Integrand size = 133, antiderivative size = 27 \[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=e^{2 e^{\frac {1}{3} \left (-3+\log \left (x-\frac {3 x \log (x)}{e^4+x}\right )\right )}} \] Output:
exp(2*exp(1/3*ln(x-3*ln(x)/(x+exp(4))*x)-1))
\[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=\int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx \] Input:
Integrate[(E^(2*E^((-3 + Log[(E^4*x + x^2 - 3*x*Log[x])/(E^4 + x)])/3) + ( -3 + Log[(E^4*x + x^2 - 3*x*Log[x])/(E^4 + x)])/3)*(-2*E^8 + E^4*(6 - 4*x) + 6*x - 2*x^2 + 6*E^4*Log[x]))/(-3*E^8*x - 6*E^4*x^2 - 3*x^3 + (9*E^4*x + 9*x^2)*Log[x]),x]
Output:
Integrate[(E^(2*E^((-3 + Log[(E^4*x + x^2 - 3*x*Log[x])/(E^4 + x)])/3) + ( -3 + Log[(E^4*x + x^2 - 3*x*Log[x])/(E^4 + x)])/3)*(-2*E^8 + E^4*(6 - 4*x) + 6*x - 2*x^2 + 6*E^4*Log[x]))/(-3*E^8*x - 6*E^4*x^2 - 3*x^3 + (9*E^4*x + 9*x^2)*Log[x]), x]
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.
| \(\displaystyle \int \frac {\left (-2 x^2+6 x+e^4 (6-4 x)+6 e^4 \log (x)-2 e^8\right ) \exp \left (2 \exp \left (\frac {1}{3} \left (\log \left (\frac {x^2+e^4 x-3 x \log (x)}{x+e^4}\right )-3\right )\right )+\frac {1}{3} \left (\log \left (\frac {x^2+e^4 x-3 x \log (x)}{x+e^4}\right )-3\right )\right )}{-3 x^3-6 e^4 x^2+\left (9 x^2+9 e^4 x\right ) \log (x)-3 e^8 x} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {2 \left (x^2-3 \left (1-\frac {2 e^4}{3}\right ) x-3 e^4 \log (x)-3 e^4 \left (1-\frac {e^4}{3}\right )\right ) \exp \left (\frac {e \log \left (\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}\right )+6 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}-3 e}{3 e}\right )}{3 x \left (x+e^4\right ) \left (x-3 \log (x)+e^4\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{3} \int -\frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}} \left (-x^2+\left (3-2 e^4\right ) x+3 e^4 \log (x)+e^4 \left (3-e^4\right )\right )}{x \left (x+e^4\right ) \left (x-3 \log (x)+e^4\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {2}{3} \int \frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}} \left (-x^2+\left (3-2 e^4\right ) x+3 e^4 \log (x)+e^4 \left (3-e^4\right )\right )}{x \left (x+e^4\right ) \left (x-3 \log (x)+e^4\right )}dx\) |
| \(\Big \downarrow \) 7269 |
| \(\displaystyle -\frac {2 \sqrt [3]{x+e^4} \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}} \int \frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} \left (-x^2+\left (3-2 e^4\right ) x+3 e^4 \log (x)+e^4 \left (3-e^4\right )\right )}{x^{2/3} \left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}dx}{3 \sqrt [3]{x} \sqrt [3]{x-3 \log (x)+e^4}}\) |
| \(\Big \downarrow \) 7284 |
| \(\displaystyle -\frac {2 \sqrt [3]{x+e^4} \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}} \int \frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} \left (-x^2+\left (3-2 e^4\right ) x+3 e^4 \log (x)+e^4 \left (3-e^4\right )\right )}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}d\sqrt [3]{x}}{\sqrt [3]{x} \sqrt [3]{x-3 \log (x)+e^4}}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {2 \sqrt [3]{x+e^4} \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}} \int \left (-\frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} x^2}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}-\frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} \left (-3+2 e^4\right ) x}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}+\frac {3 e^{4-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} \log (x)}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}-\frac {e^{4-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} \left (-3+e^4\right )}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}\right )d\sqrt [3]{x}}{\sqrt [3]{x} \sqrt [3]{x-3 \log (x)+e^4}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {2 \sqrt [3]{x+e^4} \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}} \left (-\int \frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} x^2}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}d\sqrt [3]{x}+\left (3-e^4\right ) \int \frac {e^{\frac {2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}+3 e}{e}}}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}d\sqrt [3]{x}+\left (3-2 e^4\right ) \int \frac {e^{-\frac {e-2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}}{e}} x}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}d\sqrt [3]{x}+3 \int \frac {e^{\frac {2 \sqrt [3]{\frac {x \left (x-3 \log (x)+e^4\right )}{x+e^4}}+3 e}{e}} \log (x)}{\left (x+e^4\right )^{4/3} \left (x-3 \log (x)+e^4\right )^{2/3}}d\sqrt [3]{x}\right )}{\sqrt [3]{x} \sqrt [3]{x-3 \log (x)+e^4}}\) |
Input:
Int[(E^(2*E^((-3 + Log[(E^4*x + x^2 - 3*x*Log[x])/(E^4 + x)])/3) + (-3 + L og[(E^4*x + x^2 - 3*x*Log[x])/(E^4 + x)])/3)*(-2*E^8 + E^4*(6 - 4*x) + 6*x - 2*x^2 + 6*E^4*Log[x]))/(-3*E^8*x - 6*E^4*x^2 - 3*x^3 + (9*E^4*x + 9*x^2 )*Log[x]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(121\) vs. \(2(22)=44\).
Time = 60.92 (sec) , antiderivative size = 122, normalized size of antiderivative = 4.52
| method | result | size |
| parallelrisch | \(\frac {9 \,{\mathrm e}^{2 \,{\mathrm e}^{\frac {\ln \left (-\frac {x \left (3 \ln \left (x \right )-{\mathrm e}^{4}-x \right )}{x +{\mathrm e}^{4}}\right )}{3}-1}} x^{2}-27 \,{\mathrm e}^{2 \,{\mathrm e}^{\frac {\ln \left (-\frac {x \left (3 \ln \left (x \right )-{\mathrm e}^{4}-x \right )}{x +{\mathrm e}^{4}}\right )}{3}-1}} x \ln \left (x \right )+9 \,{\mathrm e}^{4} x \,{\mathrm e}^{2 \,{\mathrm e}^{\frac {\ln \left (-\frac {x \left (3 \ln \left (x \right )-{\mathrm e}^{4}-x \right )}{x +{\mathrm e}^{4}}\right )}{3}-1}}}{9 x \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}\) | \(122\) |
| risch | \({\mathrm e}^{\frac {2 x^{\frac {1}{3}} \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )^{\frac {1}{3}} {\mathrm e}^{-1-\frac {i \pi {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}^{3}}{6}+\frac {i \pi {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}^{2} \operatorname {csgn}\left (\frac {i}{x +{\mathrm e}^{4}}\right )}{6}+\frac {i \pi {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}^{2} \operatorname {csgn}\left (i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )\right )}{6}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right ) \operatorname {csgn}\left (\frac {i}{x +{\mathrm e}^{4}}\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )\right )}{6}-\frac {i \pi {\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}^{3}}{6}+\frac {i \pi {\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}^{2} \operatorname {csgn}\left (i x \right )}{6}+\frac {i \pi {\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}^{2} \operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}{6}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{4}+x -3 \ln \left (x \right )\right )}{x +{\mathrm e}^{4}}\right )}{6}}}{\left (x +{\mathrm e}^{4}\right )^{\frac {1}{3}}}}\) | \(308\) |
Input:
int((6*exp(4)*ln(x)-2*exp(4)^2+(6-4*x)*exp(4)-2*x^2+6*x)*exp(1/3*ln((-3*x* ln(x)+x*exp(4)+x^2)/(x+exp(4)))-1)*exp(2*exp(1/3*ln((-3*x*ln(x)+x*exp(4)+x ^2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x^2)*ln(x)-3*x*exp(4)^2-6*x^2*exp(4)-3* x^3),x,method=_RETURNVERBOSE)
Output:
1/9/x*(9*exp(2*exp(1/3*ln(-x*(3*ln(x)-exp(4)-x)/(x+exp(4)))-1))*x^2-27*exp (2*exp(1/3*ln(-x*(3*ln(x)-exp(4)-x)/(x+exp(4)))-1))*x*ln(x)+9*exp(4)*x*exp (2*exp(1/3*ln(-x*(3*ln(x)-exp(4)-x)/(x+exp(4)))-1)))/(exp(4)+x-3*ln(x))
Exception generated. \[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((6*exp(4)*log(x)-2*exp(4)^2+(6-4*x)*exp(4)-2*x^2+6*x)*exp(1/3*lo g((-3*x*log(x)+x*exp(4)+x^2)/(x+exp(4)))-1)*exp(2*exp(1/3*log((-3*x*log(x) +x*exp(4)+x^2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x^2)*log(x)-3*x*exp(4)^2-6*x ^2*exp(4)-3*x^3),x, algorithm="fricas")
Output:
Exception raised: TypeError >> Error detected within library code: do_a lg_rde: unimplemented kernel
Timed out. \[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=\text {Timed out} \] Input:
integrate((6*exp(4)*ln(x)-2*exp(4)**2+(6-4*x)*exp(4)-2*x**2+6*x)*exp(1/3*l n((-3*x*ln(x)+x*exp(4)+x**2)/(x+exp(4)))-1)*exp(2*exp(1/3*ln((-3*x*ln(x)+x *exp(4)+x**2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x**2)*ln(x)-3*x*exp(4)**2-6*x **2*exp(4)-3*x**3),x)
Output:
Timed out
Time = 0.23 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=e^{\left (\frac {2 \, {\left (x + e^{4} - 3 \, \log \left (x\right )\right )}^{\frac {1}{3}} x^{\frac {1}{3}} e^{\left (-1\right )}}{{\left (x + e^{4}\right )}^{\frac {1}{3}}}\right )} \] Input:
integrate((6*exp(4)*log(x)-2*exp(4)^2+(6-4*x)*exp(4)-2*x^2+6*x)*exp(1/3*lo g((-3*x*log(x)+x*exp(4)+x^2)/(x+exp(4)))-1)*exp(2*exp(1/3*log((-3*x*log(x) +x*exp(4)+x^2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x^2)*log(x)-3*x*exp(4)^2-6*x ^2*exp(4)-3*x^3),x, algorithm="maxima")
Output:
e^(2*(x + e^4 - 3*log(x))^(1/3)*x^(1/3)*e^(-1)/(x + e^4)^(1/3))
\[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=\int { \frac {2 \, {\left (x^{2} + {\left (2 \, x - 3\right )} e^{4} - 3 \, e^{4} \log \left (x\right ) - 3 \, x + e^{8}\right )} e^{\left (2 \, e^{\left (\frac {1}{3} \, \log \left (\frac {x^{2} + x e^{4} - 3 \, x \log \left (x\right )}{x + e^{4}}\right ) - 1\right )} + \frac {1}{3} \, \log \left (\frac {x^{2} + x e^{4} - 3 \, x \log \left (x\right )}{x + e^{4}}\right ) - 1\right )}}{3 \, {\left (x^{3} + 2 \, x^{2} e^{4} + x e^{8} - 3 \, {\left (x^{2} + x e^{4}\right )} \log \left (x\right )\right )}} \,d x } \] Input:
integrate((6*exp(4)*log(x)-2*exp(4)^2+(6-4*x)*exp(4)-2*x^2+6*x)*exp(1/3*lo g((-3*x*log(x)+x*exp(4)+x^2)/(x+exp(4)))-1)*exp(2*exp(1/3*log((-3*x*log(x) +x*exp(4)+x^2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x^2)*log(x)-3*x*exp(4)^2-6*x ^2*exp(4)-3*x^3),x, algorithm="giac")
Output:
integrate(2/3*(x^2 + (2*x - 3)*e^4 - 3*e^4*log(x) - 3*x + e^8)*e^(2*e^(1/3 *log((x^2 + x*e^4 - 3*x*log(x))/(x + e^4)) - 1) + 1/3*log((x^2 + x*e^4 - 3 *x*log(x))/(x + e^4)) - 1)/(x^3 + 2*x^2*e^4 + x*e^8 - 3*(x^2 + x*e^4)*log( x)), x)
Timed out. \[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=\int \frac {{\mathrm {e}}^{2\,{\mathrm {e}}^{\frac {\ln \left (\frac {x\,{\mathrm {e}}^4-3\,x\,\ln \left (x\right )+x^2}{x+{\mathrm {e}}^4}\right )}{3}-1}}\,{\mathrm {e}}^{\frac {\ln \left (\frac {x\,{\mathrm {e}}^4-3\,x\,\ln \left (x\right )+x^2}{x+{\mathrm {e}}^4}\right )}{3}-1}\,\left (2\,{\mathrm {e}}^8-6\,x-6\,{\mathrm {e}}^4\,\ln \left (x\right )+2\,x^2+{\mathrm {e}}^4\,\left (4\,x-6\right )\right )}{3\,x\,{\mathrm {e}}^8-\ln \left (x\right )\,\left (9\,x^2+9\,{\mathrm {e}}^4\,x\right )+6\,x^2\,{\mathrm {e}}^4+3\,x^3} \,d x \] Input:
int((exp(2*exp(log((x*exp(4) - 3*x*log(x) + x^2)/(x + exp(4)))/3 - 1))*exp (log((x*exp(4) - 3*x*log(x) + x^2)/(x + exp(4)))/3 - 1)*(2*exp(8) - 6*x - 6*exp(4)*log(x) + 2*x^2 + exp(4)*(4*x - 6)))/(3*x*exp(8) - log(x)*(9*x*exp (4) + 9*x^2) + 6*x^2*exp(4) + 3*x^3),x)
Output:
int((exp(2*exp(log((x*exp(4) - 3*x*log(x) + x^2)/(x + exp(4)))/3 - 1))*exp (log((x*exp(4) - 3*x*log(x) + x^2)/(x + exp(4)))/3 - 1)*(2*exp(8) - 6*x - 6*exp(4)*log(x) + 2*x^2 + exp(4)*(4*x - 6)))/(3*x*exp(8) - log(x)*(9*x*exp (4) + 9*x^2) + 6*x^2*exp(4) + 3*x^3), x)
\[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=\int \frac {\left (6 \,{\mathrm e}^{4} \mathrm {log}\left (x \right )-2 \left ({\mathrm e}^{4}\right )^{2}+\left (6-4 x \right ) {\mathrm e}^{4}-2 x^{2}+6 x \right ) {\mathrm e}^{\frac {\mathrm {log}\left (\frac {-3 \,\mathrm {log}\left (x \right ) x +x \,{\mathrm e}^{4}+x^{2}}{x +{\mathrm e}^{4}}\right )}{3}-1} {\mathrm e}^{2 \,{\mathrm e}^{\frac {\mathrm {log}\left (\frac {-3 \,\mathrm {log}\left (x \right ) x +x \,{\mathrm e}^{4}+x^{2}}{x +{\mathrm e}^{4}}\right )}{3}-1}}}{\left (9 x \,{\mathrm e}^{4}+9 x^{2}\right ) \mathrm {log}\left (x \right )-3 x \left ({\mathrm e}^{4}\right )^{2}-6 x^{2} {\mathrm e}^{4}-3 x^{3}}d x \] Input:
int((6*exp(4)*log(x)-2*exp(4)^2+(6-4*x)*exp(4)-2*x^2+6*x)*exp(1/3*log((-3* x*log(x)+x*exp(4)+x^2)/(x+exp(4)))-1)*exp(2*exp(1/3*log((-3*x*log(x)+x*exp (4)+x^2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x^2)*log(x)-3*x*exp(4)^2-6*x^2*exp (4)-3*x^3),x)
Output:
int((6*exp(4)*log(x)-2*exp(4)^2+(6-4*x)*exp(4)-2*x^2+6*x)*exp(1/3*log((-3* x*log(x)+x*exp(4)+x^2)/(x+exp(4)))-1)*exp(2*exp(1/3*log((-3*x*log(x)+x*exp (4)+x^2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x^2)*log(x)-3*x*exp(4)^2-6*x^2*exp (4)-3*x^3),x)