^10 - E^20)) + ((-2)^(2/5)*Defer[Int][1/((E^2 - (-2)^(
1/5)*x)*Log[x*(3 - x - x^2)]), x])/(5*E^6) + (2^(2/5)*Defer[Int][1/((E^2 + 2^(1/5)*x)*Log[x*(3 - x - x^2)]), x
])/(5*E^6) + ((-1)^(4/5)*2^(2/5)*Defer[Int][1/((E^2 + (-1)^(2/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]), x])/(5*E^6)
- ((-1)^(1/5)*2^(2/5)*Defer[Int][1/((E^2 - (-1)^(3/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]), x])/(5*E^6) - ((-1)^(
3/5)*2^(2/5)*Defer[Int][1/((E^2 + (-1)^(4/5)*2^(1/5)*x)*Log[x*(3 - x - x^2)]), x])/(5*E^6) + 10*E^6*Defer[Int]
[x^3/((E^10 + 2*x^5)^2*Log[x*(3 - x - x^2)]), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x^3 \left (\left (-3+2 x+3 x^2\right ) \left (e^{10}+2 x^5\right )+2 \left (-3+x+x^2\right ) \left (-2 e^{10}+x^5\right ) \log \left (-x \left (-3+x+x^2\right )\right )\right )}{e^4 \left (3-x-x^2\right ) \left (e^{10}+2 x^5\right )^2 \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx \\ & = \frac {2 \int \frac {x^3 \left (\left (-3+2 x+3 x^2\right ) \left (e^{10}+2 x^5\right )+2 \left (-3+x+x^2\right ) \left (-2 e^{10}+x^5\right ) \log \left (-x \left (-3+x+x^2\right )\right )\right )}{\left (3-x-x^2\right ) \left (e^{10}+2 x^5\right )^2 \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4} \\ & = \frac {2 \int \left (\frac {x^3 \left (-3+2 x+3 x^2\right )}{\left (3-x-x^2\right ) \left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}+\frac {2 x^3 \left (2 e^{10}-x^5\right )}{\left (e^{10}+2 x^5\right )^2 \log \left (x \left (3-x-x^2\right )\right )}\right ) \, dx}{e^4} \\ & = \frac {2 \int \frac {x^3 \left (-3+2 x+3 x^2\right )}{\left (3-x-x^2\right ) \left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4}+\frac {4 \int \frac {x^3 \left (2 e^{10}-x^5\right )}{\left (e^{10}+2 x^5\right )^2 \log \left (x \left (3-x-x^2\right )\right )} \, dx}{e^4} \\ & = \frac {2 \int \left (\frac {6 \left (189+5 e^{10}\right )+\left (162-31 e^{10}\right ) x}{\left (972+122 e^{10}-e^{20}\right ) \left (3-x-x^2\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}+\frac {-2 e^{10} \left (189+5 e^{10}\right )-e^{10} \left (180-7 e^{10}\right ) x-e^{10} \left (186+e^{10}\right ) x^2-\left (972+244 e^{10}-3 e^{20}\right ) x^3+2 \left (162-31 e^{10}\right ) x^4}{\left (972+122 e^{10}-e^{20}\right ) \left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}\right ) \, dx}{e^4}+\frac {4 \int \left (\frac {x^3}{2 \left (-e^{10}-2 x^5\right ) \log \left (x \left (3-x-x^2\right )\right )}+\frac {5 e^{10} x^3}{2 \left (e^{10}+2 x^5\right )^2 \log \left (x \left (3-x-x^2\right )\right )}\right ) \, dx}{e^4} \\ & = \frac {2 \int \frac {x^3}{\left (-e^{10}-2 x^5\right ) \log \left (x \left (3-x-x^2\right )\right )} \, dx}{e^4}+\left (10 e^6\right ) \int \frac {x^3}{\left (e^{10}+2 x^5\right )^2 \log \left (x \left (3-x-x^2\right )\right )} \, dx+\frac {2 \int \frac {6 \left (189+5 e^{10}\right )+\left (162-31 e^{10}\right ) x}{\left (3-x-x^2\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )}+\frac {2 \int \frac {-2 e^{10} \left (189+5 e^{10}\right )-e^{10} \left (180-7 e^{10}\right ) x-e^{10} \left (186+e^{10}\right ) x^2-\left (972+244 e^{10}-3 e^{20}\right ) x^3+2 \left (162-31 e^{10}\right ) x^4}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )} \\ & = \frac {2 \int \left (\frac {(-1)^{2/5}}{5\ 2^{3/5} e^2 \left (e^2-\sqrt [5]{-2} x\right ) \log \left (x \left (3-x-x^2\right )\right )}+\frac {1}{5\ 2^{3/5} e^2 \left (e^2+\sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )}+\frac {(-1)^{4/5}}{5\ 2^{3/5} e^2 \left (e^2+(-1)^{2/5} \sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )}-\frac {\sqrt [5]{-1}}{5\ 2^{3/5} e^2 \left (e^2-(-1)^{3/5} \sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )}-\frac {\left (-\frac {1}{2}\right )^{3/5}}{5 e^2 \left (e^2+(-1)^{4/5} \sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )}\right ) \, dx}{e^4}+\left (10 e^6\right ) \int \frac {x^3}{\left (e^{10}+2 x^5\right )^2 \log \left (x \left (3-x-x^2\right )\right )} \, dx+\frac {2 \int \left (\frac {6 \left (189+5 e^{10}\right )}{\left (3-x-x^2\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}+\frac {\left (162-31 e^{10}\right ) x}{\left (3-x-x^2\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}\right ) \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )}+\frac {2 \int \left (\frac {2 e^{10} \left (-189-5 e^{10}\right )}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}+\frac {e^{10} \left (-180+7 e^{10}\right ) x}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}+\frac {e^{10} \left (-186-e^{10}\right ) x^2}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}+\frac {\left (-972-244 e^{10}+3 e^{20}\right ) x^3}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}+\frac {2 \left (162-31 e^{10}\right ) x^4}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )}\right ) \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )} \\ & = \frac {(-2)^{2/5} \int \frac {1}{\left (e^2-\sqrt [5]{-2} x\right ) \log \left (x \left (3-x-x^2\right )\right )} \, dx}{5 e^6}+\frac {2^{2/5} \int \frac {1}{\left (e^2+\sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )} \, dx}{5 e^6}-\frac {\left (\sqrt [5]{-1} 2^{2/5}\right ) \int \frac {1}{\left (e^2-(-1)^{3/5} \sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )} \, dx}{5 e^6}-\frac {\left ((-1)^{3/5} 2^{2/5}\right ) \int \frac {1}{\left (e^2+(-1)^{4/5} \sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )} \, dx}{5 e^6}+\frac {\left ((-1)^{4/5} 2^{2/5}\right ) \int \frac {1}{\left (e^2+(-1)^{2/5} \sqrt [5]{2} x\right ) \log \left (x \left (3-x-x^2\right )\right )} \, dx}{5 e^6}+\left (10 e^6\right ) \int \frac {x^3}{\left (e^{10}+2 x^5\right )^2 \log \left (x \left (3-x-x^2\right )\right )} \, dx+\frac {\left (2 \left (162-31 e^{10}\right )\right ) \int \frac {x}{\left (3-x-x^2\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )}+\frac {\left (4 \left (162-31 e^{10}\right )\right ) \int \frac {x^4}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )}-\frac {\left (2 e^6 \left (180-7 e^{10}\right )\right ) \int \frac {x}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{972+122 e^{10}-e^{20}}-\frac {\left (2 e^6 \left (186+e^{10}\right )\right ) \int \frac {x^2}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{972+122 e^{10}-e^{20}}+\frac {\left (12 \left (189+5 e^{10}\right )\right ) \int \frac {1}{\left (3-x-x^2\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )}-\frac {\left (4 e^6 \left (189+5 e^{10}\right )\right ) \int \frac {1}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{972+122 e^{10}-e^{20}}-\frac {\left (2 \left (972+244 e^{10}-3 e^{20}\right )\right ) \int \frac {x^3}{\left (e^{10}+2 x^5\right ) \log ^2\left (x \left (3-x-x^2\right )\right )} \, dx}{e^4 \left (972+122 e^{10}-e^{20}\right )} \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.07 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.94 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 x^4}{e^4 \left (e^{10}+2 x^5\right ) \log \left (-x \left (-3+x+x^2\right )\right )} \]

[In]

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]

[Out]

(2*x^4)/(E^4*(E^10 + 2*x^5)*Log[-(x*(-3 + x + x^2))])

Maple [A] (verified)

Time = 6.42 (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	\(\frac {2 x^{4} {\mathrm e}^{-4}}{\left ({\mathrm e}^{10}+2 x^{5}\right ) \ln \left (-x^{3}-x^{2}+3 x \right )}\)	\(39\)

[In]

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^1
0-8*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)

[Out]

2*x^4*exp(-4)/(exp(10)+2*x^5)/ln(-x^3-x^2+3*x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 \, x^{4}}{{\left (2 \, x^{5} e^{4} + e^{14}\right )} \log \left (-x^{3} - x^{2} + 3 \, x\right )} \]

[In]

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)
*exp(4))/log(-x^3-x^2+3*x)^2,x, algorithm="fricas")

[Out]

2*x^4/((2*x^5*e^4 + e^14)*log(-x^3 - x^2 + 3*x))

Sympy [A] (verification not implemented)

Time = 0.13 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.82 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 x^{4}}{\left (2 x^{5} e^{4} + e^{14}\right ) \log {\left (- x^{3} - x^{2} + 3 x \right )}} \]

[In]

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)

[Out]

2*x**4/((2*x**5*exp(4) + exp(14))*log(-x**3 - x**2 + 3*x))

Maxima [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.30 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 \, x^{4}}{{\left (2 \, x^{5} e^{4} + e^{14}\right )} \log \left (-x^{2} - x + 3\right ) + {\left (2 \, x^{5} e^{4} + e^{14}\right )} \log \left (x\right )} \]

[In]

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)
*exp(4))/log(-x^3-x^2+3*x)^2,x, algorithm="maxima")

[Out]

2*x^4/((2*x^5*e^4 + e^14)*log(-x^2 - x + 3) + (2*x^5*e^4 + e^14)*log(x))

Giac [A] (verification not implemented)

none

Time = 0.41 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.45 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2 \, x^{4}}{2 \, x^{5} e^{4} \log \left (-x^{3} - x^{2} + 3 \, x\right ) + e^{14} \log \left (-x^{3} - x^{2} + 3 \, x\right )} \]

[In]

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)
*exp(4))/log(-x^3-x^2+3*x)^2,x, algorithm="giac")

[Out]

2*x^4/(2*x^5*e^4*log(-x^3 - x^2 + 3*x) + e^14*log(-x^3 - x^2 + 3*x))

Mupad [B] (verification not implemented)

Time = 11.57 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03 \[ \int \frac {12 x^8-8 x^9-12 x^{10}+e^{10} \left (6 x^3-4 x^4-6 x^5\right )+\left (12 x^8-4 x^9-4 x^{10}+e^{10} \left (-24 x^3+8 x^4+8 x^5\right )\right ) \log \left (3 x-x^2-x^3\right )}{\left (e^{24} \left (-3+x+x^2\right )+e^{14} \left (-12 x^5+4 x^6+4 x^7\right )+e^4 \left (-12 x^{10}+4 x^{11}+4 x^{12}\right )\right ) \log ^2\left (3 x-x^2-x^3\right )} \, dx=\frac {2\,x^4\,{\mathrm {e}}^{-4}}{\ln \left (-x^3-x^2+3\,x\right )\,\left (2\,x^5+{\mathrm {e}}^{10}\right )} \]

[In]

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)

[Out]

(2*x^4*exp(-4))/(log(3*x - x^2 - x^3)*(exp(10) + 2*x^5))