Integrand size = 96, antiderivative size = 27 \[ \int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx=\frac {5 x \log (x)}{5-e^{\frac {e^{e^6}}{x}}+3 (-4+x)} \]
Time = 0.55 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx=-\frac {5 x \log (x)}{7+e^{\frac {e^{e^6}}{x}}-3 x} \]
Integrate[(-35*x + 15*x^2 - 35*x*Log[x] + E^(E^E^6/x)*(-5*x + (-5*E^E^6 - 5*x)*Log[x]))/(49*x + E^((2*E^E^6)/x)*x - 42*x^2 + 9*x^3 + E^(E^E^6/x)*(14 *x - 6*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.
\(\displaystyle \int \frac {15 x^2-35 x-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (\left (-5 x-5 e^{e^6}\right ) \log (x)-5 x\right )}{9 x^3-42 x^2+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )+e^{\frac {2 e^{e^6}}{x}} x+49 x} \, dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \int \frac {15 x^2-35 x-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (\left (-5 x-5 e^{e^6}\right ) \log (x)-5 x\right )}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2 x}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {5 \left (3 x^2+3 e^{e^6} x-7 e^{e^6}\right ) \log (x)}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2 x}-\frac {5 \left (x+x \log (x)+e^{e^6} \log (x)\right )}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right ) x}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -5 \int \frac {1}{-3 x+e^{\frac {e^{e^6}}{x}}+7}dx+15 e^{e^6} \int \frac {\int \frac {1}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2}dx}{x}dx+5 \int \frac {\int \frac {1}{-3 x+e^{\frac {e^{e^6}}{x}}+7}dx}{x}dx-35 e^{e^6} \int \frac {\int \frac {1}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2 x}dx}{x}dx+5 e^{e^6} \int \frac {\int \frac {1}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right ) x}dx}{x}dx+15 \int \frac {\int \frac {x}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2}dx}{x}dx-15 e^{e^6} \log (x) \int \frac {1}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2}dx-5 \log (x) \int \frac {1}{-3 x+e^{\frac {e^{e^6}}{x}}+7}dx+35 e^{e^6} \log (x) \int \frac {1}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2 x}dx-5 e^{e^6} \log (x) \int \frac {1}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right ) x}dx-15 \log (x) \int \frac {x}{\left (-3 x+e^{\frac {e^{e^6}}{x}}+7\right )^2}dx\) |
Int[(-35*x + 15*x^2 - 35*x*Log[x] + E^(E^E^6/x)*(-5*x + (-5*E^E^6 - 5*x)*L og[x]))/(49*x + E^((2*E^E^6)/x)*x - 42*x^2 + 9*x^3 + E^(E^E^6/x)*(14*x - 6 *x^2)),x]
3.10.34.3.1 Defintions of rubi rules used
Time = 0.60 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85
method | result | size |
risch | \(\frac {5 x \ln \left (x \right )}{3 x -7-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{6}}}{x}}}\) | \(23\) |
parallelrisch | \(\frac {5 x \ln \left (x \right )}{3 x -7-{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{6}}}{x}}}\) | \(23\) |
int((((-5*exp(exp(6))-5*x)*ln(x)-5*x)*exp(exp(exp(6))/x)-35*x*ln(x)+15*x^2 -35*x)/(x*exp(exp(exp(6))/x)^2+(-6*x^2+14*x)*exp(exp(exp(6))/x)+9*x^3-42*x ^2+49*x),x,method=_RETURNVERBOSE)
Time = 0.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.81 \[ \int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx=\frac {5 \, x \log \left (x\right )}{3 \, x - e^{\left (\frac {e^{\left (e^{6}\right )}}{x}\right )} - 7} \]
integrate((((-5*exp(exp(6))-5*x)*log(x)-5*x)*exp(exp(exp(6))/x)-35*x*log(x )+15*x^2-35*x)/(x*exp(exp(exp(6))/x)^2+(-6*x^2+14*x)*exp(exp(exp(6))/x)+9* x^3-42*x^2+49*x),x, algorithm=\
Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.74 \[ \int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx=- \frac {5 x \log {\left (x \right )}}{- 3 x + e^{\frac {e^{e^{6}}}{x}} + 7} \]
integrate((((-5*exp(exp(6))-5*x)*ln(x)-5*x)*exp(exp(exp(6))/x)-35*x*ln(x)+ 15*x**2-35*x)/(x*exp(exp(exp(6))/x)**2+(-6*x**2+14*x)*exp(exp(exp(6))/x)+9 *x**3-42*x**2+49*x),x)
Time = 0.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.81 \[ \int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx=\frac {5 \, x \log \left (x\right )}{3 \, x - e^{\left (\frac {e^{\left (e^{6}\right )}}{x}\right )} - 7} \]
integrate((((-5*exp(exp(6))-5*x)*log(x)-5*x)*exp(exp(exp(6))/x)-35*x*log(x )+15*x^2-35*x)/(x*exp(exp(exp(6))/x)^2+(-6*x^2+14*x)*exp(exp(exp(6))/x)+9* x^3-42*x^2+49*x),x, algorithm=\
Timed out. \[ \int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx=\text {Timed out} \]
integrate((((-5*exp(exp(6))-5*x)*log(x)-5*x)*exp(exp(exp(6))/x)-35*x*log(x )+15*x^2-35*x)/(x*exp(exp(exp(6))/x)^2+(-6*x^2+14*x)*exp(exp(exp(6))/x)+9* x^3-42*x^2+49*x),x, algorithm=\
Time = 12.91 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.56 \[ \int \frac {-35 x+15 x^2-35 x \log (x)+e^{\frac {e^{e^6}}{x}} \left (-5 x+\left (-5 e^{e^6}-5 x\right ) \log (x)\right )}{49 x+e^{\frac {2 e^{e^6}}{x}} x-42 x^2+9 x^3+e^{\frac {e^{e^6}}{x}} \left (14 x-6 x^2\right )} \, dx=-\frac {5\,\left (3\,x^5\,\ln \left (x\right )-7\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^6}\,\ln \left (x\right )+3\,x^4\,{\mathrm {e}}^{{\mathrm {e}}^6}\,\ln \left (x\right )\right )}{\left (3\,x^4+3\,{\mathrm {e}}^{{\mathrm {e}}^6}\,x^3-7\,{\mathrm {e}}^{{\mathrm {e}}^6}\,x^2\right )\,\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^6}}{x}}-3\,x+7\right )} \]
int(-(35*x + exp(exp(exp(6))/x)*(5*x + log(x)*(5*x + 5*exp(exp(6)))) + 35* x*log(x) - 15*x^2)/(49*x + exp(exp(exp(6))/x)*(14*x - 6*x^2) + x*exp((2*ex p(exp(6)))/x) - 42*x^2 + 9*x^3),x)