Optimal. Leaf size=26 \[ \frac {x (1+x)}{-2 x+\frac {e^{-11 x/10}}{x \log (x)}} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 4.46, 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 {-20 e^{\frac {1}{5} (11 x+10 \log (3 x))} x^2 \log ^2(x)+e^{\frac {1}{10} (11 x+10 \log (3 x))} \left (30+30 x+\left (60+123 x+33 x^2\right ) \log (x)\right )}{90-120 e^{\frac {1}{10} (11 x+10 \log (3 x))} x \log (x)+40 e^{\frac {1}{5} (11 x+10 \log (3 x))} x^2 \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{11 x/10} x \left (10 (1+x)+\left (20+41 x+11 x^2\right ) \log (x)-20 e^{11 x/10} x^3 \log ^2(x)\right )}{10 \left (1-2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx\\ &=\frac {1}{10} \int \frac {e^{11 x/10} x \left (10 (1+x)+\left (20+41 x+11 x^2\right ) \log (x)-20 e^{11 x/10} x^3 \log ^2(x)\right )}{\left (1-2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx\\ &=\frac {1}{10} \int \left (\frac {e^{11 x/10} x (1+x) (10+20 \log (x)+11 x \log (x))}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2}-\frac {10 e^{11 x/10} x^2 \log (x)}{-1+2 e^{11 x/10} x^2 \log (x)}\right ) \, dx\\ &=\frac {1}{10} \int \frac {e^{11 x/10} x (1+x) (10+20 \log (x)+11 x \log (x))}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx-\int \frac {e^{11 x/10} x^2 \log (x)}{-1+2 e^{11 x/10} x^2 \log (x)} \, dx\\ &=\frac {1}{10} \int \left (\frac {e^{11 x/10} x (10+20 \log (x)+11 x \log (x))}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2}+\frac {e^{11 x/10} x^2 (10+20 \log (x)+11 x \log (x))}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2}\right ) \, dx-\int \left (\frac {1}{2}+\frac {1}{2 \left (-1+2 e^{11 x/10} x^2 \log (x)\right )}\right ) \, dx\\ &=-\frac {x}{2}+\frac {1}{10} \int \frac {e^{11 x/10} x (10+20 \log (x)+11 x \log (x))}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx+\frac {1}{10} \int \frac {e^{11 x/10} x^2 (10+20 \log (x)+11 x \log (x))}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx-\frac {1}{2} \int \frac {1}{-1+2 e^{11 x/10} x^2 \log (x)} \, dx\\ &=-\frac {x}{2}+\frac {1}{10} \int \left (\frac {10 e^{11 x/10} x^2}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2}+\frac {20 e^{11 x/10} x^2 \log (x)}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2}+\frac {11 e^{11 x/10} x^3 \log (x)}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2}\right ) \, dx-\frac {1}{2} \int \frac {1}{-1+2 e^{11 x/10} x^2 \log (x)} \, dx+\frac {1}{2} \text {Subst}\left (\int \frac {1}{(1+x)^2} \, dx,x,-\frac {e^{-11 x/10}}{2 x^2 \log (x)}\right )\\ &=-\frac {x}{2}-\frac {1}{2-\frac {e^{-11 x/10}}{x^2 \log (x)}}-\frac {1}{2} \int \frac {1}{-1+2 e^{11 x/10} x^2 \log (x)} \, dx+\frac {11}{10} \int \frac {e^{11 x/10} x^3 \log (x)}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx+2 \int \frac {e^{11 x/10} x^2 \log (x)}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx+\int \frac {e^{11 x/10} x^2}{\left (-1+2 e^{11 x/10} x^2 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.29, size = 31, normalized size = 1.19 \begin {gather*} \frac {1}{10} \left (-5 x-\frac {5 (1+x)}{-1+2 e^{11 x/10} x^2 \log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.25, size = 25, normalized size = 0.96
method | result | size |
risch | \(-\frac {x}{2}-\frac {3 \left (x +1\right )}{2 \left (6 x^{2} \ln \left (x \right ) {\mathrm e}^{\frac {11 x}{10}}-3\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 30, normalized size = 1.15 \begin {gather*} -\frac {2 \, x^{3} e^{\left (\frac {11}{10} \, x\right )} \log \left (x\right ) + 1}{2 \, {\left (2 \, x^{2} e^{\left (\frac {11}{10} \, x\right )} \log \left (x\right ) - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.51, size = 38, normalized size = 1.46 \begin {gather*} -\frac {2 \, x^{2} e^{\left (\frac {11}{10} \, x + \log \left (3\right ) + \log \left (x\right )\right )} \log \left (x\right ) + 3}{2 \, {\left (2 \, x e^{\left (\frac {11}{10} \, x + \log \left (3\right ) + \log \left (x\right )\right )} \log \left (x\right ) - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.10, size = 24, normalized size = 0.92 \begin {gather*} - \frac {x}{2} + \frac {- x - 1}{4 x^{2} e^{\frac {11 x}{10}} \log {\left (x \right )} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.43, size = 30, normalized size = 1.15 \begin {gather*} -\frac {2 \, x^{3} e^{\left (\frac {11}{10} \, x\right )} \log \left (x\right ) + 1}{2 \, {\left (2 \, x^{2} e^{\left (\frac {11}{10} \, x\right )} \log \left (x\right ) - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 8.40, size = 26, normalized size = 1.00 \begin {gather*} -\frac {x}{2}-\frac {\frac {x}{2}+\frac {1}{2}}{2\,x^2\,{\mathrm {e}}^{\frac {11\,x}{10}}\,\ln \left (x\right )-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________