Optimal. Leaf size=34 \[ \frac {x^2 \log (x)}{-1-e^{\frac {\frac {3}{4}+\log (x)}{3 \log (x)}}+\frac {\log (2)}{5}} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 2.56, 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 {(-100 x+20 x \log (2)) \log (x)+(-200 x+40 x \log (2)) \log ^2(x)+e^{\frac {3+4 \log (x)}{12 \log (x)}} \left (-25 x-100 x \log (x)-200 x \log ^2(x)\right )}{100 e^{\frac {3+4 \log (x)}{6 \log (x)}} \log (x)+e^{\frac {3+4 \log (x)}{12 \log (x)}} (200-40 \log (2)) \log (x)+\left (100-40 \log (2)+4 \log ^2(2)\right ) \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(-100 x+20 x \log (2)) \log (x)+(-200 x+40 x \log (2)) \log ^2(x)+e^{\frac {3+4 \log (x)}{12 \log (x)}} \left (-25 x-100 x \log (x)-200 x \log ^2(x)\right )}{4 \left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right )^2 \log (x)} \, dx\\ &=\frac {1}{4} \int \frac {(-100 x+20 x \log (2)) \log (x)+(-200 x+40 x \log (2)) \log ^2(x)+e^{\frac {3+4 \log (x)}{12 \log (x)}} \left (-25 x-100 x \log (x)-200 x \log ^2(x)\right )}{\left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right )^2 \log (x)} \, dx\\ &=\frac {1}{4} \int \left (\frac {5 x (5-\log (2))}{\left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right )^2 \log (x)}+\frac {5 x \left (-1-4 \log (x)-8 \log ^2(x)\right )}{\left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right ) \log (x)}\right ) \, dx\\ &=\frac {5}{4} \int \frac {x \left (-1-4 \log (x)-8 \log ^2(x)\right )}{\left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right ) \log (x)} \, dx+\frac {1}{4} (5 (5-\log (2))) \int \frac {x}{\left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right )^2 \log (x)} \, dx\\ &=\frac {5}{4} \int \left (\frac {4 x}{-5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}-5 \left (1-\frac {\log (2)}{5}\right )}+\frac {x}{\left (-5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}-5 \left (1-\frac {\log (2)}{5}\right )\right ) \log (x)}+\frac {8 x \log (x)}{-5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}-5 \left (1-\frac {\log (2)}{5}\right )}\right ) \, dx+\frac {1}{4} (5 (5-\log (2))) \int \frac {x}{\left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right )^2 \log (x)} \, dx\\ &=\frac {5}{4} \int \frac {x}{\left (-5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}-5 \left (1-\frac {\log (2)}{5}\right )\right ) \log (x)} \, dx+5 \int \frac {x}{-5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}-5 \left (1-\frac {\log (2)}{5}\right )} \, dx+10 \int \frac {x \log (x)}{-5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}-5 \left (1-\frac {\log (2)}{5}\right )} \, dx+\frac {1}{4} (5 (5-\log (2))) \int \frac {x}{\left (5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}+5 \left (1-\frac {\log (2)}{5}\right )\right )^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.14, size = 31, normalized size = 0.91 \begin {gather*} -\frac {5 x^2 \log (x)}{5+5 e^{\frac {1}{3}+\frac {1}{4 \log (x)}}-\log (2)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.75, size = 29, normalized size = 0.85
method | result | size |
norman | \(\frac {5 x^{2} \ln \left (x \right )}{-5+\ln \left (2\right )-5 \,{\mathrm e}^{\frac {4 \ln \left (x \right )+3}{12 \ln \left (x \right )}}}\) | \(29\) |
risch | \(\frac {5 x^{2} \ln \left (x \right )}{-5+\ln \left (2\right )-5 \,{\mathrm e}^{\frac {4 \ln \left (x \right )+3}{12 \ln \left (x \right )}}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 30, normalized size = 0.88 \begin {gather*} -\frac {5 \, x^{2} \log \left (x\right )}{5 \, e^{\left (\frac {4 \, \log \left (x\right ) + 3}{12 \, \log \left (x\right )}\right )} - \log \left (2\right ) + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 29, normalized size = 0.85 \begin {gather*} - \frac {5 x^{2} \log {\left (x \right )}}{5 e^{\frac {\frac {\log {\left (x \right )}}{3} + \frac {1}{4}}{\log {\left (x \right )}}} - \log {\left (2 \right )} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.53, size = 26, normalized size = 0.76 \begin {gather*} -\frac {5 \, x^{2} \log \left (x\right )}{5 \, e^{\left (\frac {1}{4 \, \log \left (x\right )} + \frac {1}{3}\right )} - \log \left (2\right ) + 5} \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}}^{\frac {\frac {\ln \left (x\right )}{3}+\frac {1}{4}}{\ln \left (x\right )}}\,\left (200\,x\,{\ln \left (x\right )}^2+100\,x\,\ln \left (x\right )+25\,x\right )+{\ln \left (x\right )}^2\,\left (200\,x-40\,x\,\ln \left (2\right )\right )+\ln \left (x\right )\,\left (100\,x-20\,x\,\ln \left (2\right )\right )}{\ln \left (x\right )\,\left (4\,{\ln \left (2\right )}^2-40\,\ln \left (2\right )+100\right )+100\,{\mathrm {e}}^{\frac {2\,\left (\frac {\ln \left (x\right )}{3}+\frac {1}{4}\right )}{\ln \left (x\right )}}\,\ln \left (x\right )-{\mathrm {e}}^{\frac {\frac {\ln \left (x\right )}{3}+\frac {1}{4}}{\ln \left (x\right )}}\,\ln \left (x\right )\,\left (40\,\ln \left (2\right )-200\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________