Optimal. Leaf size=23 \[ \frac {4 x^2}{3-x \log (x)}+4 \log ^2(5+x) \]
________________________________________________________________________________________
Rubi [F] time = 1.27, 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 {120 x+44 x^2+4 x^3+\left (-20 x^2-4 x^3\right ) \log (x)+\left (72-48 x \log (x)+8 x^2 \log ^2(x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2\right ) \log (x)+\left (5 x^2+x^3\right ) \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 {120 x+44 x^2+4 x^3+\left (-20 x^2-4 x^3\right ) \log (x)+\left (72-48 x \log (x)+8 x^2 \log ^2(x)\right ) \log (5+x)}{(5+x) (3-x \log (x))^2} \, dx\\ &=\int \left (\frac {120 x}{(5+x) (-3+x \log (x))^2}+\frac {44 x^2}{(5+x) (-3+x \log (x))^2}+\frac {4 x^3}{(5+x) (-3+x \log (x))^2}-\frac {4 x^2 \log (x)}{(-3+x \log (x))^2}+\frac {8 \log (5+x)}{5+x}\right ) \, dx\\ &=4 \int \frac {x^3}{(5+x) (-3+x \log (x))^2} \, dx-4 \int \frac {x^2 \log (x)}{(-3+x \log (x))^2} \, dx+8 \int \frac {\log (5+x)}{5+x} \, dx+44 \int \frac {x^2}{(5+x) (-3+x \log (x))^2} \, dx+120 \int \frac {x}{(5+x) (-3+x \log (x))^2} \, dx\\ &=4 \int \left (\frac {25}{(-3+x \log (x))^2}-\frac {5 x}{(-3+x \log (x))^2}+\frac {x^2}{(-3+x \log (x))^2}-\frac {125}{(5+x) (-3+x \log (x))^2}\right ) \, dx-4 \int \left (\frac {3 x}{(-3+x \log (x))^2}+\frac {x}{-3+x \log (x)}\right ) \, dx+8 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,5+x\right )+44 \int \left (-\frac {5}{(-3+x \log (x))^2}+\frac {x}{(-3+x \log (x))^2}+\frac {25}{(5+x) (-3+x \log (x))^2}\right ) \, dx+120 \int \left (\frac {1}{(-3+x \log (x))^2}-\frac {5}{(5+x) (-3+x \log (x))^2}\right ) \, dx\\ &=4 \log ^2(5+x)+4 \int \frac {x^2}{(-3+x \log (x))^2} \, dx-4 \int \frac {x}{-3+x \log (x)} \, dx-12 \int \frac {x}{(-3+x \log (x))^2} \, dx-20 \int \frac {x}{(-3+x \log (x))^2} \, dx+44 \int \frac {x}{(-3+x \log (x))^2} \, dx+100 \int \frac {1}{(-3+x \log (x))^2} \, dx+120 \int \frac {1}{(-3+x \log (x))^2} \, dx-220 \int \frac {1}{(-3+x \log (x))^2} \, dx-500 \int \frac {1}{(5+x) (-3+x \log (x))^2} \, dx-600 \int \frac {1}{(5+x) (-3+x \log (x))^2} \, dx+1100 \int \frac {1}{(5+x) (-3+x \log (x))^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.17, size = 22, normalized size = 0.96 \begin {gather*} -\frac {4 x^2}{-3+x \log (x)}+4 \log ^2(5+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.32, size = 29, normalized size = 1.26 \begin {gather*} \frac {4 \, {\left ({\left (x \log \relax (x) - 3\right )} \log \left (x + 5\right )^{2} - x^{2}\right )}}{x \log \relax (x) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 22, normalized size = 0.96 \begin {gather*} 4 \, \log \left (x + 5\right )^{2} - \frac {4 \, x^{2}}{x \log \relax (x) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 23, normalized size = 1.00
method | result | size |
default | \(4 \ln \left (5+x \right )^{2}-\frac {4 x^{2}}{x \ln \relax (x )-3}\) | \(23\) |
risch | \(4 \ln \left (5+x \right )^{2}-\frac {4 x^{2}}{x \ln \relax (x )-3}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.38, size = 29, normalized size = 1.26 \begin {gather*} \frac {4 \, {\left ({\left (x \log \relax (x) - 3\right )} \log \left (x + 5\right )^{2} - x^{2}\right )}}{x \log \relax (x) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 7.54, size = 22, normalized size = 0.96 \begin {gather*} 4\,{\ln \left (x+5\right )}^2-\frac {4\,x^2}{x\,\ln \relax (x)-3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.35, size = 19, normalized size = 0.83 \begin {gather*} - \frac {4 x^{2}}{x \log {\relax (x )} - 3} + 4 \log {\left (x + 5 \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________