Integrand size = 288, antiderivative size = 34 \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\frac {-e^{\frac {1}{3 \left (x+\log (2)+\frac {1}{9} x^2 (x-\log (x))\right )}}+\log (x)}{x} \] Output:
(ln(x)-exp(1/3/(x+1/9*x^2*(x-ln(x))+ln(2))))/x
\[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx \] Input:
Integrate[(81*x^2 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-81*x^2 - 18*x^3 - 18*x^4 - 2*x^5 - x^6 + (-162*x - 18*x^2 - 18*x^3)*Log [2] - 81*Log[2]^2)*Log[x] + (18*x^3 + x^4 + 2*x^5 + 18*x^2*Log[2])*Log[x]^ 2 - x^4*Log[x]^3 + (27*x + 78*x^2 + 9*x^3 + 18*x^4 + x^6 + (162*x + 18*x^3 )*Log[2] + 81*Log[2]^2 + (-6*x^2 - 18*x^3 - 2*x^5 - 18*x^2*Log[2])*Log[x] + x^4*Log[x]^2)/E^(3/(-9*x - x^3 - 9*Log[2] + x^2*Log[x])))/(81*x^4 + 18*x ^6 + x^8 + (162*x^3 + 18*x^5)*Log[2] + 81*x^2*Log[2]^2 + (-18*x^5 - 2*x^7 - 18*x^4*Log[2])*Log[x] + x^6*Log[x]^2),x]
Output:
Integrate[(81*x^2 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-81*x^2 - 18*x^3 - 18*x^4 - 2*x^5 - x^6 + (-162*x - 18*x^2 - 18*x^3)*Log [2] - 81*Log[2]^2)*Log[x] + (18*x^3 + x^4 + 2*x^5 + 18*x^2*Log[2])*Log[x]^ 2 - x^4*Log[x]^3 + (27*x + 78*x^2 + 9*x^3 + 18*x^4 + x^6 + (162*x + 18*x^3 )*Log[2] + 81*Log[2]^2 + (-6*x^2 - 18*x^3 - 2*x^5 - 18*x^2*Log[2])*Log[x] + x^4*Log[x]^2)/E^(3/(-9*x - x^3 - 9*Log[2] + x^2*Log[x])))/(81*x^4 + 18*x ^6 + x^8 + (162*x^3 + 18*x^5)*Log[2] + 81*x^2*Log[2]^2 + (-18*x^5 - 2*x^7 - 18*x^4*Log[2])*Log[x] + x^6*Log[x]^2), 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.
| \(\displaystyle \int \frac {x^6+18 x^4-x^4 \log ^3(x)+\left (18 x^3+162 x\right ) \log (2)+81 x^2+\left (2 x^5+x^4+18 x^3+18 x^2 \log (2)\right ) \log ^2(x)+\left (-x^6-2 x^5-18 x^4-18 x^3-81 x^2+\left (-18 x^3-18 x^2-162 x\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+e^{-\frac {3}{-x^3+x^2 \log (x)-9 x-9 \log (2)}} \left (x^6+18 x^4+x^4 \log ^2(x)+9 x^3+\left (18 x^3+162 x\right ) \log (2)+78 x^2+\left (-2 x^5-18 x^3-6 x^2-18 x^2 \log (2)\right ) \log (x)+27 x+81 \log ^2(2)\right )+81 \log ^2(2)}{x^8+18 x^6+x^6 \log ^2(x)+81 x^4+81 x^2 \log ^2(2)+\left (18 x^5+162 x^3\right ) \log (2)+\left (-2 x^7-18 x^5-18 x^4 \log (2)\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {x^6+18 x^4-x^4 \log ^3(x)+\left (18 x^3+162 x\right ) \log (2)+81 x^2+\left (2 x^5+x^4+18 x^3+18 x^2 \log (2)\right ) \log ^2(x)+\left (-x^6-2 x^5-18 x^4-18 x^3-81 x^2+\left (-18 x^3-18 x^2-162 x\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+e^{-\frac {3}{-x^3+x^2 \log (x)-9 x-9 \log (2)}} \left (x^6+18 x^4+x^4 \log ^2(x)+9 x^3+\left (18 x^3+162 x\right ) \log (2)+78 x^2+\left (-2 x^5-18 x^3-6 x^2-18 x^2 \log (2)\right ) \log (x)+27 x+81 \log ^2(2)\right )+81 \log ^2(2)}{x^2 \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \log ^3(x)}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {\left (2 x^3+x^2+18 x+18 \log (2)\right ) \log ^2(x)}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {81 \log ^2(2)}{x^2 \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {18 x^2}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {81}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {18 \left (x^2+9\right ) \log (2)}{x \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}-\frac {\left (x^3+9 x+\log (512)\right ) \left (x^3+2 x^2+9 x+\log (512)\right ) \log (x)}{x^2 \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {x^4}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {e^{\frac {3}{x^3-x^2 \log (x)+9 x+\log (512)}} \left (x^6-2 x^5 \log (x)+18 x^4+x^4 \log ^2(x)-18 x^3 \log (x)+9 x^3 (1+\log (4))+78 x^2-6 x^2 (1+\log (8)) \log (x)+27 x (1+\log (64))+81 \log ^2(2)\right )}{x^2 \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (-\frac {x^2 \log ^3(x)}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {\left (2 x^3+x^2+18 x+18 \log (2)\right ) \log ^2(x)}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {81 \log ^2(2)}{x^2 \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {18 x^2}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {81}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {18 \left (x^2+9\right ) \log (2)}{x \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}-\frac {\left (x^3+9 x+\log (512)\right ) \left (x^3+2 x^2+9 x+\log (512)\right ) \log (x)}{x^2 \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {x^4}{\left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}+\frac {e^{\frac {3}{x^3-x^2 \log (x)+9 x+\log (512)}} \left (x^6-2 x^5 \log (x)+18 x^4+x^4 \log ^2(x)-18 x^3 \log (x)+9 x^3 (1+\log (4))+78 x^2-6 x^2 (1+\log (8)) \log (x)+27 x (1+\log (64))+81 \log ^2(2)\right )}{x^2 \left (x^3-x^2 \log (x)+9 x+\log (512)\right )^2}\right )dx\) |
Input:
Int[(81*x^2 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[2] + 81*Log[2]^2 + (-81* x^2 - 18*x^3 - 18*x^4 - 2*x^5 - x^6 + (-162*x - 18*x^2 - 18*x^3)*Log[2] - 81*Log[2]^2)*Log[x] + (18*x^3 + x^4 + 2*x^5 + 18*x^2*Log[2])*Log[x]^2 - x^ 4*Log[x]^3 + (27*x + 78*x^2 + 9*x^3 + 18*x^4 + x^6 + (162*x + 18*x^3)*Log[ 2] + 81*Log[2]^2 + (-6*x^2 - 18*x^3 - 2*x^5 - 18*x^2*Log[2])*Log[x] + x^4* Log[x]^2)/E^(3/(-9*x - x^3 - 9*Log[2] + x^2*Log[x])))/(81*x^4 + 18*x^6 + x ^8 + (162*x^3 + 18*x^5)*Log[2] + 81*x^2*Log[2]^2 + (-18*x^5 - 2*x^7 - 18*x ^4*Log[2])*Log[x] + x^6*Log[x]^2),x]
Output:
$Aborted
Time = 50.97 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06
| method | result | size |
| risch | \(\frac {\ln \left (x \right )}{x}-\frac {{\mathrm e}^{\frac {3}{-x^{2} \ln \left (x \right )+9 \ln \left (2\right )+x^{3}+9 x}}}{x}\) | \(36\) |
| parallelrisch | \(\frac {4 x +\ln \left (x \right )-{\mathrm e}^{-\frac {3}{x^{2} \ln \left (x \right )-9 \ln \left (2\right )-x^{3}-9 x}}}{x}\) | \(37\) |
Input:
int(((x^4*ln(x)^2+(-18*x^2*ln(2)-2*x^5-18*x^3-6*x^2)*ln(x)+81*ln(2)^2+(18* x^3+162*x)*ln(2)+x^6+18*x^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*ln(x)-9*ln(2)-x ^3-9*x))-x^4*ln(x)^3+(18*x^2*ln(2)+2*x^5+x^4+18*x^3)*ln(x)^2+(-81*ln(2)^2+ (-18*x^3-18*x^2-162*x)*ln(2)-x^6-2*x^5-18*x^4-18*x^3-81*x^2)*ln(x)+81*ln(2 )^2+(18*x^3+162*x)*ln(2)+x^6+18*x^4+81*x^2)/(x^6*ln(x)^2+(-18*x^4*ln(2)-2* x^7-18*x^5)*ln(x)+81*x^2*ln(2)^2+(18*x^5+162*x^3)*ln(2)+x^8+18*x^6+81*x^4) ,x,method=_RETURNVERBOSE)
Output:
ln(x)/x-1/x*exp(3/(-x^2*ln(x)+9*ln(2)+x^3+9*x))
Time = 0.11 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.97 \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=-\frac {e^{\left (\frac {3}{x^{3} - x^{2} \log \left (x\right ) + 9 \, x + 9 \, \log \left (2\right )}\right )} - \log \left (x\right )}{x} \] Input:
integrate(((x^4*log(x)^2+(-18*x^2*log(2)-2*x^5-18*x^3-6*x^2)*log(x)+81*log (2)^2+(18*x^3+162*x)*log(2)+x^6+18*x^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*log( x)-9*log(2)-x^3-9*x))-x^4*log(x)^3+(18*x^2*log(2)+2*x^5+x^4+18*x^3)*log(x) ^2+(-81*log(2)^2+(-18*x^3-18*x^2-162*x)*log(2)-x^6-2*x^5-18*x^4-18*x^3-81* x^2)*log(x)+81*log(2)^2+(18*x^3+162*x)*log(2)+x^6+18*x^4+81*x^2)/(x^6*log( x)^2+(-18*x^4*log(2)-2*x^7-18*x^5)*log(x)+81*x^2*log(2)^2+(18*x^5+162*x^3) *log(2)+x^8+18*x^6+81*x^4),x, algorithm="fricas")
Output:
-(e^(3/(x^3 - x^2*log(x) + 9*x + 9*log(2))) - log(x))/x
Exception generated. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((x**4*ln(x)**2+(-18*x**2*ln(2)-2*x**5-18*x**3-6*x**2)*ln(x)+81* ln(2)**2+(18*x**3+162*x)*ln(2)+x**6+18*x**4+9*x**3+78*x**2+27*x)*exp(-3/(x **2*ln(x)-9*ln(2)-x**3-9*x))-x**4*ln(x)**3+(18*x**2*ln(2)+2*x**5+x**4+18*x **3)*ln(x)**2+(-81*ln(2)**2+(-18*x**3-18*x**2-162*x)*ln(2)-x**6-2*x**5-18* x**4-18*x**3-81*x**2)*ln(x)+81*ln(2)**2+(18*x**3+162*x)*ln(2)+x**6+18*x**4 +81*x**2)/(x**6*ln(x)**2+(-18*x**4*ln(2)-2*x**7-18*x**5)*ln(x)+81*x**2*ln( 2)**2+(18*x**5+162*x**3)*ln(2)+x**8+18*x**6+81*x**4),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
Exception generated. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\text {Exception raised: RuntimeError} \] Input:
integrate(((x^4*log(x)^2+(-18*x^2*log(2)-2*x^5-18*x^3-6*x^2)*log(x)+81*log (2)^2+(18*x^3+162*x)*log(2)+x^6+18*x^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*log( x)-9*log(2)-x^3-9*x))-x^4*log(x)^3+(18*x^2*log(2)+2*x^5+x^4+18*x^3)*log(x) ^2+(-81*log(2)^2+(-18*x^3-18*x^2-162*x)*log(2)-x^6-2*x^5-18*x^4-18*x^3-81* x^2)*log(x)+81*log(2)^2+(18*x^3+162*x)*log(2)+x^6+18*x^4+81*x^2)/(x^6*log( x)^2+(-18*x^4*log(2)-2*x^7-18*x^5)*log(x)+81*x^2*log(2)^2+(18*x^5+162*x^3) *log(2)+x^8+18*x^6+81*x^4),x, algorithm="maxima")
Output:
Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is 0which is not of the expected type LIST
Time = 0.50 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.85 \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=-\frac {e^{\left (-\frac {x^{3} - x^{2} \log \left (x\right ) + 9 \, x}{3 \, {\left (x^{3} \log \left (2\right ) - x^{2} \log \left (2\right ) \log \left (x\right ) + 9 \, x \log \left (2\right ) + 9 \, \log \left (2\right )^{2}\right )}} + \frac {1}{3 \, \log \left (2\right )}\right )} - \log \left (x\right )}{x} \] Input:
integrate(((x^4*log(x)^2+(-18*x^2*log(2)-2*x^5-18*x^3-6*x^2)*log(x)+81*log (2)^2+(18*x^3+162*x)*log(2)+x^6+18*x^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*log( x)-9*log(2)-x^3-9*x))-x^4*log(x)^3+(18*x^2*log(2)+2*x^5+x^4+18*x^3)*log(x) ^2+(-81*log(2)^2+(-18*x^3-18*x^2-162*x)*log(2)-x^6-2*x^5-18*x^4-18*x^3-81* x^2)*log(x)+81*log(2)^2+(18*x^3+162*x)*log(2)+x^6+18*x^4+81*x^2)/(x^6*log( x)^2+(-18*x^4*log(2)-2*x^7-18*x^5)*log(x)+81*x^2*log(2)^2+(18*x^5+162*x^3) *log(2)+x^8+18*x^6+81*x^4),x, algorithm="giac")
Output:
-(e^(-1/3*(x^3 - x^2*log(x) + 9*x)/(x^3*log(2) - x^2*log(2)*log(x) + 9*x*l og(2) + 9*log(2)^2) + 1/3/log(2)) - log(x))/x
Timed out. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\int \frac {\ln \left (2\right )\,\left (18\,x^3+162\,x\right )-x^4\,{\ln \left (x\right )}^3+81\,{\ln \left (2\right )}^2+81\,x^2+18\,x^4+x^6+{\ln \left (x\right )}^2\,\left (2\,x^5+x^4+18\,x^3+18\,\ln \left (2\right )\,x^2\right )-\ln \left (x\right )\,\left (\ln \left (2\right )\,\left (18\,x^3+18\,x^2+162\,x\right )+81\,{\ln \left (2\right )}^2+81\,x^2+18\,x^3+18\,x^4+2\,x^5+x^6\right )+{\mathrm {e}}^{\frac {3}{9\,x+9\,\ln \left (2\right )-x^2\,\ln \left (x\right )+x^3}}\,\left (27\,x+\ln \left (2\right )\,\left (18\,x^3+162\,x\right )+x^4\,{\ln \left (x\right )}^2+81\,{\ln \left (2\right )}^2+78\,x^2+9\,x^3+18\,x^4+x^6-\ln \left (x\right )\,\left (18\,x^2\,\ln \left (2\right )+6\,x^2+18\,x^3+2\,x^5\right )\right )}{81\,x^2\,{\ln \left (2\right )}^2+x^6\,{\ln \left (x\right )}^2+\ln \left (2\right )\,\left (18\,x^5+162\,x^3\right )-\ln \left (x\right )\,\left (2\,x^7+18\,x^5+18\,\ln \left (2\right )\,x^4\right )+81\,x^4+18\,x^6+x^8} \,d x \] Input:
int((log(2)*(162*x + 18*x^3) - x^4*log(x)^3 + 81*log(2)^2 + 81*x^2 + 18*x^ 4 + x^6 + log(x)^2*(18*x^2*log(2) + 18*x^3 + x^4 + 2*x^5) - log(x)*(log(2) *(162*x + 18*x^2 + 18*x^3) + 81*log(2)^2 + 81*x^2 + 18*x^3 + 18*x^4 + 2*x^ 5 + x^6) + exp(3/(9*x + 9*log(2) - x^2*log(x) + x^3))*(27*x + log(2)*(162* x + 18*x^3) + x^4*log(x)^2 + 81*log(2)^2 + 78*x^2 + 9*x^3 + 18*x^4 + x^6 - log(x)*(18*x^2*log(2) + 6*x^2 + 18*x^3 + 2*x^5)))/(81*x^2*log(2)^2 + x^6* log(x)^2 + log(2)*(162*x^3 + 18*x^5) - log(x)*(18*x^4*log(2) + 18*x^5 + 2* x^7) + 81*x^4 + 18*x^6 + x^8),x)
Output:
int((log(2)*(162*x + 18*x^3) - x^4*log(x)^3 + 81*log(2)^2 + 81*x^2 + 18*x^ 4 + x^6 + log(x)^2*(18*x^2*log(2) + 18*x^3 + x^4 + 2*x^5) - log(x)*(log(2) *(162*x + 18*x^2 + 18*x^3) + 81*log(2)^2 + 81*x^2 + 18*x^3 + 18*x^4 + 2*x^ 5 + x^6) + exp(3/(9*x + 9*log(2) - x^2*log(x) + x^3))*(27*x + log(2)*(162* x + 18*x^3) + x^4*log(x)^2 + 81*log(2)^2 + 78*x^2 + 9*x^3 + 18*x^4 + x^6 - log(x)*(18*x^2*log(2) + 6*x^2 + 18*x^3 + 2*x^5)))/(81*x^2*log(2)^2 + x^6* log(x)^2 + log(2)*(162*x^3 + 18*x^5) - log(x)*(18*x^4*log(2) + 18*x^5 + 2* x^7) + 81*x^4 + 18*x^6 + x^8), x)
Time = 0.18 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.79 \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\frac {e^{\frac {3}{\mathrm {log}\left (x \right ) x^{2}-9 \,\mathrm {log}\left (2\right )-x^{3}-9 x}} \mathrm {log}\left (x \right )-1}{e^{\frac {3}{\mathrm {log}\left (x \right ) x^{2}-9 \,\mathrm {log}\left (2\right )-x^{3}-9 x}} x} \] Input:
int(((x^4*log(x)^2+(-18*x^2*log(2)-2*x^5-18*x^3-6*x^2)*log(x)+81*log(2)^2+ (18*x^3+162*x)*log(2)+x^6+18*x^4+9*x^3+78*x^2+27*x)*exp(-3/(x^2*log(x)-9*l og(2)-x^3-9*x))-x^4*log(x)^3+(18*x^2*log(2)+2*x^5+x^4+18*x^3)*log(x)^2+(-8 1*log(2)^2+(-18*x^3-18*x^2-162*x)*log(2)-x^6-2*x^5-18*x^4-18*x^3-81*x^2)*l og(x)+81*log(2)^2+(18*x^3+162*x)*log(2)+x^6+18*x^4+81*x^2)/(x^6*log(x)^2+( -18*x^4*log(2)-2*x^7-18*x^5)*log(x)+81*x^2*log(2)^2+(18*x^5+162*x^3)*log(2 )+x^8+18*x^6+81*x^4),x)
Output:
(e**(3/(log(x)*x**2 - 9*log(2) - x**3 - 9*x))*log(x) - 1)/(e**(3/(log(x)*x **2 - 9*log(2) - x**3 - 9*x))*x)