\(\int \frac {-27+3 e^{256}-36 x^3+(27-3 e^{256}+9 x-18 x^3) \log (x)+(-27+3 e^{256}-9 x+18 x^3) \log (\frac {1}{3} (-9+e^{256}-3 x+6 x^3))}{(-9+e^{256}-3 x+6 x^3) \log ^2(x)+(18-2 e^{256}+6 x-12 x^3) \log (x) \log (\frac {1}{3} (-9+e^{256}-3 x+6 x^3))+(-9+e^{256}-3 x+6 x^3) \log ^2(\frac {1}{3} (-9+e^{256}-3 x+6 x^3))} \, dx\) [6657]

Optimal result

Integrand size = 156, antiderivative size = 28 \[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=\frac {3 x}{-\log (x)+\log \left (-3+\frac {e^{256}}{3}-x+2 x^3\right )} \]

[Out]

3/(ln(1/3*exp(256)+2*x^3-x-3)-ln(x))*x

Rubi [F]

\[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=\int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx \]

[In]

Int[(-27 + 3*E^256 - 36*x^3 + (27 - 3*E^256 + 9*x - 18*x^3)*Log[x] + (-27 + 3*E^256 - 9*x + 18*x^3)*Log[(-9 +
E^256 - 3*x + 6*x^3)/3])/((-9 + E^256 - 3*x + 6*x^3)*Log[x]^2 + (18 - 2*E^256 + 6*x - 12*x^3)*Log[x]*Log[(-9 +
E^256 - 3*x + 6*x^3)/3] + (-9 + E^256 - 3*x + 6*x^3)*Log[(-9 + E^256 - 3*x + 6*x^3)/3]^2),x]

[Out]

-6*Defer[Int][(Log[3] + Log[x] - Log[-9 + E^256 - 3*x + 6*x^3])^(-2), x] - 9*(9 - E^256)*Defer[Int][1/((-9 + E
^256 - 3*x + 6*x^3)*(Log[3] + Log[x] - Log[-9 + E^256 - 3*x + 6*x^3])^2), x] - 18*Defer[Int][x/((-9 + E^256 -
3*x + 6*x^3)*(Log[3] + Log[x] - Log[-9 + E^256 - 3*x + 6*x^3])^2), x] - 3*Defer[Int][Log[x]/(Log[3] + Log[x] -
Log[-9 + E^256 - 3*x + 6*x^3])^2, x] + 3*Defer[Int][Log[(-9 + E^256 - 3*x + 6*x^3)/3]/(Log[3] + Log[x] - Log[
-9 + E^256 - 3*x + 6*x^3])^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {3 \left (9 \left (1-\frac {e^{256}}{9}\right )+12 x^3+\left (-9+e^{256}-3 x+6 x^3\right ) \log (x)-\left (-9+e^{256}-3 x+6 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )\right )}{\left (9-e^{256}+3 x-6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx \\ & = 3 \int \frac {9 \left (1-\frac {e^{256}}{9}\right )+12 x^3+\left (-9+e^{256}-3 x+6 x^3\right ) \log (x)-\left (-9+e^{256}-3 x+6 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (9-e^{256}+3 x-6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx \\ & = 3 \int \left (\frac {-9+e^{256}}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {12 x^3}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {9 \left (1-\frac {e^{256}}{9}\right ) \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {3 x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {6 x^3 \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {9 \left (1-\frac {e^{256}}{9}\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {3 x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {6 x^3 \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx \\ & = 9 \int \frac {x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-9 \int \frac {x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-18 \int \frac {x^3 \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+18 \int \frac {x^3 \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-36 \int \frac {x^3}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx \\ & = 9 \int \frac {x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-9 \int \frac {x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-18 \int \left (\frac {\log (x)}{6 \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {\left (-9+e^{256}-3 x\right ) \log (x)}{6 \left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx+18 \int \left (\frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{6 \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {\left (-9+e^{256}-3 x\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{6 \left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx-36 \int \left (\frac {1}{6 \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {9-e^{256}+3 x}{6 \left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx \\ & = -\left (3 \int \frac {\log (x)}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\right )+3 \int \frac {\left (-9+e^{256}-3 x\right ) \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+3 \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-3 \int \frac {\left (-9+e^{256}-3 x\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-6 \int \frac {1}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-6 \int \frac {9-e^{256}+3 x}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+9 \int \frac {x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-9 \int \frac {x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx \\ & = 3 \int \left (-\frac {9 \left (1-\frac {e^{256}}{9}\right ) \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {3 x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx-3 \int \left (-\frac {9 \left (1-\frac {e^{256}}{9}\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {3 x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx-3 \int \frac {\log (x)}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+3 \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-6 \int \left (\frac {9 \left (1-\frac {e^{256}}{9}\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {3 x}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx-6 \int \frac {1}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+9 \int \frac {x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-9 \int \frac {x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx \\ & = -\left (3 \int \frac {\log (x)}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\right )+3 \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-6 \int \frac {1}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-18 \int \frac {x}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (6 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.30 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=-\frac {3 x}{\log (3 x)-\log \left (-9+e^{256}-3 x+6 x^3\right )} \]

[In]

Integrate[(-27 + 3*E^256 - 36*x^3 + (27 - 3*E^256 + 9*x - 18*x^3)*Log[x] + (-27 + 3*E^256 - 9*x + 18*x^3)*Log[
(-9 + E^256 - 3*x + 6*x^3)/3])/((-9 + E^256 - 3*x + 6*x^3)*Log[x]^2 + (18 - 2*E^256 + 6*x - 12*x^3)*Log[x]*Log
[(-9 + E^256 - 3*x + 6*x^3)/3] + (-9 + E^256 - 3*x + 6*x^3)*Log[(-9 + E^256 - 3*x + 6*x^3)/3]^2),x]

[Out]

(-3*x)/(Log[3*x] - Log[-9 + E^256 - 3*x + 6*x^3])

Maple [A] (verified)

Time = 4.16 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93

method	result	size
default	\(-\frac {3 x}{\ln \left (x \right )+\ln \left (3\right )-\ln \left ({\mathrm e}^{256}+6 x^{3}-3 x -9\right )}\)	\(26\)
risch	\(-\frac {3 x}{\ln \left (x \right )-\ln \left (\frac {{\mathrm e}^{256}}{3}+2 x^{3}-x -3\right )}\)	\(26\)
parallelrisch	\(-\frac {3 x}{\ln \left (x \right )-\ln \left (\frac {{\mathrm e}^{256}}{3}+2 x^{3}-x -3\right )}\)	\(26\)

[In]

int(((3*exp(256)+18*x^3-9*x-27)*ln(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*ln(x)+3*exp(256)-36*x^3
-27)/((exp(256)+6*x^3-3*x-9)*ln(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*ln(x)*ln(1/3*exp(256)+2*
x^3-x-3)+(exp(256)+6*x^3-3*x-9)*ln(x)^2),x,method=_RETURNVERBOSE)

[Out]

-3*x/(ln(x)+ln(3)-ln(exp(256)+6*x^3-3*x-9))

Fricas [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=\frac {3 \, x}{\log \left (2 \, x^{3} - x + \frac {1}{3} \, e^{256} - 3\right ) - \log \left (x\right )} \]

[In]

integrate(((3*exp(256)+18*x^3-9*x-27)*log(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*log(x)+3*exp(256
)-36*x^3-27)/((exp(256)+6*x^3-3*x-9)*log(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*log(x)*log(1/3*
exp(256)+2*x^3-x-3)+(exp(256)+6*x^3-3*x-9)*log(x)^2),x, algorithm="fricas")

[Out]

3*x/(log(2*x^3 - x + 1/3*e^256 - 3) - log(x))

Sympy [A] (verification not implemented)

Time = 0.15 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.71 \[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=\frac {3 x}{- \log {\left (x \right )} + \log {\left (2 x^{3} - x - 3 + \frac {e^{256}}{3} \right )}} \]

[In]

integrate(((3*exp(256)+18*x**3-9*x-27)*ln(1/3*exp(256)+2*x**3-x-3)+(-3*exp(256)-18*x**3+9*x+27)*ln(x)+3*exp(25
6)-36*x**3-27)/((exp(256)+6*x**3-3*x-9)*ln(1/3*exp(256)+2*x**3-x-3)**2+(-2*exp(256)-12*x**3+6*x+18)*ln(x)*ln(1
/3*exp(256)+2*x**3-x-3)+(exp(256)+6*x**3-3*x-9)*ln(x)**2),x)

[Out]

3*x/(-log(x) + log(2*x**3 - x - 3 + exp(256)/3))

Maxima [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=-\frac {3 \, x}{\log \left (3\right ) - \log \left (6 \, x^{3} - 3 \, x + e^{256} - 9\right ) + \log \left (x\right )} \]

[In]

integrate(((3*exp(256)+18*x^3-9*x-27)*log(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*log(x)+3*exp(256
)-36*x^3-27)/((exp(256)+6*x^3-3*x-9)*log(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*log(x)*log(1/3*
exp(256)+2*x^3-x-3)+(exp(256)+6*x^3-3*x-9)*log(x)^2),x, algorithm="maxima")

[Out]

-3*x/(log(3) - log(6*x^3 - 3*x + e^256 - 9) + log(x))

Giac [F(-2)]

Exception generated. \[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((3*exp(256)+18*x^3-9*x-27)*log(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*log(x)+3*exp(256
)-36*x^3-27)/((exp(256)+6*x^3-3*x-9)*log(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*log(x)*log(1/3*
exp(256)+2*x^3-x-3)+(exp(256)+6*x^3-3*x-9)*log(x)^2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> an error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Francis algorithm failure for[-1.0,0.0,1.23157876138e+243,undef]proot error [1.0,-0.0,-1.23157876138e+243,u
ndef]Franci

Mupad [B] (verification not implemented)

Time = 12.39 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx=\frac {3\,x}{\ln \left (2\,x^3-x+\frac {{\mathrm {e}}^{256}}{3}-3\right )-\ln \left (x\right )} \]

[In]

int((log(exp(256)/3 - x + 2*x^3 - 3)*(9*x - 3*exp(256) - 18*x^3 + 27) - 3*exp(256) - log(x)*(9*x - 3*exp(256)
- 18*x^3 + 27) + 36*x^3 + 27)/(log(exp(256)/3 - x + 2*x^3 - 3)^2*(3*x - exp(256) - 6*x^3 + 9) + log(x)^2*(3*x
- exp(256) - 6*x^3 + 9) - log(exp(256)/3 - x + 2*x^3 - 3)*log(x)*(6*x - 2*exp(256) - 12*x^3 + 18)),x)

[Out]

(3*x)/(log(exp(256)/3 - x + 2*x^3 - 3) - log(x))