Integrand size = 200, antiderivative size = 34 \[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=\frac {\log \left (\frac {1}{5} e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-x^2\right )}{\log (x)} \]
[Out]
\[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=\int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{x^2 \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right ) \log ^2(x) \log ^2(3 x)} \, dx \\ & = \int \left (-\frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}} \left (25+\log ^2(3 x)\right )}{x^2 \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right ) \log (x) \log ^2(3 x)}+\frac {-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x} x \log (x)+10 x^2 \log (x)+e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x} \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )-5 x^2 \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{x \left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log ^2(x)}\right ) \, dx \\ & = -\int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}} \left (25+\log ^2(3 x)\right )}{x^2 \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right ) \log (x) \log ^2(3 x)} \, dx+\int \frac {-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x} x \log (x)+10 x^2 \log (x)+e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x} \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )-5 x^2 \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{x \left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log ^2(x)} \, dx \\ & = -\int \left (-\frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3)+\log (x)}}}{x}+x}+5 x^2\right ) \log (x)}-\frac {25 e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x) \log ^2(3 x)}\right ) \, dx+\int \left (-\frac {5 (-2+x) x}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)}+\frac {x \log (x)-\log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{x \log ^2(x)}\right ) \, dx \\ & = -\left (5 \int \frac {(-2+x) x}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx\right )+25 \int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x) \log ^2(3 x)} \, dx+\int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3)+\log (x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx+\int \frac {x \log (x)-\log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{x \log ^2(x)} \, dx \\ & = -\left (5 \int \left (-\frac {2 x}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)}+\frac {x^2}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)}\right ) \, dx\right )+25 \int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x) \log ^2(3 x)} \, dx+\int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3)+\log (x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx+\int \left (\frac {1}{\log (x)}-\frac {\log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{x \log ^2(x)}\right ) \, dx \\ & = -\left (5 \int \frac {x^2}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx\right )+10 \int \frac {x}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx+25 \int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x) \log ^2(3 x)} \, dx+\int \frac {1}{\log (x)} \, dx+\int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3)+\log (x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx-\int \frac {\log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{x \log ^2(x)} \, dx \\ & = \operatorname {LogIntegral}(x)-5 \int \frac {x^2}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx+10 \int \frac {x}{\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx+25 \int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}+5 x^2\right ) \log (x) \log ^2(3 x)} \, dx+\int \frac {e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x+\frac {25}{\log (3 x)}}}{x^2 \left (-e^{\frac {e^{\frac {25}{\log (3)+\log (x)}}}{x}+x}+5 x^2\right ) \log (x)} \, dx-\int \frac {\log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{x \log ^2(x)} \, dx \\ \end{align*}
Time = 0.70 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00 \[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=\frac {\log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}}{x}+x}-5 x^2\right )\right )}{\log (x)} \]
[In]
[Out]
Time = 0.17 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00
\[\frac {\ln \left (\frac {{\mathrm e}^{\frac {{\mathrm e}^{\frac {25}{\ln \left (x \right )+\ln \left (3\right )}}+x^{2}}{x}}}{5}-x^{2}\right )}{\ln \left (x \right )}\]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.97 \[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=\frac {\log \left (-x^{2} + \frac {1}{5} \, e^{\left (\frac {x^{2} + e^{\left (\frac {25}{\log \left (3\right ) + \log \left (x\right )}\right )}}{x}\right )}\right )}{\log \left (x\right )} \]
[In]
[Out]
Timed out. \[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=\text {Timed out} \]
[In]
[Out]
none
Time = 0.59 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.03 \[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=-\frac {\log \left (5\right ) - \log \left (-5 \, x^{2} + e^{\left (x + \frac {e^{\left (\frac {25}{\log \left (3\right ) + \log \left (x\right )}\right )}}{x}\right )}\right )}{\log \left (x\right )} \]
[In]
[Out]
Timed out. \[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=\text {Timed out} \]
[In]
[Out]
Timed out. \[ \int \frac {-10 x^3 \log (x) \log ^2(3 x)+e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} \left (x^2 \log (x) \log ^2(3 x)+e^{\frac {25}{\log (3 x)}} \left (-25 \log (x)-\log (x) \log ^2(3 x)\right )\right )+\left (-e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x \log ^2(3 x)+5 x^3 \log ^2(3 x)\right ) \log \left (\frac {1}{5} \left (e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}}-5 x^2\right )\right )}{e^{\frac {e^{\frac {25}{\log (3 x)}}+x^2}{x}} x^2 \log ^2(x) \log ^2(3 x)-5 x^4 \log ^2(x) \log ^2(3 x)} \, dx=\int \frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {25}{\ln \left (3\,x\right )}}+x^2}{x}}\,\left ({\mathrm {e}}^{\frac {25}{\ln \left (3\,x\right )}}\,\left (\ln \left (x\right )\,{\ln \left (3\,x\right )}^2+25\,\ln \left (x\right )\right )-x^2\,{\ln \left (3\,x\right )}^2\,\ln \left (x\right )\right )-\ln \left (\frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {25}{\ln \left (3\,x\right )}}+x^2}{x}}}{5}-x^2\right )\,\left (5\,x^3\,{\ln \left (3\,x\right )}^2-x\,{\ln \left (3\,x\right )}^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {25}{\ln \left (3\,x\right )}}+x^2}{x}}\right )+10\,x^3\,{\ln \left (3\,x\right )}^2\,\ln \left (x\right )}{5\,x^4\,{\ln \left (3\,x\right )}^2\,{\ln \left (x\right )}^2-x^2\,{\ln \left (3\,x\right )}^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{\frac {25}{\ln \left (3\,x\right )}}+x^2}{x}}\,{\ln \left (x\right )}^2} \,d x \]
[In]
[Out]