Optimal. Leaf size=30 \[ \frac {\left (\log (2-x)+3 \left (x+\frac {16 e^{-5-x}}{\log (x)}\right )\right )^2}{x} \]
________________________________________________________________________________________
Rubi [F] time = 14.58, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{-10-2 x} \left (9216-4608 x+\left (4608+6912 x-4608 x^2+e^{5+x} \left (576 x-288 x^2\right )+e^{5+x} (192-96 x) \log (2-x)\right ) \log (x)+\left (e^{5+x} \left (96 x+576 x^2-288 x^3\right )+e^{5+x} \left (192+96 x-96 x^2\right ) \log (2-x)\right ) \log ^2(x)+\left (e^{10+2 x} \left (-12 x^2+9 x^3\right )+2 e^{10+2 x} x \log (2-x)+e^{10+2 x} (2-x) \log ^2(2-x)\right ) \log ^3(x)\right )}{\left (-2 x^2+x^3\right ) \log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-10-2 x} \left (9216-4608 x+\left (4608+6912 x-4608 x^2+e^{5+x} \left (576 x-288 x^2\right )+e^{5+x} (192-96 x) \log (2-x)\right ) \log (x)+\left (e^{5+x} \left (96 x+576 x^2-288 x^3\right )+e^{5+x} \left (192+96 x-96 x^2\right ) \log (2-x)\right ) \log ^2(x)+\left (e^{10+2 x} \left (-12 x^2+9 x^3\right )+2 e^{10+2 x} x \log (2-x)+e^{10+2 x} (2-x) \log ^2(2-x)\right ) \log ^3(x)\right )}{(-2+x) x^2 \log ^3(x)} \, dx\\ &=\int \left (\frac {-12 x^2+9 x^3+2 x \log (2-x)+2 \log ^2(2-x)-x \log ^2(2-x)}{(-2+x) x^2}-\frac {2304 e^{-10-2 x} (2+\log (x)+2 x \log (x))}{x^2 \log ^3(x)}-\frac {96 e^{-5-x} \left (-6 x+3 x^2-2 \log (2-x)+x \log (2-x)-x \log (x)-6 x^2 \log (x)+3 x^3 \log (x)-2 \log (2-x) \log (x)-x \log (2-x) \log (x)+x^2 \log (2-x) \log (x)\right )}{(-2+x) x^2 \log ^2(x)}\right ) \, dx\\ &=-\left (96 \int \frac {e^{-5-x} \left (-6 x+3 x^2-2 \log (2-x)+x \log (2-x)-x \log (x)-6 x^2 \log (x)+3 x^3 \log (x)-2 \log (2-x) \log (x)-x \log (2-x) \log (x)+x^2 \log (2-x) \log (x)\right )}{(-2+x) x^2 \log ^2(x)} \, dx\right )-2304 \int \frac {e^{-10-2 x} (2+\log (x)+2 x \log (x))}{x^2 \log ^3(x)} \, dx+\int \frac {-12 x^2+9 x^3+2 x \log (2-x)+2 \log ^2(2-x)-x \log ^2(2-x)}{(-2+x) x^2} \, dx\\ &=\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-96 \int \frac {e^{-5-x} \left (-((-2+x) \log (2-x) (1+(1+x) \log (x)))-x \left (3 (-2+x)+\left (-1-6 x+3 x^2\right ) \log (x)\right )\right )}{(2-x) x^2 \log ^2(x)} \, dx+\int \left (\frac {3 (-4+3 x)}{-2+x}+\frac {2 \log (2-x)}{(-2+x) x}-\frac {\log ^2(2-x)}{x^2}\right ) \, dx\\ &=\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+2 \int \frac {\log (2-x)}{(-2+x) x} \, dx+3 \int \frac {-4+3 x}{-2+x} \, dx-96 \int \left (\frac {e^{-5-x} (3 x+\log (2-x))}{x^2 \log ^2(x)}+\frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{(-2+x) x^2 \log (x)}\right ) \, dx-\int \frac {\log ^2(2-x)}{x^2} \, dx\\ &=\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+2 \operatorname {Subst}\left (\int \frac {\log (x)}{(2-x) x} \, dx,x,2-x\right )+3 \int \left (3+\frac {2}{-2+x}\right ) \, dx-96 \int \frac {e^{-5-x} (3 x+\log (2-x))}{x^2 \log ^2(x)} \, dx-96 \int \frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{(-2+x) x^2 \log (x)} \, dx+\int \frac {\log (2-x)}{x} \, dx\\ &=9 x+6 \log (2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+\log (2) \log (x)-96 \int \left (\frac {3 e^{-5-x}}{x \log ^2(x)}+\frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)}\right ) \, dx-96 \int \left (\frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{2 x^2 \log (x)}+\frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{4 x \log (x)}+\frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{4 (-2+x) \log (x)}\right ) \, dx+\int \frac {\log \left (1-\frac {x}{2}\right )}{x} \, dx+\operatorname {Subst}\left (\int \frac {\log (x)}{2-x} \, dx,x,2-x\right )+\operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,2-x\right )\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-\text {Li}_2\left (\frac {x}{2}\right )-24 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{x \log (x)} \, dx-24 \int \frac {e^{-5-x} \left (-x-6 x^2+3 x^3-2 \log (2-x)-x \log (2-x)+x^2 \log (2-x)\right )}{(-2+x) \log (x)} \, dx-48 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+2 \log (2-x)+x \log (2-x)-x^2 \log (2-x)\right )}{x^2 \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx+\operatorname {Subst}\left (\int \frac {\log \left (\frac {x}{2}\right )}{2-x} \, dx,x,2-x\right )\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-24 \int \left (-\frac {e^{-5-x} x}{(-2+x) \log (x)}-\frac {6 e^{-5-x} x^2}{(-2+x) \log (x)}+\frac {3 e^{-5-x} x^3}{(-2+x) \log (x)}-\frac {2 e^{-5-x} \log (2-x)}{(-2+x) \log (x)}-\frac {e^{-5-x} x \log (2-x)}{(-2+x) \log (x)}+\frac {e^{-5-x} x^2 \log (2-x)}{(-2+x) \log (x)}\right ) \, dx-24 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+\left (2+x-x^2\right ) \log (2-x)\right )}{x \log (x)} \, dx-48 \int \frac {e^{-5-x} \left (x+6 x^2-3 x^3+\left (2+x-x^2\right ) \log (2-x)\right )}{x^2 \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}-24 \int \left (\frac {e^{-5-x}}{\log (x)}+\frac {6 e^{-5-x} x}{\log (x)}-\frac {3 e^{-5-x} x^2}{\log (x)}+\frac {e^{-5-x} \log (2-x)}{\log (x)}+\frac {2 e^{-5-x} \log (2-x)}{x \log (x)}-\frac {e^{-5-x} x \log (2-x)}{\log (x)}\right ) \, dx+24 \int \frac {e^{-5-x} x}{(-2+x) \log (x)} \, dx+24 \int \frac {e^{-5-x} x \log (2-x)}{(-2+x) \log (x)} \, dx-24 \int \frac {e^{-5-x} x^2 \log (2-x)}{(-2+x) \log (x)} \, dx-48 \int \left (\frac {6 e^{-5-x}}{\log (x)}+\frac {e^{-5-x}}{x \log (x)}-\frac {3 e^{-5-x} x}{\log (x)}-\frac {e^{-5-x} \log (2-x)}{\log (x)}+\frac {2 e^{-5-x} \log (2-x)}{x^2 \log (x)}+\frac {e^{-5-x} \log (2-x)}{x \log (x)}\right ) \, dx+48 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx-72 \int \frac {e^{-5-x} x^3}{(-2+x) \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx+144 \int \frac {e^{-5-x} x^2}{(-2+x) \log (x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+24 \int \left (\frac {e^{-5-x}}{\log (x)}+\frac {2 e^{-5-x}}{(-2+x) \log (x)}\right ) \, dx+24 \int \left (\frac {e^{-5-x} \log (2-x)}{\log (x)}+\frac {2 e^{-5-x} \log (2-x)}{(-2+x) \log (x)}\right ) \, dx-24 \int \left (\frac {2 e^{-5-x} \log (2-x)}{\log (x)}+\frac {4 e^{-5-x} \log (2-x)}{(-2+x) \log (x)}+\frac {e^{-5-x} x \log (2-x)}{\log (x)}\right ) \, dx-24 \int \frac {e^{-5-x}}{\log (x)} \, dx-24 \int \frac {e^{-5-x} \log (2-x)}{\log (x)} \, dx+24 \int \frac {e^{-5-x} x \log (2-x)}{\log (x)} \, dx-48 \int \frac {e^{-5-x}}{x \log (x)} \, dx+48 \int \frac {e^{-5-x} \log (2-x)}{\log (x)} \, dx+48 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx-2 \left (48 \int \frac {e^{-5-x} \log (2-x)}{x \log (x)} \, dx\right )-72 \int \left (\frac {4 e^{-5-x}}{\log (x)}+\frac {8 e^{-5-x}}{(-2+x) \log (x)}+\frac {2 e^{-5-x} x}{\log (x)}+\frac {e^{-5-x} x^2}{\log (x)}\right ) \, dx+72 \int \frac {e^{-5-x} x^2}{\log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log (x)} \, dx+144 \int \left (\frac {2 e^{-5-x}}{\log (x)}+\frac {4 e^{-5-x}}{(-2+x) \log (x)}+\frac {e^{-5-x} x}{\log (x)}\right ) \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{\log (x)} \, dx\\ &=9 x+6 \log (2-x)+\frac {1}{2} \log ^2(2-x)+\frac {(2-x) \log ^2(2-x)}{2 x}+\frac {2304 e^{-10-2 x}}{x \log ^2(x)}+48 \int \frac {e^{-5-x}}{(-2+x) \log (x)} \, dx-48 \int \frac {e^{-5-x}}{x \log (x)} \, dx+2 \left (48 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx\right )-2 \left (48 \int \frac {e^{-5-x} \log (2-x)}{x \log (x)} \, dx\right )-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log ^2(x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{(-2+x) \log (x)} \, dx-96 \int \frac {e^{-5-x} \log (2-x)}{x^2 \log (x)} \, dx-288 \int \frac {e^{-5-x}}{x \log ^2(x)} \, dx-288 \int \frac {e^{-5-x}}{\log (x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [C] time = 0.31, size = 116, normalized size = 3.87 \begin {gather*} 9 x+6 \log (2-x)-\log (2) \log (2-x)+\frac {\log ^2(2-x)}{x}+\frac {2304 e^{-2 (5+x)}}{x \log ^2(x)}+\frac {288 e^{-5-x}}{\log (x)}+\frac {96 e^{-5-x} \log (2-x)}{x \log (x)}-\log (2) \log (x)+\log (2-x) \log (x)+\text {Li}_2\left (1-\frac {x}{2}\right )+\text {Li}_2\left (\frac {x}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.64, size = 86, normalized size = 2.87 \begin {gather*} \frac {{\left ({\left (9 \, x^{2} e^{\left (2 \, x + 10\right )} + 6 \, x e^{\left (2 \, x + 10\right )} \log \left (-x + 2\right ) + e^{\left (2 \, x + 10\right )} \log \left (-x + 2\right )^{2}\right )} \log \relax (x)^{2} + 96 \, {\left (3 \, x e^{\left (x + 5\right )} + e^{\left (x + 5\right )} \log \left (-x + 2\right )\right )} \log \relax (x) + 2304\right )} e^{\left (-2 \, x - 10\right )}}{x \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.17, size = 85, normalized size = 2.83 \begin {gather*} \frac {{\left (9 \, x^{2} e^{15} \log \relax (x)^{2} + 6 \, x e^{15} \log \left (x - 2\right ) \log \relax (x)^{2} + e^{15} \log \relax (x)^{2} \log \left (-x + 2\right )^{2} + 288 \, x e^{\left (-x + 10\right )} \log \relax (x) + 96 \, e^{\left (-x + 10\right )} \log \relax (x) \log \left (-x + 2\right ) + 2304 \, e^{\left (-2 \, x + 5\right )}\right )} e^{\left (-15\right )}}{x \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.38, size = 93, normalized size = 3.10
method | result | size |
risch | \(\frac {\ln \left (2-x \right )^{2}}{x}+\frac {96 \,{\mathrm e}^{-x -5} \ln \left (2-x \right )}{x \ln \relax (x )}+\frac {3 \left (2 \ln \left (x -2\right ) x \,{\mathrm e}^{2 x +10} \ln \relax (x )^{2}+3 \ln \relax (x )^{2} x^{2} {\mathrm e}^{2 x +10}+96 \ln \relax (x ) {\mathrm e}^{5+x} x +768\right ) {\mathrm e}^{-2 x -10}}{x \ln \relax (x )^{2}}\) | \(93\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.43, size = 81, normalized size = 2.70 \begin {gather*} \frac {{\left (9 \, x^{2} e^{10} \log \relax (x)^{2} + e^{10} \log \relax (x)^{2} \log \left (-x + 2\right )^{2} + 288 \, x e^{\left (-x + 5\right )} \log \relax (x) + 6 \, {\left (x e^{10} \log \relax (x)^{2} + 16 \, e^{\left (-x + 5\right )} \log \relax (x)\right )} \log \left (-x + 2\right ) + 2304 \, e^{\left (-2 \, x\right )}\right )} e^{\left (-10\right )}}{x \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{-2\,x-10}\,\left (\left (-{\mathrm {e}}^{2\,x+10}\,\left (x-2\right )\,{\ln \left (2-x\right )}^2+2\,x\,{\mathrm {e}}^{2\,x+10}\,\ln \left (2-x\right )-{\mathrm {e}}^{2\,x+10}\,\left (12\,x^2-9\,x^3\right )\right )\,{\ln \relax (x)}^3+\left ({\mathrm {e}}^{x+5}\,\left (-288\,x^3+576\,x^2+96\,x\right )+{\mathrm {e}}^{x+5}\,\ln \left (2-x\right )\,\left (-96\,x^2+96\,x+192\right )\right )\,{\ln \relax (x)}^2+\left (6912\,x+{\mathrm {e}}^{x+5}\,\left (576\,x-288\,x^2\right )-4608\,x^2-{\mathrm {e}}^{x+5}\,\ln \left (2-x\right )\,\left (96\,x-192\right )+4608\right )\,\ln \relax (x)-4608\,x+9216\right )}{{\ln \relax (x)}^3\,\left (2\,x^2-x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.71, size = 71, normalized size = 2.37 \begin {gather*} 9 x + 6 \log {\left (x - 2 \right )} + \frac {\log {\left (2 - x \right )}^{2}}{x} + \frac {2304 x e^{- 2 x - 10} \log {\relax (x )} + \left (288 x^{2} \log {\relax (x )}^{2} + 96 x \log {\relax (x )}^{2} \log {\left (2 - x \right )}\right ) e^{- x - 5}}{x^{2} \log {\relax (x )}^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________